Patent Publication Number: US-2015077720-A1

Title: Projection device, image correction method, and computer-readable recording medium

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application is a continuation of International Application No. PCT/JP2013/063463, filed on May 14, 2013 which claims the benefit of priority of the prior Japanese Patent Application No. 2012-117016, filed on May 22, 2012, the entire contents of which are incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a projection device, an image correction method, and a computer-readable recording medium. 
     2. Description of the Related Art 
     A projection device such as a projector device is known which drives display elements based on an input image signal and projects an image relating to the image signal on a projection face of a projection medium such as a screen or a wall face. In such a projection device, in a case where a projection image is projected not in a state in which an optical axis of a projection lens is perpendicular to the projection face but in a state in which the optical axis of the projection lens is inclined with respect to the projection face, a problem of a so-called trapezoidal distortion in which a projection image originally projected in an approximate rectangular shape is displayed to be distorted in a trapezoidal shape on the projection face occurs. 
     Accordingly, conventionally, by performing a trapezoidal distortion correction (keystone correction) for converting an image that is a projection target into a trapezoidal shape formed in a direction opposite to that of the trapezoidal distortion formed in the projection image displayed on the projection face, a projection image having an approximately rectangular shape without any distortion is displayed on the projection face. 
     For example, in Japanese Patent Application Laid-open No. 2004-77545, a technology for projecting an excellent video for which a trapezoidal distortion correction has been appropriately performed onto a projection face in a projector in a case where the projection face is either a wall face or a ceiling is disclosed. 
     In such a conventional technology, when a trapezoidal distortion correction (keystone correction) is performed, an image is converted into a trapezoidal shape formed in a direction opposite to a trapezoidal distortion generated in a projection image according to a projection direction, and the converted image is input to a display device, whereby the keystone correction is performed. Accordingly, on the display device, an image having the number of pixels that is smaller than the number of pixels that can be originally displayed by the display device is input in the trapezoidal shape formed in the opposite direction, and a projection image is displayed in an approximately rectangular shape on the projection face onto which the projection image is projected. 
     In the conventional technology as described above, in order not to display an area of the periphery of the projection image onto which the approximately rectangular-shaped original projection image is projected, in other words, a differential area between the area of the projection image of a case where no correction is made and the area of the projection image after the correction on the projection face, image data corresponding to black is input to the display device, or the display device is controlled not to be driven. Accordingly, there are problems in that the pixel area of the display device is not effectively used, and the brightness of the actual projection area decreases. 
     Meanwhile, recently, in accordance with wide use of high-resolution digital cameras, the resolution of a video content is improved, and thus, there are cases where the resolution of the video content is higher than the resolution of a display device. For example, in a projection device such as a projector that supports up to full HD of 1920 pixels×1080 pixels as an input image for a display device having resolution of 1280 pixels×720 pixels, the input image is scaled in a prior stage of the display device so as to match the resolution such that the whole input image can be displayed on the display device, or a partial area of the input image that corresponds to the resolution of the display device is cut out and is displayed on the display device without performing such scaling. 
     Even in such a case, in a case where projection is performed in a state in which the optical axis of the projection lens is inclined with respect to the projection face, a trapezoidal distortion occurs, and accordingly, in order to perform the trapezoidal distortion correction, similar problems occur. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to at least partially solve the problems in the conventional technology. 
     There is provided a projection device that includes a projection unit that converts input image data into light and projects a converted image as a projection image onto a projection face with a predetermined view angle; a correction control unit that calculates a correction amount used for eliminating a geometric distortion occurring in the projection image according to a projection direction and determines a cut out range including also an area other than an area of the image data after the geometric distortion correction estimated according to the correction amount based on the correction amount; and a correction unit that generates cut out image data acquired by cutting out an area of the cut out range from the input image data and performs a geometric distortion correction for the cut out image data based on the correction amount. 
     There is also provided a projection device that includes a projection unit that converts input image data into light and projects a converted image as a projection image onto a projection face with a predetermined view angle; a projection control unit that performs control changing a projection direction of the projection image using the projection unit; a projection angle deriving unit that derives a projection angle of the projection direction; a correction control unit that calculates a correction amount used for correcting a geometric distortion occurring in the projection image according to the projection direction based on the projection angle and the view angle and determines a cut out range including also an area other than an area of the image data after the geometric distortion correction estimated according to the correction amount based on the correction amount; and a correction unit that generates cut out image data acquired by cutting out an area of the cut out range from the input image data and performs a geometric distortion correction for the cut out image data based on the correction amount. 
     There is further provided an image correction method executed by a projection device, the image correction method including converting input image data into light and projecting a converted image as a projection image onto a projection face with a predetermined view angle using a projection unit; calculating a correction amount used for eliminating a geometric distortion occurring in the projection image according to a projection direction and determining a cut out range including also an area other than an area of the image data after the geometric distortion correction estimated according to the correction amount based on the correction amount; and generating cut out image data acquired by cutting out an area of the cut out range from the input image data and performing a geometric distortion correction for the cut out image data based on the correction amount. 
     There is also provided an image correction method executed by a projection device, the image correction method including converting input image data into light and projecting a converted image as a projection image onto a projection face with a predetermined view angle using a projection unit; performing control changing a projection direction of the projection image using the projection unit; deriving a projection angle of the projection direction; calculating a correction amount used for correcting a geometric distortion occurring in the projection image according to the projection direction based on the projection angle and the view angle and determining a cut out range including also an area other than an area of the image data after the geometric distortion correction estimated according to the correction amount based on the correction amount; and generating cut out image data acquired by cutting out an area of the cut out range from the input image data and performing a geometric distortion correction for the cut out image data based on the correction amount. 
     There is further provided a computer readable recording medium that stores therein a computer program causing a computer to execute an image correction method, the method including converting input image data into light and projecting a converted image as a projection image onto a projection face with a predetermined view angle using a projection unit; calculating a correction amount used for eliminating a geometric distortion occurring in the projection image according to a projection direction and determining a cut out range including also an area other than an area of the image data after the geometric distortion correction estimated according to the correction amount based on the correction amount; and generating cut out image data acquired by cutting out an area of the cut out range from the input image data and performing a geometric distortion correction for the cut out image data based on the correction amount. The above and other objects, features, advantages and technical and industrial significance of this invention will be better understood by reading the following detailed description of presently preferred embodiments of the invention, when considered in connection with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a schematic diagram that illustrates an example of the external view of a projector device according to a first embodiment; 
         FIG. 1B  is a schematic diagram that illustrates an example of the external view of the projector device according to the first embodiment; 
         FIG. 2A  is a schematic diagram that illustrates an example of the configuration for performing rotary drive of a drum unit according to the first embodiment; 
         FIG. 2B  is a schematic diagram that illustrates an example of the configuration for performing rotary drive of the drum unit according to the first embodiment; 
         FIG. 3  is a schematic diagram that illustrates each posture of the drum unit according to the first embodiment; 
         FIG. 4  is a block diagram that illustrates the functional configuration of the projector device according to the first embodiment; 
         FIG. 5  is a conceptual diagram that illustrates a cutting out process of image data stored in a memory according to the first embodiment; 
         FIG. 6  is a schematic diagram that illustrates an example of designation of a cut out area of a case where the drum unit according to the first embodiment is located at an initial position; 
         FIG. 7  is a schematic diagram that illustrates setting of a cut out area for a projection angle θ according to the first embodiment; 
         FIG. 8  is a schematic diagram that illustrates designation of a cut out area of a case where optical zooming is performed in accordance with the first embodiment; 
         FIG. 9  is a schematic diagram that illustrates a case where an offset is given for a projection position of an image according to the first embodiment; 
         FIG. 10  is a schematic diagram that illustrates access control of a memory according to the first embodiment; 
         FIG. 11  is a timing diagram that illustrates access control of a memory according to the first embodiment; 
         FIG. 12A  is a schematic diagram that illustrates access control of a memory according to the first embodiment; 
         FIG. 12B  is a schematic diagram that illustrates access control of a memory according to the first embodiment; 
         FIG. 12C  is a schematic diagram that illustrates access control of a memory according to the first embodiment; 
         FIG. 13A  is a schematic diagram that illustrates access control of a memory according to the first embodiment; 
         FIG. 13B  is a schematic diagram that illustrates access control of a memory according to the first embodiment; 
         FIG. 14  is a diagram that illustrates the relation between a projection direction and a projection image projected onto a screen; 
         FIG. 15  is a diagram that illustrates the relation between a projection direction and a projection image projected onto a screen; 
         FIG. 16A  is a diagram that illustrates a conventional trapezoidal distortion correction; 
         FIG. 16B  is a diagram that illustrates a conventional trapezoidal distortion correction; 
         FIG. 17A  is a diagram that illustrates cutting out an image of a partial area of input image data according to a conventional technology; 
         FIG. 17B  is a diagram that illustrates cutting out an image of a partial area of input image data according to a conventional technology; 
         FIG. 18A  is a diagram that illustrates problems in a conventional trapezoidal distortion correction; 
         FIG. 18B  is a diagram that illustrates problems in a conventional trapezoidal distortion correction; 
         FIG. 19  is a diagram that illustrates an image of an unused area remaining after the cutting from the input image data according to a conventional technology; 
         FIG. 20  is a diagram that illustrates a projection image of a case where a geometric distortion correction according to this embodiment is performed; 
         FIG. 21  is a diagram that illustrates major projection directions and projection angles of the projection face according to the first embodiment; 
         FIG. 22  is a graph that illustrates relation between a projection angle and a correction coefficient according to the first embodiment; 
         FIG. 23  is a diagram that illustrates the calculation of the correction coefficient according to the first embodiment; 
         FIG. 24  is a diagram that illustrates the calculation of lengths of lines from the upper side to the lower side according to the first embodiment; 
         FIG. 25  is a diagram that illustrates the calculation of a second correction coefficient according to the first embodiment; 
         FIG. 26  is a diagram that illustrates the calculation of the second correction coefficient according to the first embodiment; 
         FIG. 27A  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is 0° in accordance with the first embodiment; 
         FIG. 27B  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is 0° in accordance with the first embodiment; 
         FIG. 27C  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is 0° in accordance with the first embodiment; 
         FIG. 27D  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is 0° in accordance with the first embodiment; 
         FIG. 28A  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is greater than 0°, and a geometric distortion correction is not performed; 
         FIG. 28B  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is greater than 0°, and a geometric distortion correction is not performed; 
         FIG. 28C  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is greater than 0°, and a geometric distortion correction is not performed; 
         FIG. 28D  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is greater than 0°, and a geometric distortion correction is not performed; 
         FIG. 29A  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is greater than 0°, and a conventional trapezoidal distortion correction is performed; 
         FIG. 29B  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is greater than 0°, and a conventional trapezoidal distortion correction is performed; 
         FIG. 29C  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is greater than 0°, and a conventional trapezoidal distortion correction is performed; 
         FIG. 29D  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is greater than 0°, and a conventional trapezoidal distortion correction is performed; 
         FIG. 30A  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is greater than 0°, and the geometric distortion correction according to this first embodiment is performed; 
         FIG. 30B  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is greater than 0°, and the geometric distortion correction according to this first embodiment is performed; 
         FIG. 30C  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is greater than 0°, and the geometric distortion correction according to this first embodiment is performed; 
         FIG. 30D  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is greater than 0°, and the geometric distortion correction according to this first embodiment is performed; 
         FIG. 31  is a flowchart that illustrates the sequence of an image projection process according to the first embodiment; 
         FIG. 32  is a flowchart that illustrates the sequence of an image data cutting out and geometric distortion correction process according to the first embodiment; 
         FIG. 33  is a flowchart that illustrates the sequence of an image data cutting out and geometric distortion correction process according to a second embodiment; 
         FIG. 34A  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is greater than 0°, and the geometric distortion correction according to this second embodiment is performed; 
         FIG. 34B  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is greater than 0°, and the geometric distortion correction according to this second embodiment is performed; 
         FIG. 34C  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is greater than 0°, and the geometric distortion correction according to this second embodiment is performed; and 
         FIG. 34D  is a diagram that illustrates an example of cutting out of image data, image data on a display element, and a projection image in a case where the projection angle is greater than 0°, and the geometric distortion correction according to this second embodiment is performed. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, a projection device, an image correction method and a computer-readable recording medium according to embodiments will be described in detail with reference to the accompanying drawings. Specific numerical values, external configurations, and the like represented in the embodiments are merely examples for easy understanding of the present invention but are not for the purpose of limiting the present invention unless otherwise mentioned. In addition, elements not directly relating to the present invention are not described in detail and are not presented in the drawings. 
     First Embodiment 
     External View of Projection Device 
       FIGS. 1A and 1B  are schematic diagrams that illustrate an example of the external views of a projection device (projector device)  1  according to a first embodiment.  FIG. 1A  is a perspective view of the projector device  1  viewed from a first face side on which an operation unit is disposed, and  FIG. 1B  is a perspective view of the projector device  1  viewed from a second face side that is a side facing the operation unit. The projector device  1  includes a drum unit  10  and a base  20 . The drum unit  10  is a rotor that is driven to be rotatable with respect to the base  20 . In addition, the base  20  includes a support portion supporting the drum unit  10  to be rotatable and a circuit unit performing various control operations such as rotation driving control of the drum unit  10  and image processing control. 
     The drum unit  10  is supported to be rotatable by a rotation shaft, which is not illustrated in the figure, that is disposed on the inner side of side plate portions  21   a  and  21   b  that are parts of the base  20  and is configured by a bearing and the like. Inside the drum unit  10 , a light source, a display element that modulates light emitted from the light source based on image data, a drive circuit that drives the display element, an optical engine unit that includes an optical system projecting the light modulated by the display element to the outside, and a cooling means configured by a fan and the like used for cooling the light source and the like are disposed. 
     In the drum unit  10 , window portions  11  and  13  are disposed. The window portion  11  is disposed such that light projected from a projection lens  12  of the optical system described above is emitted to the outside. In the window portion  13 , a distance sensor deriving a distance up to a projection medium, for example, using an infrared ray, an ultrasonic wave, or the like is disposed. In addition, the drum unit  10  includes an intake/exhaust hole  22   a  that performs air in-taking/exhausting for heat rejection using a fan. 
     Inside the base  20 , various substrates of the circuit unit, a power supply unit, a drive unit used for driving the drum unit  10  to be rotated, and the like are disposed. The rotary drive of the drum unit  10  that is performed by this drive unit will be described later. On the first face of the base  20 , an operation unit  14  used for a user inputting various operations for controlling the projector device  1  and a reception unit  15  that receives a signal transmitted by a user from a remote control commander not illustrated in the figure when the projector device  1  is remotely controlled are disposed. The operation unit  14  includes various operators receiving user&#39;s operation inputs, a display unit used for displaying the state of the projector device  1 , and the like. 
     On the first face side and the second face side of the base  20 , the intake/exhaust holes  16   a  and  16   b  are respectively disposed. Thus, even in a case where the intake/exhaust hole  22   a  of the drum unit  10  that is driven to be rotated takes a posture toward the base  20  side, air in-taking or air exhaust can be performed so as not to decrease the rejection efficiency of the inside of the drum unit  10 . In addition, the intake/exhaust hole  17  disposed on the side face of the casing performs air in-taking and air exhaust for heat rejection of the circuit unit. 
     Rotary Drive of Drum Unit 
       FIGS. 2A and 2B  are diagrams that illustrate the rotary drive of the drum unit  10  that is performed by the drive unit  32  disposed in the base  20 .  FIG. 2A  is a diagram that illustrates the configuration of the drum  30  in a state in which a cover and the like of the drum unit  10  are removed and the drive unit  32  disposed in the base  20 . In the drum  30 , a window portion  34  corresponding to the window portion  11  described above and a window portion  33  corresponding to the window portion  13  are disposed. The drum  30  includes a rotation shaft  36  and is attached to a bearing  37  using bearings disposed in support portions  31   a  and  31   b  to be driven to rotate by the rotation shaft  36 . 
     On one face of the drum  30 , a gear  35  is disposed on the circumference. The drum  30  is driven to be rotated through the gear  35  by the drive unit  32  disposed in the support portion  31   b . Here, protrusions  46   a  and  46   b  disposed in the inner circumference portion of the gear  35  are disposed so as to detect a start point and an end point at the time of the rotation operation of the drum  30 . 
       FIG. 2B  is an enlarged diagram that illustrates the configuration of the drum  30  and the drive unit  32  disposed in the base  20  in more detail. The drive unit  32  includes a motor  40  and a gear group including a worm gear  41  that is directly driven by the rotation shaft of the motor  40 , gears  42   a  and  42   b  that transfer rotation according to the worm gear  41 , and a gear  43  that transfers the rotation transferred from the gear  42   b  to the gear  35  of the drum  30 . By transferring the rotation of the motor  40  to the gear  35  using the gear group, the drum  30  can be rotated in accordance with the rotation of the motor  40 . As the motor  40 , for example, a stepping motor performing rotation control for each predetermined angle using a drive pulse may be used. 
     In addition, photo interrupters  51   a  and  51   b  are disposed on the support portion  31   b . The photo interrupters  51   a  and  51   b  respectively detect the protrusions  46   b  and  46   a  disposed in the inner circumference portion of the gear  35 . Output signals of the photo interrupters  51   a  and  51   b  are supplied to a rotation control unit  104  to be described later. In the embodiment, by detecting the protrusion  46   b  using the photo interrupter  51   a , the rotation control unit  104  determines that the posture of the drum  30  is a posture arriving at an end point of the rotation operation. In addition, by detecting the protrusion  46   a  using the photo interrupter  51   b , the rotation control unit  104  determines that the posture of the drum  30  is a posture arriving at a start point of the rotation operation. 
     Hereinafter, a direction in which the drum  30  rotates from a position at which the protrusion  46   a  is detected by the photo interrupter  51   b  to a position at which the protrusion  46   b  is detected by the photo interrupter  51   a  through a longer arc in the circumference of the drum  30  will be represented as a forward direction. In other words, the rotation angle of the drum  30  increases toward the forward direction. 
     In addition, the photo interrupters  51   a  and  51   b  and the protrusions  46   a  and  46   b  are arranged such that an angle formed with the rotation shaft  36  is 270° between the detection position at which the photo interrupter  51   b  detects the protrusion  46   a  and the detection position at which the photo interrupter  51   a  detects the protrusion  46   b.    
     For example, in a case where a stepping motor is used as the motor  40 , by specifying the posture of the drum  30  based on timing at which the protrusion  46   a  is detected by the photo interrupter  51   b  and the number of drive pulses used for driving the motor  40 , a projection angle according to the projection lens  12  can be acquired. 
     Here, the motor  40  is not limited to the stepping motor but, for example, a DC motor may be used. In such a case, for example, as illustrated in  FIG. 2B , a code wheel  44  rotating together with the gear  43  on the same shaft as that of the gear  43  is disposed, and photo reflectors  50   a  and  50   b  are disposed in the support portion  31   b , whereby a rotary encoder is configured. 
     In the code wheel  44 , for example, a transmission portion  45   a  and a reflection unit  45   b  having phases changing in the radial direction are disposed. By receiving reflected light having each phase from the code wheel  44  using the photo reflectors  50   a  and  50   b , the rotation speed and the rotation direction of the gear  43  can be detected. Then, based on the rotation speed and the rotation direction of the gear  43  that have been detected, the rotation speed and the rotation direction of the drum  30  are derived. Based on the rotation speed and the rotation direction of the drum  30  that have been derived and a result of the detection of the protrusion  46   b  that is performed by the photo interrupter  51   a , the posture of the drum  30  is specified, whereby the projection angle according to the projection lens  12  can be acquired. 
     In the configuration as described above, a state in which the projection direction according to the projection lens  12  is in the vertical direction, and the projection lens  12  is completely hidden by the base  20  will be referred to as a housed state (or housing posture).  FIG. 3  is a schematic diagram that illustrates each posture of the drum unit  10 . In  FIG. 3 , State  500  illustrates the appearance of the drum unit  10  that is in the housed state. In the embodiment, the protrusion  46   a  is detected by the photo interrupter  51   b  in the housed state, and it is determined that the drum  30  arrives at the start point of the rotation operation by the rotation control unit  104  to be described later. 
     Hereinafter, unless otherwise mentioned, the “direction of the drum unit  10 ” and the “angle of the drum unit  10 ” have the same meanings as the “projection direction according to the projection lens  12 ” and the “projection angle according to the projection lens  12 ”. 
     For example, when the projector device  1  is started up, the drive unit  32  starts to rotate the drum unit  10  such that the projection direction according to the projection lens  12  faces the above-described first face. Thereafter, the drum unit  10 , for example, is assumed to rotate up to a position at which the direction of the drum unit  10 , in other words, the projection direction according to the projection lens  12  is horizontal on the first face side and temporarily stop. The projection angle of the projection lens  12  of a case where the projection direction according to the projection lens  12  is horizontal on the first face side is defined as a projection angle of 0°. In  FIG. 3 , State  501  illustrates the appearance of the posture of the drum unit  10  (projection lens  12 ) when the projection angle is 0°. Hereinafter, the posture of the drum unit  10  (projection lens  12 ) at which the projection angle is θ with respect to the posture having a projection angle of 0° used as the reference will be referred to as a θ posture. In addition, the state of the posture having a projection angle of 0° (in other words, a 0° posture) will be referred to as an initial state. 
     For example, at the 0° posture, it is assumed that image data is input, and the light source is turned on. In the drum unit  10 , light emitted from the light source is modulated based on the image data by the display element driven by the drive circuit and is incident to the optical system. Then, the light modulated based on the image data is projected from the projection lens  12  in a horizontal direction and is emitted to the projection face of the projection medium such as a screen or a wall face. 
     By operating the operation unit  14  and the like, the user can rotate the drum unit  10  around the rotation shaft  36  as its center while projection is performed from the projection lens  12  based on the image data. For example, by getting the rotation angle to be 90° (90° posture) by rotating the drum unit  10  from the 0° posture in the forward direction, light emitted from the projection lens  12  can be projected vertically upwardly with respect to the bottom face of the base  20 . In  FIG. 3 , State  502  illustrates the appearance of the drum unit  10  at the posture having a projection angle θ of 90°, in other words, a 90° posture. 
     The drum unit  10  can be rotated further in the forward direction from the 90° posture. In such a case, the projection direction of the projection lens  12  changes from the vertically upward direction with respect to the bottom face of the base  20  to the direction of the second face side. In  FIG. 3 , State  503  illustrates an appearance acquired when a posture having a projection angle θ of 180°, in other words, a 180° posture is formed as the drum unit  10  further rotates in the forward direction from the 90° posture of State  502 . In the projector device  1  according to this embodiment, the protrusion  46   b  is detected by the photo interrupter  51   a  in this 180° posture, and it is determined that the drum has arrived at the end point of the rotation operation of the drum  30  by the rotation control unit  104  to be described later. 
     The projector device  1  according to this embodiment rotates the drum unit  10 , for example, as illustrated in States  501  to  503  with projection of an image being performed for easy understanding of description of a change in the projection posture, thereby changing (moving) a projection area of image data in accordance with the projection angle according to the projection lens  12 . The change in the projection posture will be described in detail later. Accordingly, changes in the content of a projected image and the projection position of the projected image in the projection medium and changes in the content and the position of the image area cut out as an image to be projected from the whole image area relating to input image data can be associated with each other. Accordingly, a user can intuitively perceive an area which is projected out of the whole image area relating to the input image data based on the position of the projected image in the projection medium and intuitively perform an operation of changing the content of the projected image. 
     In addition, the optical system includes an optical zoom mechanism and can enlarge or reduce the size at the time of projecting a projection image to the projection medium by operating the operation unit  14 . Hereinafter, the enlarging or reducing of the size at the time of projecting the projection image to the projection medium according to the optical system may be simply referred to as “zooming”. For example, in a case where the optical system performs zooming, the projection image is enlarged or reduced with the optical axis of the optical system at the time point of performing zooming being as its center. 
     When the user ends the projection of the projection image using the projector device  1  and stops the projector device  1  by performing an operation for instructing the operation unit  14  to stop the projector device  1 , first, rotation control is performed such that the drum unit  10  is returned to be in the housed state. When drum unit  10  is positioned toward the vertical direction, and the return of the drum unit  10  into the housed state is detected, the light source is turned off, and, after a predetermined time required for cooling the light source, the power is turned off. By turning the power off after the drum unit  10  is positioned toward the vertical direction, the projection lens  12  can be prevented from getting dirty when the projection lend is not used. 
     Functional Configuration of Projector Device  1   
     Next, a configuration for realizing each function or operation of the projector device  1  according to this embodiment, as described above, will be described.  FIG. 4  is a block diagram that illustrates the functional configuration of the projector device  1 . 
     As illustrated in  FIG. 4 , the projector device  1  mainly includes: an optical engine unit  110 , a rotation mechanism unit  105 ; a rotation control unit  104 ; a view angle control unit  106 ; an image control unit  103 ; an extended function control unit  109 ; an image memory  101 ; a geometric distortion correction unit  100 ; an input control unit  119 ; a control unit  120 ; and an operation unit  14 . Here, the optical engine unit  110  is disposed inside the drum unit  10 . In addition, the rotation control unit  104 , the view angle control unit  106 , the image control unit  103 , the extended function control unit  109 , the image memory  101 , the geometric distortion correction unit  100 , the input control unit  119 , and the control unit  120  are mounted on the substrates of the base  20  as a circuit unit. 
     The optical engine unit  110  includes a light source  111 , a display element  114 , and a projection lens  12 . The light source  111 , for example, includes three light emitting diodes (LEDs) respectively emitting red (R) light, green (G) light, and blue (B) light. Luminous fluxes of colors RGB that are emitted from the light source  111  irradiate the display element  114  through an optical system not illustrated in the figure. 
     In description presented below, the display element  114  is assumed to be a transmission-type liquid crystal display device and, for example, to have a size of horizontal 1280 pixels×vertical 720 pixels. However, the size of the display element  114  is not limited to this example. The display element  114  is driven by a drive circuit not illustrated in the figure and modulates luminous fluxes of the colors RGB based on image data and emits the modulated luminous fluxes. The luminous fluxes of the colors RGB that are emitted from the display element  114  and are modulated based on the image data are incident to the projection lens  12  through the optical system not illustrated in the figure and are projected to the outside of the projector device  1 . 
     In addition, the display element  114 , for example, may be configured by a reflection-type liquid crystal display device using liquid crystal on silicon (LCOS) or a digital micromirror device (DMD). In such a case, the projector device is configured by an optical system and a drive circuit that correspond to the used display element. 
     The projection lens  12  includes a plurality of lenses that are combined together and a lens driving unit that drives the lenses according to a control signal. For example, the lens driving unit drives a lens included in the projection lens  12  based on a result of distance measurement that is acquired based on an output signal output from a distance sensor disposed in the window portion  13 , thereby performing focus control. In addition, the lens driving unit changes the view angle by driving the lens in accordance with a zoom instruction supplied from the view angle control unit  106  to be described later, thereby controlling the optical zoom. 
     As described above, the optical engine unit  110  is disposed inside the drum unit  10  that can be rotated by 360° by the rotation mechanism unit  105 . The rotation mechanism unit  105  includes the drive unit  32  and the gear  35  that is a configuration of the drum unit  10  side described with reference to  FIGS. 2A and 2B , and rotates the drum unit  10  in a predetermined manner using the rotation of the motor  40 . In other words, the projection direction of the projection lens  12  is changed by the rotation mechanism unit  105 . 
     The input control unit  119  receives a user operation input from the operation unit  14  as an event. The control unit  120  performs overall control of the projector device  1 . 
     The rotation control unit  104 , for example, receives an instruction according to a user operation for the operation unit  14  through the input control unit  119  and instructs the rotation mechanism unit  105  based on the instruction according to the user operation. The rotation mechanism unit  105  includes the drive unit  32  and the photo interrupters  51   a  and  51   b  described above. The rotation mechanism unit  105  controls the drive unit  32  according to an instruction supplied from the rotation control unit  104 , thereby controlling the rotation operation of the drum unit (drum  30 ). For example, the rotation mechanism unit  105  generates a drive pulse according to an instruction supplied from the rotation control unit  104  and drives the motor  40  that is, for example, a stepping motor. 
     Meanwhile, outputs of the photo interrupters  51   a  and  51   b  described above and a drive pulse  122  used for driving the motor  40  are supplied from the rotation mechanism unit  105  to the rotation control unit  104 . The rotation control unit  104 , for example, includes a counter and counts the pulse number of the drive pulses  122 . The rotation control unit  104  acquires the timing of detection of the protrusion  46   a  based on the output of the photo interrupter  51   b  and resets the pulse number counted by the counter at the timing of the detection of the protrusion  46   a . The rotation control unit  104 , based on the pulse number counted by the counter, can sequentially acquire the angle of the drum unit  10  (drum  30 ), thereby acquiring the posture (in other words, the projection angle of the projection lens  12 ) of the drum unit  10 . The projection angle of the projection lens  12  is supplied to the geometric distortion correction unit  100 . In this way, in a case where the projection direction of the projection lens  12  is changed, the rotation control unit  104  can derive an angle between a projection direction before change and a projection angle after the change. 
     The view angle control unit  106 , for example, receives an instruction according to a user operation for the operation unit  14  through the input control unit  119  and gives a zoom instruction, in other words, an instruction for changing the view angle to the projection lens  12  based on an instruction according to the user operation. The lens driving unit of the projection lens  12  drives the lens based on the zoom instruction, thereby performing zoom control. The view angle control unit  106  supplies the zoom instruction and a view angle derived based on a zoom magnification relating to the zoom instruction and the like to the geometric distortion correction unit  100 . 
     The image control unit  103  receives input image data  121  as input and stores the input image data in the image memory  101  with designated output resolution. The image control unit  103 , as illustrated in  FIG. 4 , includes an output resolution control unit  1031  and a memory controller  1032 . 
     The output resolution control unit  1031  receives resolution from the geometric distortion correction unit  100  through the extended function control unit  109  and outputs the received resolution to the memory controller  1032  as output resolution. 
     The memory controller  1032  receives the input image data  121  of 1920 pixels×1080 pixels, which is a still image or a moving image, as input and stores the input image data  121  of 1920 pixels×1080 pixels that has been input in the image memory  101  with the output resolution input from the output resolution control unit  1031 . 
     The image memory  101  stores the input image data  121  in units of images. In other words, for each still image in a case where the input image data  121  is still image data and for each frame image configuring moving image data in a case where the input image data  121  is the moving image data, corresponding data is stored. The image memory  101 , for example, in compliance with the standards of digital high vision broadcasting, can store one or a plurality of frame images of 1920 pixels and 1080 pixels. 
     In addition, it is preferable that the size of the input image data  121  is shaped in advance into a size corresponding to the storage unit of the image data in the image memory  101 , and resultant input image data is input to the projector device  1 . In this example, the size of the input image data  121  is shaped into 1920 pixels×1080 pixels, and resultant input image is input to the projector device  1 . However, the configuration is not limited thereto, but an image shaping unit that shapes the input image data  121  input with an arbitrary size into image data of a size of 1920 pixels and 1080 pixels may be disposed in a previous stage of the memory controller  1032  in the projector device  1 . 
     The geometric distortion correction unit  100  calculates a first correction coefficient relating to a horizontal correction of the geometric distortion and a second correction coefficient relating to a vertical correction, acquires a cut out range, cuts out an image of an area of the cut range from the input image data  121  stored in the image memory  101 , performs a geometric distortion correction and image processing for the image, and outputs a resultant image to the display element  114 . 
     The geometric distortion correction unit  100 , as illustrated in  FIG. 4 , includes a correction control unit  108 , a memory controller  107 , and an image processing unit  102 . 
     The correction control unit  108  receives a projection angle  123  from the rotation control unit  104  as input and receives a view angle  125  from the view angle control unit  106  as input. Then, the correction control unit  108  calculates the first correction coefficient and the second correction coefficient used for eliminating a geometric distortion occurring in the projection image according to the projection direction based on the projection angle  123  and the view angle  125  that have been input and outputs the first correction coefficient and the second correction coefficient to the memory controller  107 . 
     In addition, the correction control unit  108  determines a cut out range from the input image data such that the size of the image data after the geometric distortion correction includes a displayable size of the display device based on the projection angle  123 , the view angle  125 , the first correction coefficient, and the second correction coefficient and outputs the determined cut out range to the memory controller  107  and the extended function control unit  109 . At this time, the correction control unit  108  designates a cut out area of the image data based on the angle of the projection direction of the projection lens  12 . 
     The memory controller  107  cuts out (extracts) an image area of the cut out range determined by the correction control unit  108  from the whole area of a frame image relating to the image data stored in the image memory  101  and outputs the cut out image area as image data. 
     In addition, the memory controller  107  performs a geometric distortion correction for the image data cut out from the image memory  101  by using the first correction coefficient and the second correction coefficient and outputs the image data after the geometric distortion correction to the image processing unit  102 . Here, the first correction coefficient, the second correction coefficient, and the geometric distortion correction will be described in detail later. 
     The image data output from the memory controller  107  is supplied to the image processing unit  102 . The image processing unit  102 , for example, by using a memory not illustrated in the figure, performs image processing for the supplied image data and outputs the image data for which the image processing has been performed to the display element  114  as image data of 1280 pixels×720 pixels. The image processing unit  102  outputs the image data for which the image processing has been performed based on timing represented in a vertical synchronization signal  124  supplied from a timing generator not illustrated in the figure. The image processing unit  102 , for example, performs a size converting process for the image data supplied from the memory controller  107  such that the size matches the size of the display element  114 . In addition, other than the process, the image processing unit  102  may perform various kinds of image processing. For example, the image processing unit  102  may perform a size converting process for the image data using a general linear transformation process. In addition, in a case where the size of the image data supplied from the memory controller  107  matches the size of the display element  114 , the image data may be directly output. 
     In addition, by performing interpolation (over sampling) with the aspect ratio of the image being maintained to be constant, a part or the whole of the image may be enlarged through an interpolation filter having a predetermined characteristic, in order to extract an aliasing distortion, by thinning (sub sampling) the image through a low pass filter according to a reduction rate, a part or the whole of the image may be reduced, or the image may be configured to maintain the size without passing through a filter. 
     Furthermore, when an image is projected in an inclined direction, in order to prevent an image from being blurred due to out-of focus on a periphery portion, an edge enhancement process using an operator such as Laplacian or an edge enhancement process applying one-dimensional filters in horizontal and vertical directions may be performed. Through this edge enhancement process, the edge of a blurred image portion that is projected can be enhanced. 
     In addition, in a case where a periphery portion of a projected image texture includes a diagonal line, in order not to allow an edge jag to be visually noticed, by mixing a local halftone or applying a local low pass filter using the image processing unit  102 , the edge jag is shaded off, whereby the diagonal line can be prevented from being observed as a jagged line. 
     The image data output from the image processing unit  102  is supplied to the display element  114 . Actually, this image data is supplied to the drive circuit that drives the display element  114 . The drive circuit drives the display element  114  based on the supplied image data. 
     The extended function control unit  109  receives a cut out range from the correction control unit  108  as input and outputs resolution including the cut out range to the output resolution control unit  1031  as output resolution. 
     Cutting Out Process of Image Data 
     Next, a cutting out process of image data stored in the image memory  101  that is performed by the memory controller  107  according to this embodiment will be described.  FIG. 5  is a conceptual diagram that illustrates the cutting out process of image data stored in the image memory  101 . An example of cutting out the image data  141  of the cut out area designated from the image data  140  stored in the image memory  101  will be described with reference to a left diagram in  FIG. 5 . In description presented below with reference to  FIGS. 6 to 9 , for simple description, a case where a geometric distortion correction is not performed for the image data and a case where the pixel size of the image data in the horizontal direction coincides with the pixel size of the display element  114  in the horizontal direction will be premised. 
     In the image memory  101 , for example, addresses are set in the vertical direction in units of lines and are set in the horizontal direction in units of pixels. In addition, it is assumed that the address of a line increases from the lower end of an image (screen) toward the upper end thereof, and the address of a pixel increases from the left end of the image toward the right end thereof. 
     The correction control unit  108 , for the memory controller  107 , designates addresses of lines q 0  and q 1  in the vertical direction and designates addresses of pixels p 0  and p 1  in the horizontal direction as a cut out area of image data  140  of Q lines×P pixels stored in the image memory  101 . The memory controller  107  reads lines within the range of the lines q 0  and q 1  over the pixels p 0  and p 1  from the image memory  101  in accordance with the designation of the addresses. At this time, as the sequence of reading, for example, it is assumed that the lines are read from the upper end toward the lower end of the image, and the pixels are read from the left end toward the right end of the image. The access control for the image memory  101  will be described in detail later. 
     The memory controller  107  supplies the image data  141  of the range of the lines q 0  and q 1  and the pixels p 0  and p 1 , which has been read from the image memory  101 , to the image processing unit  102 . The image processing unit  102  performs a size conversion process in which the size of an image according to the supplied image data  141  is adjusted to the size of the display element  114 . As an example, in a case where the size of the display element  114  is V lines×H pixels, a maximum multiplication m satisfying both Equations (1) and (2) as represented below is acquired. Then, the image processing unit  102  enlarges the image data  141  with this multiplication m and, as illustrated in  FIG. 5  as an example, size-converted image data  141 ′ is acquired. 
         m ×( p   1   −p   0 )≦ H   (1)
 
         m ×( q   1   −q   0 )≦ V   (2)
 
     Next, the designation (update) of a cut out area according to the projection angle according to this embodiment will be described.  FIG. 6  illustrates an example of designation of a cut-out area of a case where the drum unit  10  is at the 0° posture, in other words, in a case where the projection angle is 0° that is in the initial state. 
     In  FIG. 5  described above, a case has been described as an example in which the image data  141  of the range between the pixels p 0  and p 1  that is a partial range of pixels of one line of the image data  140  of Q lines×P pixels stored in the image memory  101  is cut out. Also in examples illustrated in  FIGS. 6 to 8 , actually, pixels of a partial range of one line of the image data  140  stored in the image memory  101  may be cut out. However, in order to simplify the description of the designation (update) of a cut out area according to the projection angle, in the examples represented in  FIGS. 6 to 8  illustrated below, all the pixels of one line are assumed to be cut out. 
     In the projector device (PJ)  1 , a projection position of a case where an image  131   0  is projected with a projection angle of 0° onto a projection face  130  that is a projection medium such as a screen by using a projection lens  12  having a view angle α is assumed to be a position Pos 0  corresponding to the luminous flux center of light projected from the projection lens  12 . In addition, at the projection angle of 0°, an image according to image data from the S-th line that is the lower end of an area designated in advance to the L-th line is assumed to be projected such that the image data stored in the image memory  101  is projected at the posture of a projection angle of 0°. In the area formed by lines of the S-th line to the L-th line, lines corresponding to the line number ln are included. In addition, a value representing a line position such as the S-th line or the L-th line, for example, is a value increasing from the lower end toward the upper end of the display element  114  with the line positioned at the lower end of the display element  114  set as the 0-th line. 
     Here, the line number ln is the number of lines of a maximal effective area of the display element  114 . In addition, the view angle α is an angle for viewing a projection image in the vertical direction from the projection lens  12  in a case where the image is projected when an effective area in the vertical direction, in which the display is effective in the display element  114 , has a maximum value, in other words, in a case where an image of the line number ln is projected. 
     The view angle α and the effective area of the display element  114  will be described using a more specific example. The display element  114  is assumed to have a vertical size of 720 lines. For example, in a case where the vertical size of the projection image data is 720 lines, and projection image data is projected using all the lines of the display element  114 , the effective area of the display element  114  in the vertical direction has a maximum value of 720 lines (=line number ln). In this case, the view angle α is an angle for viewing 1st to 720th lines of the projection image from the projection lens  12 . 
     In addition, a case may be also considered in which the vertical size of projection image data is 600 lines, and the projection image data is projected using only 600 lines out of 720 lines (=line number ln) of the display element  114 . In such a case, the effective area of the display element  114  in the vertical direction is 600 lines. In this case, only a portion of the effective area according to the projection image data with respect to a maximal value of the effective area of the view angle α is projected. 
     The correction control unit  108  instructs the memory controller  107  to cut out and read the S-th line to L-th line of the image data  140  stored in the image memory  101 . Here, in the horizontal direction, all the image data  140  of the left end to the right end is read. The memory controller  107  sets an area of the S-th line to the L-th line of the image data  140  as a cut out area in accordance with an instruction from the correction control unit  108 , reads the image data  141  of the set cut out area, and supplies the read image data to the image processing unit  102 . In the example illustrated in  FIG. 6 , onto the projection face  130 , an image  131   0  according to image data  141   0  of the line number ln from the S-th line to the L-th line of the image data  140  is projected. In such a case, an image according to image data  142  of an area relating to the L-th line to the upper-end line out of the whole area of the image data  140  is not projected. 
     Next, a case will be described in which the drum unit  10  is rotated, for example, according to a user operation for the operation unit  14 , and the projection angle of the projection lens  12  becomes an angle θ. In this embodiment, in a case where the drum unit  10  is rotated, and the projection angle according to the projection lens  12  is changed, the cut out area from the image memory  101  of the image data  140  is changed in accordance with the projection angle θ. 
     The setting of a cut out area for the projection angle θ will be described more specifically with reference to  FIG. 7 . For example, a case will be considered in which the drum unit  10  is rotated in the forward direction from a projection position of the 0° posture according to the projection lens  12 , and the projection angle of the projection lens  12  becomes an angle θ (&gt;0°). In such a case, the projection position for the projection face  130  moves to a projection position Pos 1  that is located on the upper side of a projection position Pos 0  corresponding to a projection angle of 0°. At this time, the correction control unit  108 , for the memory controller  107 , designates a cut out area for the image data  140  stored in the image memory  101  based on the following Equations (3) and (4). Equation (3) represents an R S -th line located at the lower end of the cut out area, and Equation (4) represents an R L -th line located at the upper end of the cut out area. 
         R   S =0×(ln/α)+ S   (3)
 
         R   L =0×(ln/α)+ S +ln  (4)
 
     In Equations (3) and (4), a value ln represents the number of lines (for example, the number of lines of the display element  114 ) included within the projection area. In addition, a value α represents a view angle of the projection lens  12 , and a value S represents a position of a line located at the lower end of the cut out area at the 0° posture described with reference to  FIG. 6 . 
     In Equations (3) and (4), (ln/α) represents the number of lines (including a concept of an approximately averaged number of lines changing in accordance with the shape of the projection face) per unit angle of a case where the view angle α projects the line number ln. Accordingly, θ×(ln/α) represents the number of lines corresponding to the projection angle θ according to the projection lens  12  in the projector device  1 . This means that, when the projection angle changes by an angle Δθ, the position of the projection image is moved by a distance corresponding to the number of lines {Δθ×(ln/α)} in the projection image. Accordingly, Equations (3) and (4) respectively represent the positions of lines located at the lower end and the upper end of the image data  140  in the projection image of a case where the projection angle is the angle θ. This corresponds to a read address for the image data  140  on the memory  101  at the projection angle θ. 
     In this way, in this embodiment, an address at the time of reading the image data  140  from the image memory  101  is designated in accordance with the projection angle θ. Accordingly, image data  141   1  of the image data  140  that is located at a position corresponding to the projection angle θ is read from the image memory  101 , and an image  131   1  relating to the read image data  141   1  is projected to the projection position Pos 1  corresponding to the projection angle θ of the projection face  130 . 
     Thus, according to this embodiment, in a case where the image data  140  having a size larger than the size of the display element  114  is projected, a correspondence relation between the position within the projected image and the position within the image data is maintained. In addition, since the projection angle θ is acquired based on a drive pulse of the motor  40  used for driving the drum  30  to be rotated, the projection angle θ can be acquired in a state in which there is substantially no delay with respect to the rotation of the drum unit  10 , and the projection angle θ can be acquired without being influenced by the projection image or the surrounding environment. 
     Next, the setting of a cut out area of a case where optical zooming according to the projection lens  12  is performed will be described. As described above, in the case of the projector device  1 , the view angle α of the projection lens  12  is increased or decreased by driving the lens driving unit, whereby optical zooming is performed. An increase in the view angle according to the optical zooming is assumed to be an angle Δ, and the view angle of the projection lens  12  after the optical zooming is assumed to be a view angle (α+Δ). 
     In such a case, even when the view angle is increased according to the optical zooming, the cut out area for the image memory  101  does not change. In other words, the number of lines included in a projection image according to the view angle α before the optical zooming and the number of lines included in a projection image according to the view angle (α+Δ) after the optical zooming are the same. Accordingly, after the optical zooming, the number of lines included per unit angle is changed from that before the optical zooming. 
     The setting of a cut out area of a case where optical zooming is performed will be described more specifically with reference to  FIG. 8 . In the example illustrated in  FIG. 8 , optical zooming is performed in which the view angle α is increased by an amount corresponding to the view angle Δ in the state of the projection angle θ. By performing the optical zooming, for example, a projection image projected onto the projection face  130 , as illustrated as an image  131   2 , is enlarged by an amount corresponding to the view angle Δ with respect to that of a case where the optical zooming is not performed with the center (the projection position Pos 2 ) of the luminous fluxes of light projected to the projection lens  12  in common. 
     In a case where optical zooming corresponding to the view angle Δ is performed, when the number of lines designated as a cut out area for the image data  140  is ln, the number of lines included per unit angle is represented by {ln/(α+Δ)}. Accordingly, the cut out area for the image data  140  is designated based on the following Equations (5) and (6). The meaning of each variable in Equations (5) and (6) is common to that in Equations (3) and (4) described above. 
         R   S =0×{ln/(α+Δ)}+ S   (5)
 
         R   L =0×{ln/(α+Δ)}+ S +ln  (6)
 
     Image data  141   2  of an area represented in Equations (5) and (6) is read from the image data  140 , and an image  131   2  relating to the read image data  141   2  is projected to a projection position Pos 2  of the projection face  130  by the projection lens  12 . 
     In this way, in a case where optical zooming is performed, the number of lines included per unit angle is changed with respect to a case where the optical zooming is not performed, and the amount of change in the number of lines with respect to a change in the projection angle θ is different from that of a case where the optical zooming is not performed. This is a state in which a gain corresponding to the view angle Δ increased according to the optical zooming is changed in the designation of a read address according to the projection angle θ for the image memory  101 . 
     In this embodiment, an address at the time of reading the image data  140  from the image memory  101  is designated in accordance with the projection angle θ and the view angle α of the projection lens  12 . In this way, even in a case where optical zooming is performed, the address of the image data  141   2  to be projected can be appropriately designated for the image memory  101 . Accordingly, even in a case where the optical zooming is performed, in a case where the image data  140  of a size larger than the size of the display element  114  is projected, a correspondence relation between the position within the projected image and the position within the image data is maintained. 
     Next, a case will be described with reference to  FIG. 9  in which an offset is given to the projection position of the image. When the projector device  1  is used, it cannot be determined that the 0° posture (projection angle 0°) is necessarily the lowest end of the projection position. For example, as illustrated in  FIG. 9 , a case may be considered in which a projection position Pos 3  according to a predetermined projection angle θ ofst  is set as the projection position located at the lowest end. In such a case, the image  131   3  according to the image data  141   3  is projected to a position shifted to the upper side by a height corresponding to the projection angle θ ofst  compared to a case where the offset is not given. The projection angle θ at the time of projecting an image having a line located at the lowest end of the image data  140  as its lowest end is set as the offset angle θ ofst  according to the offset. 
     In such a case, for example, a case may be considered in which the offset angle θ ofst  is regarded as the projection angle 0°, and a cut out area for the image memory  101  is designated. By applying Equations (3) and (4) described above, the following Equations (7) and (8) are formed. The meaning of each variable in Equations (7) and (8) is common to that in Equations (3) and (4) described above. 
         R   S =(θ−θ ofst )×(ln/α)+ S   (7)
 
         R   L =(θ−θ ofst )×(ln/α)+ S +ln  (8)
 
     The image data  141   3  of the area represented in Equations (7) and (8) is read from the image data  140 , and the image  131   3  relating to the read image data  141   3  is projected to the projection position Pos 3  of the projection face  130  by the projection lens  12 . 
     Memory Control 
     Next, access control of the image memory  101  will be described with reference to  FIGS. 10 to 13 . Here, also in the description presented below with reference to  FIGS. 10 to 13 , in order to simplify the description, a case will be premised for the description in which a geometric distortion correction is not performed for the image data. 
     In the image data, for each vertical synchronization signal VD, pixels are sequentially transmitted from the left end toward the right end of an image for each line in the horizontal direction on the screen, and lines are sequentially transmitted from upper end toward the lower end of the image. Hereinafter, a case will be described as an example in which the image data has a size of horizontal 1920 pixels×vertical 1080 pixels (lines) corresponding to the digital high vision standard. 
     Hereinafter, an example of the access control of a case where the image memory  101  includes four memory areas for which the access control can be independently performed will be described. In other words, as illustrated in  FIG. 10 , in the image memory  101 , areas of memories  101 Y 1  and  101 Y 2  used for writing and reading image data with a size of horizontal 1920 pixels and vertical 1080 pixels (line) and areas of memories  101 T 2  and  101 T 2  used for writing and reading image data with a size of horizontal 1080 pixels×vertical 1920 pixels (lines) are arranged. Hereinafter, the memories  101 Y 1 ,  101 Y 2 ,  101 T 2 , and  101 T 2  will be described as memories Y 1 , Y 2 , T 1 , and T 2 . 
       FIG. 11  is a timing diagram that illustrates access control of the image memory  101  using the memory controller  107  according to the first embodiment. Chart  210  represents the projection angle θ of the projection lens  12 , and Chart  211  represents the vertical synchronization signal VD. In addition, Chart  212  represents input timings of image data D 1 , D 2 , and . . . input to the memory controller  107 , and Charts  213  to  216  represent examples of accesses to the memories Y 1 , Y 2 , T 1  and T 2  from the memory controller  107 . In addition, in Charts  213  to  216 , each block to which “R” is attached represents reading, and each block to which “W” is attached represents writing. 
     For every vertical synchronization signal VD, image data D 1 , D 2 , D 3 , D 4 , D 5 , D 6 , . . . each having an image size of 1920 pixels×1080 lines are input to the memory controller  107 . Each of the image data D 1 , D 2 , . . . is synchronized with the vertical synchronization signal VD and is input after the vertical synchronization signal VD. In addition, the projection angles of the projection lens  12  corresponding to the vertical synchronization signals VD are denoted as projection angles θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , θ 6 , . . . . The projection angle θ is acquired for every vertical synchronization signal VD as above. 
     First, the image data D 1  is input to the memory controller  107 . As described above, the projector device  1  according to this embodiment changes the projection angle θ according to the projection lens  12  by rotating the drum unit  10  so as to move the projection position of the projection image and designates a read position for the image data in accordance with the projection angle θ. Accordingly, it is preferable that the image data is longer in the vertical direction. Generally, image data frequently has a horizontal size longer than a vertical size. Thus, for example, it may be considered for a user to rotate the camera by 90° in an imaging process and input image data acquired by the imaging process to the projector device  1 . 
     In other words, an image according to the image data D 1 , D 2 , . . . input to the memory controller  107 , similarly to an image  160  illustrated as an image in  FIG. 12A , is a sideways image acquired by rotating a right-direction image by 90° that is determined based on the content of the image. 
     The memory controller  107  writes the input image data D 1  into the memory Y 1  at timing WD 1  corresponding to the input timing of the image data D 1  (timing WD 1  illustrated in Chart  213 ). The memory controller  107  writes the image data D 1  into the memory Y 1 , as illustrated on the left side of  FIG. 12B , in the sequence of lines toward the horizontal direction. On the right side of  FIG. 12B , an image  161  according to the image data D 1  written into the memory Y 1  as such is illustrated as an image. The image data D 1  is written into the memory Y 1  as the image  161  that is the same as the input image  160 . 
     The memory controller  107 , as illustrated in  FIG. 12C , reads the image data D 1  written into the memory Y 1  from the memory Y 1  at timing RD 1  that is the same as the timing of start of a next vertical synchronization signal VD after the vertical synchronization signal VD for writing the image data D 1  (timing RD 1  illustrated in Chart  213 ). 
     At this time, the memory controller  107  sequentially reads the image data D 1  in the vertical direction over the lines for each pixel with a pixel positioned on the lower left corner of the image being set as a reading start pixel. When pixels positioned at the upper end of the image are read, next, pixels are read in the vertical direction with a pixel positioned on the right side neighboring to the pixel positioned at the reading start position of the vertical direction being set as a reading start pixel. This operation is repeated until the reading of a pixel positioned on the upper right corner of the image is completed. 
     In other words, the memory controller  107  sequentially reads the image data D 1  from the memory Y 1  for each line in the vertical direction from the left end toward the right end of the image for each pixel in the line direction being set as the vertical direction from the lower end toward the upper end of the image. 
     The memory controller  107  sequentially writes the pixels of the image data D 1  read from the memory Y 1  in this way, as illustrated on the left side in  FIG. 13A , into the memory T 1  toward the line direction for each pixel (timing WD 1  illustrated in Chart  214 ). In other words, for example, every time when one pixel is read from the memory Y 1 , the memory controller  107  writes one pixel that has been read into the memory T 1 . 
     On the right side in  FIG. 13A , the image  162  according to the image data D 1  written into the memory T 1  in this way is illustrated. The image data D 1  is written into the memory T 1  with a size of horizontal 1080 pixels×vertical 1920 pixels (lines) and is the image  162  acquired by rotating the input image  160  by 90° in the clockwise direction and interchanging the horizontal direction and the vertical direction. 
     The memory controller  107  designates an address of the cut out area that is designated by the correction control unit  108  to the memory T 1  and reads image data of the area designated as the cut out area from the memory T 1 . The timing of this reading process, as represented by timing RD 1  in Chart  214 , is delayed from the timing at which the image data D 1  is input to the memory controller  107  by two vertical synchronization signals VD. 
     The projector device  1  according to this embodiment, as described above, moves the projection position of the projection image by rotating the drum unit  10  so as to change the projection angle θ according to the projection lens  12  and designates a reading position for image data in accordance with the projection angle θ. For example, the image data D 1  is input to the memory controller  107  at the timing of the projection angle θ 1 . The projection angle θ at the timing when an image according to the image data D 1  is actually projected may be changed from the projection angle θ 1  to a projection angle θ 3  different from the projection angle θ 1 . 
     Accordingly, the cut out area at the time of reading the image data D 1  from the memory T 1  is read from a range that is larger than the area of image data corresponding to the projected image in consideration of a change in the projection angle θ. 
     The description will be described more specifically with reference to  FIG. 13B . The left side in  FIG. 13B  illustrates an image  163  according to the image data D 1  stored in the memory T 1 . In this image  163 , an area that is actually projected is represented as a projection area  163   a , and the other area  163   b  is represented as a non-projection area. In this case, the correction control unit  108  designates the cut out area  170  that is larger than the area of the image data corresponding to the image of the projection area  163  by at least the number of lines corresponding to a change of a case where the projection angle θ according to the projection lens  12  maximally changes during a period of two vertical synchronization signals VD for the memory T 1  (see the right side in  FIG. 13B ). 
     The memory controller  107  reads the image data from this cut out area  170  at the timing of a next vertical synchronization signal VD after the vertical synchronization signal VD for writing the image data D 1  into the memory T 1 . In this way, at the timing of the projection angle θ 3 , the image data to be projected is read from the memory T 1 , is supplied to the display element  114  through the image processing unit  102  of a later stage, and is projected from the projection lens  12 . 
     At the timing of the next vertical synchronization signal VD after the vertical synchronization signal VD for which the image data D 1  is input, the image data D 2  is input to the memory controller  107 . At this timing, the image data D 1  is written into the memory Y 1 . Accordingly, the memory controller  107  writes the image data D 2  into the memory Y 2  (timing WD 2  illustrated in Chart  215 ). The sequence of writing the image data D 2  into the memory Y 2  at this time is similar to the sequence of writing the image data D 1  described above into the memory Y 1 , and the sequence for the image is similar to that described above (see  FIG. 12B ). 
     In other words, the memory controller  107  sequentially reads the image data D 2  in the vertical direction over the lines for each pixel up to the pixel positioned at the upper end of the image with a pixel positioned on the lower left corner of the image being set as a reading start pixel, and next, pixels are read in the vertical direction with a pixel positioned on the right side neighboring to the pixel positioned at the reading start position of the vertical direction being set as a reading start pixel (timing RD 2  illustrated in Chart  215 ). This operation is repeated until the reading of a pixel positioned on the upper right corner of the image is completed. The memory controller  107  sequentially writes (timing WD 2  represented in Chart  216 ) the pixel of the image data D 2  read from the memory Y 2  in this way into the memory T 2  toward the line direction for each pixel (see the left side in  FIG. 13A ). 
     The memory controller  107  designates an address of the cut out area that is designated by the correction control unit  108  to the memory T 2  and reads image data of the area designated as the cut out area from the memory T 2  at timing RD 2  represented in Chart  216 . At this time, as described above, the correction control unit  108  designates an area lager than the area of the image data corresponding to the projected image as the cut out area  170  in consideration of a change in the projection angle θ for the memory T 2  (see the right side in  FIG. 13B ). 
     The memory controller  107  reads the image data from this cut out area  170  at the timing of a next vertical synchronization signal VD after the vertical synchronization signal VD for writing the image data D 2  into the memory T 2 . In this way, the image data of the cut out area  170  of the image data D 2  input to the memory controller  107  at the timing of the projection angle θ 2  is read from the memory  12  at the timing of the projection angle θ 4 , is supplied to the display element  114  through the image processing unit  102  of a later stage, and is projected from the projection lens  12 . 
     Thereafter, similarly, for the image data D 3 , D 4 , D 5 , . . . , the process is sequentially performed using a set of the memories Y 1  and T 1  and a set of the memories Y 2  and T 2  in an alternate manner. 
     As described above, according to this embodiment, in the image memory  101 , an area of the memories Y 1  and Y 2  used for writing and reading image data with the size of horizontal 1920 pixels×vertical 1080 pixels (lines) and an area of the memories T 1  and T 2  used for writing and reading image data with the size of horizontal 1080 pixels×vertical 1920 pixels (lines) are arranged. The reason for this is that, generally, a dynamic random access memory (DRAM) used in an image memory has an access speed for the vertical direction that is lower than an access speed for the horizontal direction. In a case where another memory, which is easily randomly accessible, having access speeds of the same level for the horizontal direction and the vertical direction is used, a configuration may be employed in which a memory having a capacity corresponding to the image data is used in both the cases. 
     Geometric Distortion Correction 
     Next, the geometric distortion correction for the image data that is performed by the projector device  1  according to this embodiment will be described. 
       FIGS. 14 and 15  are diagrams that illustrate the relation between the projection direction of the projection lens  12  of the projector device  1  for a screen  1401  and the projection image projected onto the screen  1401  that is the projection face. As illustrated in  FIG. 14 , in a case where the projection angle is 0°, and the optical axis of the projection lens  12  is perpendicular to the screen  1401 , a projection image  1402  has a rectangular shape that is the same as the image data projected from the projector device  1 , and a distortion does not occur in the projection image  1402 . 
     However, as illustrated in  FIG. 15 , in a case where the image data is projected in an inclined state with respect to the screen  1401 , the projection image  1502  to be a rectangular shape is distorted to be in a trapezoidal shape, in other words, a so-called trapezoidal distortion occurs. 
     For this reason, conventionally, by performing a geometric distortion correction such as a trapezoidal distortion correction (keystone correction) transforming image data to be projected into a trapezoidal shape in a direction opposite to a trapezoidal shape generated in a projection image on a projection face such as a screen, as illustrated in  FIGS. 16A and 16B , a projection image having a rectangular shape without any distortion on the projection face is displayed on a non-projection face.  FIG. 16A  illustrates an example of a projection image before a geometric distortion correction is performed for the image data of the projection image.  FIG. 16B  illustrates an example of a projection image after a geometric distortion correction is performed for the image data of the projection image illustrated in  FIG. 16A . 
     However, in the conventional trapezoidal distortion correction (keystone correction), as illustrated in  FIG. 16B , in order not to perform display of a peripheral area  1602  of a corrected projection image  1601 , in other words, display of the area  1602  of a difference between an area  1603  of the projection image of a case where a correction is not performed and the area  1601  of the projection image after the correction, image data corresponding to black is input to the display device, or the display device is controlled so as not to drive the display device. Accordingly, the pixel area of the display device is not effectively used, but the brightness of the actual projection area is caused to be lowered. 
     Recently, in accordance with wide use of high-resolution digital cameras and the like, the resolution of a video content is improved, and there are cases where the resolution of the video content is higher than the resolution of the display device. For example, in a projector device supporting up to the full HD of 1920 pixels×1080 pixels as an input image for a display device having resolution of 1280 pixels×720 pixels, the input image is scaled in a former stage of the display device, and accordingly, the resolution is matched for enabling the whole input image to be displayed on the display device. 
     On the other hand, instead of performing such a scaling process, as illustrated in  FIGS. 17A and 17B , an image of a partial area of input image data may be cut out and displayed on the display device. For example, from input image data having 1920 pixels×1080 pixels illustrated in  FIG. 17A , as illustrated in  FIG. 17B , an image of an area of 1280 pixels×720 pixels corresponding to the resolution of an output device is cut out and is displayed on the display device. Even in such a case, when the projection lens is inclined, as illustrated in  FIG. 18A , a trapezoidal distortion occurs in the projection image. Thus, when the trapezoidal distortion correction (keystone correction) is performed, as illustrated in  FIG. 18B , in order not to perform display of a differential area between the area of the projection image of a case where any correction is not performed and the area of the projection image after the correction, image data corresponding to black is input to the display device, or the display device is controlled so as not to be driven. Accordingly, a state is formed in which the pixel area of the display device is not effectively used. However, in such a case, as illustrated in  FIGS. 17A and 17B , the projection image that is output is a part of the input image data. 
     For this reason, according to the projector device  1  of this embodiment, as illustrated in  FIG. 19 , an image of the unused area remaining after being originally cut out from the input image data is used for the peripheral area  1602  of the image data after the correction described above, and, for example, as illustrated in  FIG. 20 , all the input image data is cut out, and the projection image is displayed such that the center of the projection image in the vertical direction coincides with that of the projection image for which the geometric distortion correction has not been performed, and the amount of information lacking in the peripheral area  1602  is supplemented. In this way, according to this embodiment, by effectively utilizing the image of the unused area, the effective use of the displayable area is realized. By comparing  FIG. 20  with  FIG. 18B , it can be understood that the area of the peripheral area is decreased in  FIG. 20 , and more information can be represented (in other words, the pixel area of the display device is effectively used). Hereinafter, for details of such a geometric distortion correction, first, the calculation of correction coefficients used for performing the geometric distortion correction and next, a method of supplementing the amount of information will be described. 
     The correction control unit  108  of the geometric distortion correction unit  100 , as described above, calculates a first correction coefficient and a second correction coefficient based on the projection angle and the view angle. Here, the first correction coefficient is a correction coefficient for performing a correction of the image data in the horizontal direction, and the second correction coefficient is a correction coefficient for performing a correction of the image data in the vertical direction. The correction control unit  108  may be configured to calculate the second correction coefficient for each line configuring the image data (cut out image data) of the cut out range. 
     In addition, the correction control unit  108 , for each line from the upper side to the lower side of the image data of the cut out range, calculates a linear reduction rate for each line based on the first correction coefficient. 
     The relation between the projection angle and the correction coefficient and the correction coefficients and a correction amount for a trapezoidal distortion calculated based on the projection angle will be described in detail.  FIG. 21  is a diagram that illustrates major projection directions and projection angles θ of the projection face according to the first embodiment. 
     Here, the projection angle θ is an inclination angle of the optical axis of projection light emitted from the projection lens  12  with respect to the horizontal direction. Hereinafter, an inclination angle of a case where the optical axis of the projection light is in the horizontal direction is set as 0°, a case where the drum unit  10  including the projection lens  12  is rotated to the upper side, in other words, the elevation angle side will be defined as positive, and a case where the drum unit  10  is rotated to the lower side, in other words, the depression angle side will be defined as negative. In such a case, a housed state in which the optical axis of the projection lens  12  faces a floor face  222  disposed right below corresponds to a projection angle (−90°), and a horizontal state in which the projection direction faces the front side of a wall face  220  corresponds to a projection angle (0°), and a state in which the projection direction faces a ceiling  221  disposed right above corresponds to a projection angle (+90°). 
     A projection direction  231  is a direction of a boundary between the wall face  220  and the ceiling  221  that are two projection faces adjacent to each other. A projection direction  232  is, the projection direction of the projection lens  12  in a case where an upper side, which corresponds to a first side, of one pair of sides disposed in a direction perpendicular to the vertical direction that is the moving direction of a projection image approximately coincides with the boundary in the projection image on the wall face  220 . 
     A projection direction  233  is the projection direction of the projection lens  12  in a case where a lower side, which corresponds to a second side, of the above-described one pair of sides of the projection image of the ceiling  221  approximately coincides with the boundary. A projection direction  234  is the direction of the ceiling  221  right above the projector device  1  and corresponds to a state in which the optical axis of the projection lens  12  and the ceiling  221  cross each other at right angles. The projection angle at this time is 90°. 
     In the example illustrated in  FIG. 21 , the projection angle θ in the case of the projection direction  230  is 0°, the projection angle in the case of the projection direction  232  is 35°, the projection angle θ in the case of the projection direction  231  is 42°, and the projection angle θ in the case of the projection direction  233  is 49°. 
     A projection direction  235  is a direction in which projection is started by the projector device  1  that is acquired by rotating the projection lens from a state in which the projection lens is positioned toward the right below side (−90°), and the projection angle θ at this time is −45°. A projection direction  236  is the projection direction of the projection lens in a case where an upper side, which corresponds to a first side, of one pair of sides disposed in a direction perpendicular to the moving direction of a projection image approximately coincides with a boundary between the floor face  222  and the wall face  220  in the projection image on the floor face  222 . The projection angle θ at this time will be referred to as a second boundary start angle, and the second boundary start angle is −19°. 
     A projection direction  237  is a direction of a boundary between the floor face  222  and the wall face  220  that are two projection faces adjacent to each other. The projection angle θ at this time will be referred to as a second boundary angle, and the second boundary angle is −12°. 
     A projection direction  238  is the projection direction of the projection lens in a case where a lower side, which corresponds to a second face, of the above-described one pair of sides of the projection image on the wall face  220  approximately coincides with a boundary between the floor face  222  and the wall face  220 . The projection angle θ at this time will be referred to as a second boundary end angle, and the second boundary end angle is −4°. 
     Hereinafter, an example of the geometric distortion correction (the trapezoidal distortion correction will be used as an example) will be described.  FIG. 22  is a graph that illustrates a relation between the projection angle and the correction coefficient according to the first embodiment. In  FIG. 22 , the horizontal axis represents the projection angle θ, and the vertical axis represents the first correction coefficient. The first correction coefficient takes a positive value or a negative value. In a case where the first correction coefficient is positive, it represents a correction direction for compressing the length of the upper side of the trapezoid of the image data. On the other hand, in a case where the first correction coefficient is negative, it represents a correction direction for compressing the length of the lower side of the trapezoid of the image data. In addition, as described above, in a case where the first correction coefficient is “1” or “−1”, the correction amount for the trapezoidal distortion is zero, whereby the trapezoidal distortion correction is completely canceled. 
     In  FIG. 22 , the projection directions  235 ,  236 ,  237 ,  238 ,  230 ,  232 ,  231 ,  233 , and  234  illustrated in  FIG. 21  are illustrated in association with projection angles thereof. As illustrated in  FIG. 22 , in a range  260  from a projection angle (−45°) for the projection direction  235  to a projection angle (−12°) for the projection direction  237 , the projection lens projects the floor face  222 . 
     In addition, as illustrated in  FIG. 22 , in a range  261  from a projection angle (−12°) for the projection direction  237  to a projection angle (0°) for the projection direction  230 , the projection lens projects the wall face  220  downward. Furthermore, as illustrated in  FIG. 22 , in a range  262  from a projection angle (0°) for the projection direction  230  to a projection angle (42°) for the projection direction  231 , the projection lens projects the wall face  220  upward. 
     In addition, as illustrated in  FIG. 22 , in a range  263  from a projection angle (42°) for the projection direction  231  to a projection angle (90°) for the projection direction  234 , the projection lens projects the ceiling  221 . 
     The correction control unit  108  calculates a trapezoidal distortion correction amount based on a correction coefficient according to each projection angle θ denoted by a solid line in  FIG. 22  and performs a trapezoidal distortion correction for the image data based on the calculated correction amount. In other words, the correction control unit  108  calculates a first correction coefficient corresponding to the projection angle output from the rotation control unit  104 . In addition, the correction control unit  108 , based on the projection angle θ, determines whether the projection direction of the projection lens  12  is the projection direction that is an upward projection direction with respect to the wall face  220 , the projection direction toward the face of the ceiling  221 , the projection direction that is a downward direction for the wall face  220 , or the projection direction toward the floor face  222  and derives a correction direction of the trapezoidal distortion correction for the image data in accordance with the projection direction. 
     Here, as illustrated in  FIG. 22 , between a projection angle (−45°) at the time of the projection direction  235  and the second boundary start angle (−19°) that is the projection angle θ at the time of the projection direction  236  and between a projection angle (0°) at the time of the projection direction  230  and the first boundary start angle (35°) that is the projection angle at the time of the projection direction  232 , the correction coefficient is positive and gradually decreases, and the correction amount for the trapezoidal distortion gradually increases. Here, the correction coefficient or the correction amount therebetween is used for maintaining the shape of the projection image projected onto the projection face to be a rectangle. 
     On the other hand, as illustrated in  FIG. 22 , between the second boundary start angle (−19°) that is the projection angle θ at the time of the projection direction  236  and the second boundary angle (−12°) that is the projection angle θ at the time of the projection direction  237  and between the first boundary start angle (35°) that is the projection angle θ of the projection direction  232  and the first boundary angle (42°) that is the projection angle θ at the time of the projection direction  231 , the correction coefficient is positive and gradually increases so as to decrease a difference from “1” and is in a direction (a direction for canceling the trapezoidal distortion correction) for weakening the degree of the trapezoidal distortion correction. In the projector device  1  according to this embodiment, as described above, the correction coefficient is positive and gradually increases, and the correction amount for the trapezoidal distortion gradually decreases. Here, this increase may not be a gradual linear increase but may be an exponential increase or a geometric increase as long as the increase is a continuous gradual increase therebetween. 
     In addition, as illustrated in  FIG. 22 , between the second boundary angle (−12°) that is the projection angle θ at the time of the projection direction  237  and the second boundary end angle (−4°) that is the projection angle θ at the time of the projection direction  238  and between the first boundary angle (42°) that is the projection angle θ at the time of the projection direction  231  and the first boundary end angle (49°) that is the projection angle θ at the time of the projection direction  233 , the correction coefficient is negative and gradually decreases, and the correction amount for the trapezoidal distortion gradually increases. In the projector device  1  according to this embodiment, as described above, the correction coefficient is negative and gradually increases, and the correction amount for the trapezoidal distortion gradually increases. Here, this increase may not be a gradual linear increase but may be an exponential increase or a geometric increase as long as the increase is a continuous gradual increase therebetween. 
     Here, as illustrated in  FIG. 22 , between the second boundary end angle (−4°) that is the projection angle θ at the time of the projection direction  238  and a projection angle (0°) at the time of the projection direction  230  and between the first boundary end angle (49°) that is the projection angle θ of the projection direction  233  and a projection angle (90°) at the time of the projection direction  234 , the correction coefficient is negative and gradually decreases, and the correction amount for the trapezoidal distortion gradually decreases. Here, the correction coefficient or the correction amount therebetween is used for maintaining the shape of the projection image projected onto the projection face to be a rectangle. 
     Here, a technique for calculating the correction coefficient will be described.  FIG. 23  is a diagram that illustrates the calculation of the first correction coefficient. The first correction coefficient is the reciprocal of a ratio between the upper side and the lower side of a projection image that is projected to the projection medium so as to be displayed thereon and is the same as d/e that is a ratio between lengths d and e in  FIG. 23 . Accordingly, in the trapezoidal distortion correction, the upper side or the lower side of the image data is reduced by d/e times. 
     Here, as illustrated in  FIG. 23 , when a ratio of a projection distance a from the projector device  1  to a lower side of the projection image that is projected to the projection medium so as to be displayed thereon to a distance b from the projector device  1  to an upper side of the projection image is represented as a/b, d/e is represented in the following Equation (9). 
     
       
         
           
             
               
                 
                   
                     d 
                     e 
                   
                   = 
                   
                     a 
                     b 
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     Then, in  FIG. 23 , when an angle θ is the projection angle, an angle β is a half of the view angle α, and a value n is a projection distance from the projector device  1  to the projection face  270  in the horizontal direction, the following Equation (10) is formed. Here, 0°≦θ&lt;90°, and 7.83°≦β≦11.52°. 
         n=b  cos(θ+β)= a  cos(θ−β)  (10)
 
     By transforming Equation (10), Equation (11) is acquired. Accordingly, based on Equation (11), the correction coefficient is determined based on the angle β that is a half of the view angle α and the projection angle θ. 
     
       
         
           
             
               
                 
                   
                     a 
                     b 
                   
                   = 
                   
                     
                       
                         cos 
                          
                         
                           ( 
                           
                             θ 
                             + 
                             β 
                           
                           ) 
                         
                       
                       
                         cos 
                          
                         
                           ( 
                           
                             θ 
                             - 
                             β 
                           
                           ) 
                         
                       
                     
                     = 
                     
                       k 
                        
                       
                         ( 
                         
                           θ 
                           , 
                           β 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     Based on this Equation (11), in a case where the projection angle θ is 0°, in other words, in a case where the projection image is projected in a direction horizontal to the projection face  270 , the first correction coefficient is “1”, and, in such a case, the trapezoidal distortion correction amount is zero. 
     In addition, based on Equation (11), the first correction coefficient decreases as the projection angle θ increases, and the trapezoidal distortion correction amount increases according to the value of the first correction coefficient. Accordingly, the trapezoidal distortion of the projection image that becomes remarkable according to an increase in the projection angle θ can be appropriately corrected. 
     Furthermore, in a case where the projection image is projected onto the ceiling that is disposed right above and is perpendicular to the projection face  270 , the correction direction of the trapezoidal distortion correction changes, and accordingly, the correction coefficient is b/a. In addition, as described above, the sign of the correction coefficient is negative. 
     In this embodiment, the correction control unit  108  calculates the correction coefficient based on Equation (11) when the projection angle θ is between the projection angle (−45°) at the time of the projection direction  235  and the second boundary start angle (−19°) that is the projection angle θ at the time of the projection direction  236 , between the projection angle (0°) at the time of the projection direction  230  and the first boundary start angle (35°) that is the projection angle at the time of the projection direction  232 , between the second boundary end angle (−4°) that is the projection angle θ at the time of the projection direction  238  and the projection angle (0°) at the time of the projection direction  230 , or between the first boundary end angle (49°) that is the projection angle θ of the projection direction  233  and the projection angle (90°) at the time of the projection direction  234 , described above. 
     On the other hand, the correction control unit  108  calculates the correction coefficient in a direction for lowering the degree of the correction without using Equation (11) when the projection angle θ is between the second boundary start angle (−19°) that is the projection angle θ at the time of the projection direction  236  and the second boundary angle (−12°) that is the projection angle θ at the time of the projection direction  237  or between the first boundary start angle (35°) that is the projection angle θ at the time of the projection direction  232  and the first boundary angle (42°) that is the projection angle θ at the time of the projection direction  231 . 
     In addition, the correction control unit  108  calculates the correction coefficient in a direction for raising the degree of the correction without using Equation (11) when the projection angle θ is between the second boundary angle (−12°) that is the projection angle θ at the time of the projection direction  237  and the second boundary end angle (−4°) that is the projection angle θ at the time of the projection direction  238  or between the first boundary angle (42°) that is the projection angle θ at the time of the projection direction  231  and the first boundary end angle (49°) that is the projection angle θ at the time of the projection direction  233 . 
     The calculation of the first correction coefficient is not limited to that described above, and the correction control unit  108  may be configured to calculate the first correction coefficient using Equation (11) for all the projection angles θ. 
     The correction control unit  108  multiplies the length H act  of the line of the upper side of the image data by a correction coefficient k(θ, β) represented in Equation (11) and calculates the length H act (θ) of the line of the upper side after the correction using the following Equation (12) for the correction. 
         H   act (θ)= k (θ,β)× H   act   (12)
 
     The correction control unit  108 , in addition to the length of the upper side of the image data, calculates a reduction rate of the length of each line in a range from the line of the upper side to the line of the lower side.  FIG. 24  is a diagram that illustrates the calculation of lengths of lines from the upper side to the lower side. 
     As illustrated in  FIG. 24 , the correction control unit  108  calculates and corrects the length H act (y) of each line from the upper side to the lower side of the image data so as to be linear using the following Equation (13). Here, V act  is the height of the image data, in other words, the number of lines, and Equation (13) is an equation for calculating the length H act (y) of the line at a position y from the upper side. In Equation (13), a portion of braces { } is a reduction rate for each line, and, as illustrated in Equation (13), the reduction rate can be acquired depending on the projection angle θ and the view angle α (actually, the angle β that is a half of the view angle α). 
     
       
         
           
             
               
                 
                   
                     
                       H 
                       act 
                     
                      
                     
                       ( 
                       y 
                       ) 
                     
                   
                   = 
                   
                     
                       { 
                       
                         1 
                         - 
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 k 
                                  
                                 
                                   ( 
                                   
                                     θ 
                                     , 
                                     β 
                                   
                                   ) 
                                 
                               
                             
                             ) 
                           
                           × 
                           
                             
                               
                                 V 
                                 act 
                               
                               - 
                               y 
                             
                             
                               V 
                               act 
                             
                           
                         
                       
                       } 
                     
                     × 
                     
                       H 
                       act 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     Another method of calculating the first correction coefficient will now be described. The first correction coefficient may be calculated from a ratio between the length of the side of the projection image at the projection angle 0° and the length of the side of the projection image at the projection angle θ. In such a case, the length H act (y) of each line from the upper side to the lower side of the image data can be represented as in Equation (14). 
     
       
         
           
             
               
                 
                   
                     
                       H 
                       act 
                     
                      
                     
                       ( 
                       y 
                       ) 
                     
                   
                   = 
                   
                     
                       cos 
                        
                       
                         ( 
                         
                           
                             ( 
                             
                               θ 
                               + 
                               β 
                             
                             ) 
                           
                           - 
                           
                             2 
                              
                             
                                 
                             
                              
                             β 
                             × 
                             
                               y 
                               
                                 V 
                                 act 
                               
                             
                           
                         
                         ) 
                       
                     
                     × 
                     
                       H 
                       act 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     In the trapezoidal distortion correction using the first correction coefficient according to this calculation method, an image having the same size as the projection image of the projection angle 0° can be projected regardless of the projection angle θ. 
       FIGS. 25 and 26  are diagrams that illustrate the calculation of the second correction coefficient. The method of designating a cut out area using Equations (3) and (4) described above is based on a cylindrical model in which the projection face  130 , for which projection is performed by the projection lens  12 , is assumed to be a cylinder having the rotation shaft  36  of the drum unit  10  as its center. However, actually, the projection face  130  is frequently considered to be a perpendicular face (hereinafter, simply referred to as a “perpendicular face”) forming an angle of 90° with respect to the projection angle θ=0°. In a case where image data of the same number of lines is cut out from the image data  140  and is projected to the perpendicular face, as the projection angle θ increases, an image projected to the perpendicular face grows in the vertical direction. Thus, the correction control unit  108  calculates the second correction coefficient as below, and a trapezoidal distortion correction for the image data is performed using the second correction coefficient by the memory controller  107 . 
     As illustrated in  FIG. 25 , a case will be considered in which an image is projected from the projection lens  12  onto a projection face  204  that is disposed to be separate from a position  201 , which is the position of the rotation shaft  36  of the drum unit  10 , by a distance r. 
     In the cylindrical model described above, a projection image is projected with an arc  202  that has the position  201  as its center and has a radius r being the projection face. Each point on the arc  202  has the same distance from the position  201 , and the center of the luminous fluxes of light projected from the projection lens  12  is a radius of a circle including the arc  202 . Accordingly, even when the projection angle θ is increased from an angle θ 0  of 0° to an angle θ 1 , an angle θ 2 , . . . , the projection image is projected onto the projection face with the same size all the time. 
     On the other hand, in a case where an image is projected from the projection lens  12  onto the projection face  204  that is a perpendicular face, when the projection angle θ is increased from an angle θ 0  to an angle θ 1 , an angle θ 2 , . . . , a position on the projection face  204  to which the center of luminous fluxes of light emitted from the projection lens  12  is projected changes according to the characteristics of a tangent function as a function of the angle θ. 
     Accordingly, the projection image grows upwardly in accordance with a ratio M represented in the following Equation (15) as the projection angle θ increases. 
     
       
         
           
             
               
                 
                   M 
                   = 
                   
                     
                       180 
                       × 
                       tan 
                        
                       
                           
                       
                        
                       θ 
                     
                     
                       θ 
                       × 
                       π 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     Here, when the angle θ is a projection angle, an angle β is a half of the view angle α, and a total number of lines of the display element  114  is a value L, a projection angle θ′ of a luminous ray projecting a line disposed at a perpendicular position dy on the display element  114  is calculated using Equation (16). 
     
       
         
           
             
               
                 
                   
                     θ 
                     ′ 
                   
                   = 
                   
                     
                       ( 
                       
                         θ 
                         + 
                         β 
                       
                       ) 
                     
                     - 
                     
                       2 
                        
                       
                           
                       
                        
                       β 
                        
                       
                         
                           d 
                            
                           
                               
                           
                            
                           y 
                         
                         L 
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     The height Lh(dy) of the line at the time of projecting the line disposed at the perpendicular position dy on the display element  114  onto the projection face  204  is calculated using Equation (17). 
         Lh ( dy )= r (tan(θ+β−2β×( dy− 1)/ L )−tan(θ+β−2β× dy/L ))  (17)
 
     Accordingly, an enlargement rate M L (dy) of the height Lh(dy) of the line at the time of projecting the line disposed at the perpendicular position dy on the display element  114  onto the projection face  204  with respect to the height of the line of the lower side (dy=L) is calculated using Equation (18). 
     
       
         
           
             
               
                 
                   
                     
                       M 
                       L 
                     
                      
                     
                       ( 
                       dy 
                       ) 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           tan 
                            
                           
                             ( 
                             
                               θ 
                               + 
                               β 
                               - 
                               
                                 2 
                                  
                                 
                                     
                                 
                                  
                                 β 
                                 × 
                                 
                                   
                                     ( 
                                     
                                       dy 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   / 
                                   L 
                                 
                               
                             
                             ) 
                           
                         
                         - 
                         
                           tan 
                            
                           
                             ( 
                             
                               θ 
                               + 
                               β 
                               - 
                               
                                 2 
                                  
                                 β 
                                 × 
                                 
                                   dy 
                                   / 
                                   L 
                                 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                     
                       ( 
                       
                         
                           tan 
                            
                           
                             ( 
                             
                               θ 
                               + 
                               β 
                               - 
                               
                                 2 
                                  
                                 β 
                                 × 
                                 
                                   
                                     ( 
                                     
                                       L 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   / 
                                   L 
                                 
                               
                             
                             ) 
                           
                         
                         - 
                         
                           tan 
                            
                           
                             ( 
                             
                               θ 
                               + 
                               β 
                               - 
                               
                                 2 
                                  
                                 β 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     The second correction coefficient is the reciprocal of the enlargement rate M L (dy) and is calculated for each line disposed at the perpendicular position dy on the display element  114 . 
     In addition, in a case where the view angle α or the projection angle θ is small, instead of calculating the second correction coefficient for each line disposed at the perpendicular position dy on the display element  114  using Equation (18), the second correction coefficient may be calculated by acquiring the enlargement rate M L (1) of the height of the line of the upper side (dy=1) with respect to the height of the line of the lower side (dy=L) using Equation (19) and approximating the second correction coefficient through linear interpolation for an intermediate value. 
     
       
         
           
             
               
                 
                   
                     
                       M 
                       L 
                     
                      
                     
                       ( 
                       dy 
                       ) 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           tan 
                            
                           
                             ( 
                             
                               θ 
                               + 
                               β 
                             
                             ) 
                           
                         
                         - 
                         
                           tan 
                            
                           
                             ( 
                             
                               θ 
                               + 
                               β 
                               - 
                               
                                 2 
                                  
                                 
                                   β 
                                   / 
                                   L 
                                 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                     
                       ( 
                       
                         
                           tan 
                            
                           
                             ( 
                             
                               θ 
                               + 
                               β 
                               - 
                               
                                 2 
                                  
                                 β 
                                 × 
                                 
                                   
                                     ( 
                                     
                                       L 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   / 
                                   L 
                                 
                               
                             
                             ) 
                           
                         
                         - 
                         
                           tan 
                            
                           
                             ( 
                             
                               θ 
                               + 
                               β 
                               - 
                               
                                 2 
                                  
                                 β 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     Another method of calculating the second correction coefficient will be described. The second correction coefficient may be calculated from a ratio between the height of the projection image of the projection angle 0° and the height of the projection image of the projection angle θ. 
     When the angle θ is the projection angle, and the angle β is a half of the view angle α, a value M 0  that is the ratio of the height of the projection image of the projection angle θ to the height of the projection image of the projection angle 0° can be calculated using the following Equation (20). 
     
       
         
           
             
               
                 
                   
                     M 
                     0 
                   
                   = 
                   
                     
                       180 
                       
                         π 
                          
                         
                             
                         
                          
                         α 
                       
                     
                     × 
                     
                       { 
                       
                         
                           tan 
                            
                           
                             ( 
                             
                               θ 
                               + 
                               β 
                             
                             ) 
                           
                         
                         - 
                         
                           tan 
                            
                           
                             ( 
                             
                               θ 
                               - 
                               β 
                             
                             ) 
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     As the second correction coefficient, the reciprocal of the value M 0  may be used. 
     Here, when the angle θ is the projection angle, and the angle β is a half of the view angle α, the height W′ of the projection image of the projection angle θ is represented as in Equation (21). 
         W′=r ×{tan(θ+β)−tan(θ−β)}  (21)
 
     The height of the projection image at a projection angle of 0° and the view angle α is approximated to a height L acquired by delimiting a tangential line at the projection angle θ of the arc  202  illustrated in  FIG. 25  using lines emitted from the center of the circle with angles of +β and −β having the projection angle θ at the center thereof. The height L is represented as in Equation (22). 
     
       
         
           
             
               
                 
                   L 
                   = 
                   
                     
                       π 
                        
                       
                           
                       
                        
                       r 
                        
                       
                           
                       
                        
                       α 
                     
                     180 
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     Based on Equations (21) and (22), a value M 0  that is the ratio of the height of the projection image of the projection angle θ to the height of the projection image of the projection angle 0° is represented as in Equation (23). 
     
       
         
           
             
               
                 
                   
                     M 
                     0 
                   
                   = 
                   
                     
                       180 
                       
                         π 
                          
                         
                             
                         
                          
                         α 
                       
                     
                     × 
                     
                       { 
                       
                         
                           tan 
                            
                           
                             ( 
                             
                               θ 
                               + 
                               β 
                             
                             ) 
                           
                         
                         - 
                         
                           tan 
                            
                           
                             ( 
                             
                               θ 
                               - 
                               β 
                             
                             ) 
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     According to Equation (15) described above, for example, in the case of the projection angle θ=45°, the projection image grows at the ratio of about 1.27 times. In addition, in a case where the projection face  204  is much higher than the length of the radius r, and projection at the projection angle θ=60° can be performed, in the case of the projection angle θ=60°, the projection image grows at the ratio of about 1.65 times. 
     In addition, as illustrated in  FIG. 26  as an example, a line gap  205  in the projection image on the projection face  204  is widened as the projection angle θ increases. In this case, the line gap  205  is widened based on Equation (15) described above in accordance with the position on the projection face  204  within one projection image. 
     Thus, the correction control unit  108 , in accordance with the projection angle θ of the projection lens  12 , performs a geometric distortion correction by performing a reduction process for image data to be projected by calculating the reciprocal of the ratio M L (dy) represented in Equation (18) described above as the second correction coefficient and multiplying the height of the line by the second correction coefficient using the memory controller  107 , thereby eliminating the vertical-direction distortion of the image data. 
     In the vertical-direction reduction process (geometric distortion correction process), image data is preferably larger than the image data cut out based on the cylindrical model. In other words, while the image data depends on the height of the projection face  204  that is a perpendicular face, in the case of the projection angle θ=22.5° and the view angle α=45°, the projection image grows at the ratio of about 1.27 times, and accordingly, the image data is reduced at the ratio of the reciprocal thereof that is about 1/1.27 times. 
     In addition, the correction control unit  108  acquires a cut out range of the image data based on the first correction coefficient, the second correction coefficient, and the reduction rate calculated as described above and outputs the acquired cut out range to the extended function control unit  109  and the memory controller  107 . 
     For example, in a case where the view angle α is 10°, and the projection angle θ is 30°, the projection image is distorted to be in a trapezoidal shape, and the length of the upper side of the trapezoid is about 1.28 times of the length of the lower side. Accordingly, in order to correct the horizontal-direction distortion, the correction control unit  108  calculates the first correction coefficient as 1/1.28, reduces a first line of the upper side of the image data at 1/1.28 times, and sets reduction rates of lines to be linear such that the final line is scaled to the original size. In other words, the number of pixels for the first line of the output of the image data is reduced from 1280 pixels to 1000 pixels (1280/1.28=1000), whereby the trapezoidal distortion is corrected. 
     However, in this state, as described above, for the first line, image data of 280 pixels (1280−1000=280) is not projected, and the number of effective projection pixels decreases. Thus, in order to supplement the amount of information as illustrated in  FIG. 20 , the memory controller  107 , for the first line, reads a signal of 1.28 times of the horizontal resolution of the image data from the image memory  101 , and the correction control unit  108  determines a cut out range of the image data so as to perform this process for each line. 
     The extended function control unit  109  achieves the role of associating the image control unit  103  with the geometric distortion correction unit  100 . In other words, in an area for which all the outputs of the image data is painted in black according to the geometric distortion correction in a conventional case, information of the image data is represented. For this reason, the extended function control unit  109 , in accordance with the cut out range input from the correction control unit  108 , sets the output resolution to be higher than the resolution of 1280 pixels×720 pixels at the time of outputting the image data in the output resolution control unit  1031 . In the example described above, since the enlargement/reduction rate is one, the extended function control unit  109  sets the output resolution as 1920 pixels×1080 pixels. 
     In this way, the memory controller  1032  of the image control unit  103  stores the input image data in the image memory  101  with the resolution of 1920 pixels×1080 pixels. Accordingly, the image data in the cut out range can be cut out in the state in which, as illustrated in  FIG. 20 , the amount of information is supplemented from the memory controller  107  of the geometric distortion correction unit  100 . 
     In addition, the memory controller  107  performs the geometric distortion correction as below by using the first correction coefficient, the reduction rate, and the second correction coefficient calculated as described above. In other words, the memory controller  107  multiplies the upper side of the image data of the cut out range by the first correction coefficient and multiplies each line of the upper side to the lower side of the image data of the cut out range by a reduction rate. In addition, the memory controller  107  generates lines corresponding to a display pixel number from the image data of the lines configuring the image data of the cut out range based on the second correction coefficient. 
     Next, an example of the cutting out of image data and the geometric distortion correction performed by the geometric distortion correction unit  100  according to this embodiment will be described with being compared with a conventional case. In  FIG. 20  described above, an example has been described in which all the input image data is cut out, and the projection image is displayed such that the center of the projection image in the vertical direction coincides with the projection image for which the geometric distortion correction has not been performed. Hereinafter, with reference to  FIGS. 27 to 30 , an example will be described in which the input image data is cut out in accordance with the number of pixels of the display element  114 , and the geometric distortion correction is performed with the cut out range also including the area of the geometric distortion that may occur in the projection image in accordance with the projection direction being set as the cut out image data. 
       FIGS. 27A to 27D  are diagrams that illustrate examples of cutting out of image data, image data on the display element  114 , and the projection image in a case where the projection angle is 0°. As illustrated in  FIG. 27A , in a case where the projection angle is 0°, when image data  2700  of 1920 pixels×1080 pixels is input, the memory controller  107  cuts outs a range of 1280 pixels×720 pixels that is the resolution of the display element  114  from the image data  2700  (image data  2701  illustrated in  FIG. 27B ). For the convenience of description, a center portion is assumed to be cut out (hereinafter, the same). Then, the memory controller  107  does not perform a geometric distortion correction for the cut out image data  2701  (image data  2702  illustrated in  FIG. 27C ) but, as illustrated in  FIG. 27D , projects the cut out image data onto the projection face as a projection image  2703 . 
       FIGS. 28A to 28D  are diagrams that illustrate examples of cutting out of image data, image data on the display element  114 , and a projection image in a case where the projection angle θ is greater than 0°, and a geometric distortion correction is not performed. 
     As illustrated in  FIG. 28A , in a case where the projection angle θ is greater than 0°, when image data  2800  of 1920 pixels×1080 pixels is input, a range of 1280 pixels×720 pixels that is the resolution of the display element  114  is cut out from the image data  2800  (image data  2801  illustrated in  FIG. 28B ). Then, since the geometric distortion correction (trapezoidal distortion correction) is not performed (image data  2802  illustrated in  FIG. 28C ), as illustrated in  FIG. 28D , a projection image  2803  in which a trapezoidal distortion has occurred is projected onto the projection face. In other words, in the horizontal direction, the projection image is distorted in a trapezoidal shape in accordance with the projection angle θ, and, in the vertical direction, a distance of the projection face is different in accordance with the projection angle θ, whereby a vertical distortion in which the height of the line increases in the upward vertical direction occurs. 
       FIGS. 29A to 29D  are diagrams that illustrate examples of cutting out of image data, image data on a display element  114 , and a projection image in a case where the projection angle θ is greater than 0°, and a conventional trapezoidal distortion correction is performed. 
     As illustrated in  FIG. 29A , in a case where the projection angle θ is greater than 0°, when image data  2900  of 1920 pixels×1080 pixels is input, a range of 1280 pixels×720 pixels that is the resolution of the display element  114  is cut out from the image data  2900  (image data  2901  illustrated in  FIG. 29B ). Then, for the image data  2901  of the cut out range, a conventional trapezoidal distortion correction is performed. More specifically, as illustrated in  FIG. 29C , in the horizontal direction, the image data is corrected in a trapezoidal shape in accordance with the projection angle θ, and, in the vertical direction, a distortion correction in which the height of the line increases in the vertical downward direction is performed. Then, image data  2902  after the correction is projected onto the projection face, and, as illustrated in  FIG. 29D , a projection image  2903  having a rectangular shape is displayed. In such a case, while the distortion is corrected in both the horizontal direction and the vertical direction for the projection image  2903 , there are pixels not contributing to the display. 
       FIGS. 30A to 30D  are diagrams that illustrate examples of cutting out of image data, image data on a display element  114 , and a projection image in a case where the projection angle θ is greater than 0°, and the geometric distortion correction (trapezoidal distortion correction) according to this embodiment is performed. 
     As illustrated in  FIG. 30A , in a case where the projection angle θ is greater than 0°, when image data  3000  of 1920 pixels×1080 pixels is input, the memory controller  107 , as illustrated in  FIG. 30B , from this image data  3000 , cuts out image data  3001  of a range of an area of a trapezoidal shape of a cut out range according to the projection angle θ from the image memory  101 . Here, as the cut out range, by the correction control unit  108 , the horizontal lower side is calculated as 1280 pixels, and the horizontal upper side is calculated as a value acquired by multiplying 1280 pixels by the reciprocal of the first correction coefficient according to the projection angle, and, as the range in the vertical direction, a value acquired by multiplying the height of the input image data by the reciprocal of the second correction coefficient is calculated. 
     Then, the memory controller  107  performs the geometric distortion correction for the image data of the cut out range. More specifically, as illustrated in  FIG. 30C , the memory controller  107 , in the horizontal direction, corrects the image data in a trapezoidal shape according to the projection angle θ, and, in the vertical direction, performs a distortion correction in which the height of the line increases in the downward vertical direction. Here, as illustrated in  FIG. 30B , since the memory controller  107  cuts out pixels corresponding to the area of the trapezoidal shape according to the projection angle θ, an image of 1280 pixels×720 pixels is expanded on the display element  114 , and, as illustrated as a projection image  3003  in  FIG. 30D , the cut out area is projected without being reduced. 
     As illustrated in the examples represented in  FIGS. 30A to 30D , an image of the unused area that originally remains after the cutting out of the input image data is used for the area of the periphery of the image data after the geometric distortion correction (trapezoidal distortion correction), whereby the projection image is displayed, and the amount of information lacking in the area of the periphery in the horizontal direction and the vertical direction is supplemented. Accordingly, compared to the conventional technique illustrated in  FIGS. 29A to 29D , the image of the conventionally unused area can be effectively used, whereby effective use of the displayable area after the geometric distortion correction (trapezoidal distortion correction) is realized. 
     Process of Projecting Image Data 
     Next, the flow of the process performed when an image according to the image data is projected by the projector device  1  will be described.  FIG. 31  is a flowchart that illustrates the sequence of an image projection process according to the first embodiment. 
     In step S 100 , in accordance with input of image data, various setting values relating to the projection of an image according to the image data are input to the projector device  1 . The input various setting values, for example, are acquired by the input control unit  119  and the like. The various setting values acquired here, for example, includes a value representing whether or not the image according to the image data is rotated, in other words, whether or not the horizontal direction and the vertical direction of the image are interchanged, an enlargement rate of the image, and an offset angle θ ofst  at the time of projection. The various setting values may be input to the projector device  1  as data in accordance with the input of the image data to the projector device  1  or may be input by operating the operation unit  14 . 
     In next step S 101 , image data corresponding to one frame is input to the projector device  1 , and the input image data is acquired by the memory controller  1032 . The acquired image data is written into the image memory  101 . 
     In next step S 102 , the image control unit  103  acquires the offset angle θ ofst . In next step S 103 , the correction control unit  108  acquires the view angle α from the view angle control unit  106 . In addition, in next step S 104 , the correction control unit  108  acquires the projection angle θ of the projection lens  12  from the rotation control unit  104 . 
     In next step S 105 , the image data cutting out and geometric distortion correction process are performed. Here, the image data cutting out and geometric distortion correction process will be described in detail.  FIG. 32  is a flowchart that illustrates the sequence of the image data cutting out and geometric distortion correction process according to the first embodiment. 
     First, in step S 301 , the correction control unit  108  calculates the first correction coefficient using Equation (11). In next step S 302 , the correction control unit  108  calculates the reduction rate of each line from the upper side (first side) to the lower side (second side) of the image data using the equation represented inside the braces { } illustrated in Equation (13). In addition, in step S 303 , the correction control unit  108  acquires the second correction coefficient for each line as the reciprocal of the enlargement rate M L (dy) calculated using Equation (18). 
     Then, next, in step S 304 , the correction control unit  108  acquires the cut out range based on the first correction coefficient and the second correction coefficient as described above. 
     Next, in step S 305 , the memory controller  107  cuts out image data of the cut out range from the image data stored in the image memory  101 . Then, in step S 306 , the memory controller  107  performs the geometric distortion correction described above for the image data of the cut out range using the first correction coefficient, the second correction coefficient, and the reduction rate and ends the process. 
     Returning to  FIG. 31 , when the image data cutting out and geometric distortion correction process are completed in step S 105 , in step S 106 , the control unit  120  determines whether or not an input of image data of a next frame after the image data input in step S 101  described above is present. 
     In a case where the input of the image data of the next frame is determined to be present, the control unit  120  returns the process to step S 101  and performs the process of steps S 101  to S 105  described above for the image data of the next frame. In other words, the process of steps S 101  to S 105  is repeated in units of frames of the image data in accordance with a vertical synchronization signal VD of the image data. Accordingly, the projector device  1  can cause each process to follow a change in the projection angle θ in units of frames. 
     On the other hand, in step S 106 , in a case where the image data of the next frame is determined not to have been input, the control unit  120  stops the image projection operation in the projector device  1 . For example, the control unit  120  controls the light source  111  so as to be turned off and issues a command for returning the posture of the drum unit  10  to be in the housed state to the rotation mechanism unit  105 . Then, after the posture of the drum unit  10  is returned to be in the housed state, the control unit  120  stops the fan cooling the light source  111  and the like. 
     As above, according to this embodiment, in a case where the geometric distortion correction is performed for the image data, a projection image is displayed by using an image of the unused area originally remaining after the cutting out of the input image data for the area of the periphery of the image data after the geometric distortion correction, and the amount of information lacking in the area of the periphery in the horizontal direction and the vertical direction is supplemented. For this reason, according to this embodiment, compared to a conventional technology, by effectively using the image of the unused area, the geometric distortion correction is performed for the content of the projection image, and a high-quality projection image effectively using the displayable area can be acquired. 
     Particularly, in a case where, for example, an environment video such as the sky or the night sky is projected using the projector device  1  according to this embodiment, even in a case where the projection image is displayed in a trapezoidal shape, when the amount of information to be displayed is large, a realistic sensation can be more effectively acquired. In addition, in a case where a map image or the like is projected using the projector device  1  according to this embodiment, compared to a conventional technique, a relatively broad range of peripheral information can be projected. 
     Second Embodiment 
     According to the projector device  1  of the first embodiment, a horizontal distortion and a vertical distortion of the projection image that occur in accordance with the projection angle θ are eliminated by the geometric distortion correction, and the amount of information is supplemented for both areas of the horizontal-direction area and the vertical-direction area. However, according to a second embodiment, a horizontal distortion is eliminated by a geometric distortion correction, and the amount of information is supplemented for the horizontal-direction area, but a distortion correction is not performed for the vertical direction. 
     The external view, the structure, and the functional configuration of a projector device  1  according to this embodiment are similar to those of the first embodiment. 
     In this embodiment, the correction control unit  108  calculates the first correction coefficient used for a horizontal distortion correction based on the projection angle θ (projection angle  123 ) input from the rotation control unit  104  and the view angle α (view angle  125 ) input from the view angle control unit  106  using Equation (11) described above and calculates the reduction rate for each line using the equation represented inside the braces { } represented in Equation (13) but does not calculate the second correction coefficient used for a vertical distortion correction. 
     In addition, based on the projection angle θ, the view angle α, and the first correction coefficient, the correction control unit  108  determines a cut out range from the input image data such that image data after the geometric distortion correction includes a displayable size of the display device and outputs the determined cut out range to the memory controller  107  and the extended function control unit  109 . 
     The memory controller  107  cuts out (extracts) an image area of the cut out range determined by the correction control unit  108  from the whole area of a frame image relating to the image data stored in the image memory  101  and outputs the image area that has been cut out as image data. 
     In addition, the memory controller  107  performs a geometric distortion correction for the image data cut out from the image memory  101  by using the first correction coefficient and outputs the image data after the geometric distortion correction to the image processing unit  102 . 
     The flow of the process of projecting the image data according to the second embodiment is similar to that of the first embodiment described with reference to  FIG. 31 . In the second embodiment, an image data cutting out and geometric distortion correction process is different from those in step S 105  illustrated in  FIG. 31  of the first embodiment.  FIG. 33  is a flowchart that illustrates the sequence of the image data cutting out and geometric distortion correction process according to the second embodiment. 
     First, in step S 401 , the correction control unit  108  calculates the first correction coefficient using Equation (11). In next step S 402 , the correction control unit  108  calculates the reduction rate of each line from the upper side (first side) to the lower side (second side) of the image data using the equation represented inside the braces { } illustrated in Equation (13). 
     Then, next, in step S 403 , the correction control unit  108  acquires a cut out range based on the first correction coefficient as described above. 
     Next, in step S 404 , the memory controller  107  cuts out image data of the cut out range from the image data stored in the image memory  101 . Then, in step S 405 , the memory controller  107  performs the geometric distortion correction described above for the image data of the cut out range using the first correction coefficient and the reduction rate and ends the process. 
     Next, an example of the cutting out of image data and the geometric distortion correction performed by the geometric distortion correction unit  100  according to this embodiment will be described. 
       FIGS. 34A to 34D  are diagrams that illustrate examples of cutting out of image data, image data on the display element  114 , and a projection image in a case where the projection angle θ is greater than 0°, and the geometric distortion correction according to this embodiment is performed. 
     In a case where the projection angle θ is greater than 0°, as illustrated in  FIG. 34A , when image data  3400  of 1920 pixels×1080 pixels is input, the memory controller  107 , as illustrated in  FIG. 34B , from this image data  3400 , cuts out image data  3401  of a range of an area of a trapezoidal shape of a cut out range according to the projection angle θ from the image memory  101 . Here, as the cut out range, by the correction control unit  108 , the horizontal lower side is calculated as 1280 pixels, and the horizontal upper side is calculated as a value acquired by multiplying 1280 pixels by the reciprocal of the first correction coefficient according to the projection angle θ. 
     Then, the memory controller  107  performs the geometric distortion correction for the image data  3401  of the cut out range. More specifically, the memory controller  107 , in the horizontal direction, corrects the image data in a trapezoidal shape according to the projection angle θ, as represented as image data  3402  in  FIG. 34C . Here, as represented as image data  3401  in  FIG. 34B , since the memory controller  107  cuts out pixels corresponding to the area of the trapezoidal shape according to the projection angle θ, an image of 1280 pixels×720 pixels is expanded on the display element  114 , and, as represented as a projection image  3403  in  FIG. 34D , the cut out area is projected without being reduced. 
     As above, according to this embodiment, the horizontal distortion is eliminated by the geometric distortion correction, and the amount of information is supplemented for the horizontal-direction area, but the geometric distortion correction is not performed for the vertical direction. Accordingly, not only the same advantages as those of the first embodiment are acquired, but the processing load of the correction control unit  108  can be reduced. 
     In the first embodiment and the second embodiment, while the method has been described in which the projection angle θ is derived by changing the projection direction of the projection unit such that the projection unit is moved while projecting the projection image onto the projection face, and a correction amount used for eliminating the geometric distortion according to the projection angle θ is calculated, a change in the projection direction does not need to be dynamic. In other words, as illustrated in  FIGS. 14 and 15 , the correction amount may be calculated using a fixed projection angle θ in the stopped state. 
     In addition, the calculation of the correction amount and the detection method are not limited to those described in this embodiment, and a cut out range including also an area other than the above-described image data area after the correction may be determined according to the correction amount. 
     Each of the projector devices  1  according to the first embodiment and the second embodiment has a configuration that includes hardware such as a control device such as a central processing unit (CPU), storage devices such as a read only memory (ROM) and a random access memory (RAM), an HDD, and an operation unit  14 . 
     In addition, the rotation control unit  104 , the view angle control unit  106 , the image control unit  103  (and each unit thereof), the extended function control unit  109 , the geometric distortion correction unit  100  (and each unit thereof), the input control unit  119 , and the control unit  120  mounted as circuit units of the projector devices  1  of the first and second embodiments may be configured to be realized by software instead of being configured by hardware. 
     In a case where the projector device is realized by the software, an image projection program (including an image correction program) executed by the projector devices  1  according to the first and second embodiments is built in a ROM or the like in advance and is provided as a computer program product. 
     The image projection program executed by the projector devices  1  according to the first and second embodiments may be configured to be recorded on a computer-readable recording medium such as a CD-ROM, a flexible disk (FD), a CD-R, or a DVD so as to be provided as a file having an installable form or an executable form. 
     In addition, the image projection program executed by the projector devices  1  according to the first and second embodiments may be configured to be stored in a computer connected to a network such as the Internet and be provided by being downloaded through the network. In addition, the image projection program executed by the projector devices  1  according to the first and second embodiments may be configured to be provided or distributed through a network such as the Internet. 
     The image projection program executed by the projector devices  1  according to the first and second embodiments has a module configuration including the above-described units (the rotation control unit  104 , the view angle control unit  106 , the image control unit  103  (and each unit thereof), the extended function control unit  109 , the geometric distortion correction unit  100  (and each unit thereof), the input control unit  119 , and the control unit  120 ). As actual hardware, as the CPU reads the image projection program from the ROM and executes the read image projection program, the above-described units are loaded into a main memory device, the rotation control unit  104 , the view angle control unit  106 , the image control unit  103  (and each unit thereof), the extended function control unit  109 , the geometric distortion correction unit  100  (and each unit thereof), the input control unit  119 , and the control unit  120  are generated on the main storage device. 
     Although the invention has been described with respect to specific embodiments for a complete and clear disclosure, the appended claims are not to be thus limited but are to be construed as embodying all modifications and alternative constructions that may occur to one skilled in the art that fairly fall within the basic teaching herein set forth.