Patent Publication Number: US-8123350-B2

Title: Computerized apparatus and method for applying graphics to surfaces

Description:
RELATED APPLICATIONS 
     This application is a continuation-in-part application of Ser. No. 11/386,180 filed on Mar. 22, 2006, which is a divisional of U.S. Pat. No. 7,044,665 entitled Computerized Apparatus and Method for Applying Graphics to Surfaces, issued to Cannell on May 16, 2006, which claims the benefit of provisional application Ser. No. 60/475,409, filed Jun. 3, 2003. This application also claims the benefit of provisional patent application Ser. No. 60/911,711 filed on Apr. 13, 2007. All of these related applications and patents are incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention is directed generally to apparatus and methods for painting or printing graphics onto walls, ceilings, floors or surfaces of non-planar or curvilinear substrates. More specifically, the invention relates to computerized apparatus and methods for applying graphics to surfaces. 
     2. Description of Related Art 
     A popular means for varying the appearance of a dwelling, storefront or other building is the application of murals or other graphic displays to a wall, ceiling or floor. The owner can customize a design or picture that adds variety to a living space or provokes conversation among guests and customers. The design is then either painted directly onto the desired surface by an artist or painted onto a material that is applied to the surface. Unfortunately, artists that can reliably paint designs onto a wall or other surface are expensive and the process can take weeks or months to complete. 
     Previous inventions have attempted to simplify the painting of walls, floors and ceilings. U.S. Pat. No. 5,935,657, to Melendez, discloses an apparatus for painting walls that uses adjustable sets of spray nozzles supplied by a pressurized paint source. The apparatus is mounted on wheels and can be manually pushed across the surface of a wall. The use of the nozzles ensures even painting of the surface. The invention is designed for painting a single color onto a wall and does not allow for customized designs to be painted. Only a single color and horizontal/vertical orientation of each set of nozzles may be altered. Additionally, the apparatus uses multiple stationary paint nozzles, spaced in such a way that an entire section of the painting surface may be covered without gaps in a single pass. Movement of the apparatus is not automated, and it must be manually pushed across the width of the surface being painted. 
     U.S. Pat. Nos. 6,398,869, 6,319,555 and 5,944,893, to Anderson, attempt to automate movement of the painting device and to provide more customized coloration. The patents claim aspects of a specific print head device, in which paint is applied to an elongated filament and then blown from the filament onto a printing medium, such as vinyl, paper or plastic film. The patents disclose the possibility of using a rigid frame on which the printing device can be mounted. The patents also disclose the computerized control of the direction and coloration of printing performed by the particular print head. 
     The Anderson inventions are not usable for painting walls, floors or ceilings. The rigid frame disclosed in the patents&#39; dicta seems to be a simple mount for the print head and does not control or possibly even allow movement of the print head about the frame. The rigidity of the frame mount prevents adaptability to surfaces of varying widths and lengths. No features are described that would maintain or vary the distance of the print head from a wall to avoid obstacles in the path of the print head. The Anderson invention is also unable to print around corners to a second surface at an angle with the first. 
     Hence, there is a great need in the art for an apparatus and method for applying graphics to surfaces such as walls, floors or ceilings. The apparatus must be portable and readily scalable to apply graphics to surfaces of varying sizes. It must be capable of painting or printing customized graphics communicated to it by a remote or connected computing device. The movement of the printing device across the surface being painted or printed must be automated. It should also be able to account for the topography of the surface and any obstacles, such as door and window frames, electrical outlets and switches, and the like. It should also be able to print seamlessly around corners. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an illustration of a first embodiment of an apparatus and method for applying graphics to surfaces. 
         FIG. 2A  is an illustration of a rear perspective view of a second embodiment of the apparatus and method for applying graphics to surfaces. 
         FIG. 2B  is an illustration of a front perspective view of a second embodiment of the apparatus and method for applying graphics to surfaces. 
         FIG. 3  is an illustration of a side perspective view of a host for receiving and directing a wall printing device, such as a print head or mapping device. 
         FIG. 4  is an illustration of a two-wall embodiment of the apparatus and method for applying graphics to surfaces. 
         FIG. 5  is a flow diagram illustrating steps for a method of using the apparatus and method for applying graphics to surfaces. 
         FIG. 6  is a high-level logical block diagram of another embodiment of the system using a portable coordinate measurement machine (PCMM) for applying graphics to surfaces. 
         FIG. 7  is a schematic representative of an embodiment of a print head array. 
         FIG. 8  is a schematic representation of color matrix maps of an image to be applied to the surface. 
         FIG. 9  is a flowchart of an embodiment of a method for applying graphics to surfaces. 
         FIG. 10  is a logical block diagram of an embodiment of a system using a PCMM for applying graphics images to a surface. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring now to the figures, wherein like elements are indicated by like numerals, an apparatus and method for applying graphics to surfaces, such as a wall, ceiling or floor are shown. As stated previously, the surfaces may be planar or curvilinear where, for example, some bowing, warping or other curvature or inconstancy lies in the shape of the surface.  FIG. 1  shows a portable scaffolding system having two vertical members  101 . Each vertical member  101  has two elongated portions that may be extended telescopically to accommodate the full height of a wall, when vertical members  101  are perpendicular to a floor; or, to accommodate the length of a floor or ceiling, when vertical members  101  are parallel to the floor or ceiling. The scaffolding also contains at least one horizontal travel bar  102  connected with and perpendicular to the vertical members. The travel bar  102  also has two lengths, such that its length may be telescopically varied to accommodate the width of the printing or painting surface. 
     Vertical members  101  may be formed of any sturdy material that will not bend or warp in response to tension applied between them or the weight of any parts attached to travel bar  102 . Examples of such materials may comprise steel, aluminum or other lightweight metal tubing, as well as poly-vinyl chloride or other suitable plastic tubing. Each vertical member  101  may be formed integrally with a base  105 , such that one length of vertical member  101  and base  105  are one piece. Alternatively, they may be formed separately and connected modularly. Preferably, they are formed separately and connected modularly, such that base  106  may be removed when painting or printing a surface that does not require vertical members  101  to stand upright. 
     The arms of travel bar  102  may be formed of any sturdy material that will not bend or warp in response to the weight of any parts attached to it. Examples of such materials may comprise steel, aluminum or other lightweight metal tubing, as well as poly-vinyl chloride or other suitable plastic tubing. The material used to form travel bar  102  may comprise the same material as that used for vertical members  101 . Alternatively, it may comprise a different material than that used for vertical members  101 . Alternatively, it may comprise the same material with different thickness or other dimensions than that used for vertical members  101 . 
     Also shown is a host device  103  that is movably attached to travel bar  102 . Host device  103  comprises a housing that is adapted to receive one or more head attachments, which may include a print or paint head, or a mapping device, such as an optical sensor. Host device  103  also comprises an electronic step motor that controls the movement of host device  103  across travel bar  102 . 
     Electronic step motors may also be placed in the base of each vertical member  101 . The step motors may be used to gradually raise or lower the telescopic arms of vertical members  101 . This allows host device  103  to move across the next highest or next lowest line to be mapped, painted or printed on the surface. Paint or ink supplies  104  may also be housed in the base of each vertical member  101 , for re-filling a print head that is placed in host device  103 . 
       FIG. 2A  illustrates a second and preferred embodiment of the apparatus and method for applying graphics to surfaces.  FIG. 2A  shows a portable scaffolding system having two vertical members  201 . Each vertical member  201  is telescopic, such that it may be extended telescopically to accommodate the full height of a wall, when vertical members  201  are perpendicular to a floor; or, to accommodate the length of a floor or ceiling, when the vertical members  201  are parallel to the floor or ceiling. Each vertical member  201  has a proximal end and a distal end, both of which are connected with a tensioning cam  204 . Each tensioning cam  204  is oriented such that its teeth face the painting or printing surface and a tensioning arm  209  extends away from the painting or printing surface. The distal end of each vertical member  201  may also be connected with a base  210  for supporting the vertical member  201  on a floor. The base  210  may be square, L-shaped, or any suitable shape for preventing tippage of the scaffolding system. 
     The scaffolding system also contains at least one horizontal brace  202  connected with and perpendicular to vertical members  201 . Each horizontal brace  202  is telescopic, such that its length may be varied to accommodate the width of the printing or painting surface. Preferably, two horizontal braces  202  are used, one about the midpoints of vertical members  201  when they are fully collapsed, and one at the distal ends of vertical members  201  or connected with platforms  209 . The scaffolding system may also contain at least one tensioning turnbuckle  205  for maintaining an exact width between vertical members  201 . Each tensioning turnbuckle  205  may grip the arms of both tensioning cams  204  at the proximal or distal ends of the vertical members  201 . Alternatively, the tensioning turnbuckles  205  may hook around the arms  209  of the tensioning cams  209 , thereby pulling the vertical members  201  toward one another. 
     The scaffolding system also contains at least one travel bar  203 . Each travel bar  203  may comprise a flexible strip having evenly spaced apertures for receiving teeth of tensioning cams  204 . Each travel bar is stretched between tensioning cams  204  at the proximal or distal ends of vertical members  201 . The flexibility of travel bars  203  allows them to be adjusted to the telescoped length of the horizontal braces  202 , while maintaining constant dimensions along the lengths of travel bars  203 . 
     Vertical members  201  may be formed of any sturdy material that will not bend or warp in response to tension applied between them or the weight of any parts in contact with to travel bars  203 . Examples of such materials may comprise steel, aluminum or other lightweight metal tubing, as well as poly-vinyl chloride or other suitable plastic tubing. Horizontal braces  202  may be formed of any sturdy material that will not bend or warp in response to the tension applied between vertical members  201  by parts attached to travel bars  203  or by tensioning turnbuckles  205 . Examples of such materials may comprise steel, aluminum or other lightweight metal tubing, as well as poly-vinyl chloride or other suitable plastic tubing. The material used to form horizontal braces  202  may comprise the same material as that used for vertical members  201 . Alternatively, it may comprise a different material than that used for vertical members  201 . Alternatively, it may comprise the same material with different thickness or other dimensions than that of vertical members  201 . 
     Tensioning cams  204  may be composed of any sturdy material that will not bend, warp or break in response to the tension of travel bars  203  against their teeth or tensioning turnbuckles  205  against their arms  209 . Vertical members  201  may be formed such that tensioning cams  204  are integrated with the ends of vertical members  201 . Alternatively, tensioning cams  204  may be separately formed and connected modularly with vertical members  201 . Preferably, tensioning cams  204  are integrated with the ends of vertical members  201 . Bases  210  may also be integrally formed with the distal end of each vertical member  201 . Alternatively, bases  210  may be separately formed and connected modularly with vertical members  201 . Preferably, bases  210  are separately formed and connected modularly with vertical members  201 , such that platforms  210  may be removed when painting or printing a surface that does not require the scaffolding system to stand upright. 
     Travel bars  203  may be composed of any flexible material that may stretch and yet not sag or tear in response to the weight of parts that travel bars  203  support. Such materials may comprise rubber or a suitable flexible or semi-rigid polymer material. 
     The embodiment shown in  FIG. 2A  also comprises a host device  207 . Host device  207 , described in further detail with reference to  FIG. 3 , is adapted to receive one or more head attachments, which may include a print or paint head, or a mapping device. 
     The embodiment shown in  FIG. 2A  also comprises a vertical drive assembly  206  having a vertical track reel  208 , a vertical drive motor  212 , a horizontal drive motor  211 , and a vertical drive belt, shown as  213  in  FIG. 2B . Vertical drive belt  213  may comprise a rubber or plastic belt or metal chain and is connected with host device  207 . Vertical drive motor  212  moves drive belt  213  about its reel, such that host device  207  moves incrementally in either direction along the length or height of the surface to be painted or printed. Vertical drive motor  212  contains motion control circuitry that receives instructions from a computing device  200  via an electronic drive board, a receiver, an antenna or other suitable communication means. 
     Horizontal drive motor  211  moves vertical drive assembly  206  horizontally across travel bars  203 , in incremental steps along the width of the surface to be painted or printed. Horizontal drive motor  211  contains motion control circuitry that receives instructions from computing device  200  via an electronic drive board, an antenna or other suitable communication means. Horizontal drive motor  211  turns horizontal drive rods  214 , simultaneously, in the same direction. Horizontal drive rods  214  contact travel bars  203 , either frictionally or with teeth that fit in the apertures of travel bars  203 . The turning of horizontal drive rods  214  moves vertical drive assembly  206  across travel bars  203  in incremental steps, according to instructions received from the computing device  200 . 
     Computing device  200  may comprise any suitable computing device for loading, displaying and editing graphic displays, storing and processing wall topography data, and communicating with the horizontal, vertical and host drive motors and other motors requiring instruction, as described herein. Computing device  200  may comprise a desktop or laptop computer or a portable computing device, such as a personal data assistant or pocket PC. Computing device  200  may communicate with the various motors described herein through direct electrical connection or via radio, infrared or other communication means. Preferably, remote communication means is used that does not interfere with other remote devices in a home or other structure, such as electronics equipment, wireless networks or cordless telephones. 
       FIG. 2B  illustrates a front perspective view of an apparatus and method for applying graphics to surfaces.  FIG. 2B  further illustrates vertical drive assembly  206 , by showing a vertical drive belt  213  connected with host device  207 . As stated, vertical motor  212  moves host device  207  in a vertical line by retracting and extending vertical drive belt  213  about the reel of vertical motor  212 . 
     Those skilled in the art will recognize that the number of vertical towers used in  FIGS. 2A and 2B  is not intended to limit the invention&#39;s scope. For instance, where painting or printing surfaces are so wide that the travel bars cannot support vertical drive assembly without sagging, additional towers may be used between the towers that frame the width of the painting or printing surface. 
       FIG. 3  illustrates a side perspective view of the host device, in accordance with the invention. The host device is primarily responsible for maintaining the distance and alignment of a head attachment with respect to a surface to be painted or printed. The host device comprises a housing  300 , a motor  301 , and guides  302 . Motor  301  moves housing  300  toward or away from the painting or printing surface along guides  302 . Motor  301  contains motion control circuitry that receives instructions from a computing device via an electronic drive board, receiver, antenna or other suitable communication means. The host device preferably contains at least two equidistant guides  302 . Most preferably, the host device contains three guides  302  placed in a triangular configuration, as shown in  FIG. 3 . The motion of housing  300  moves head attachment  304  toward and away from the painting or printing surface. Guides  302  must be sufficiently long to enable the print head to avoid thick obstacles, such as door and window frames. 
     The host device also comprises a vertical motion platform  306  that is connected with housing  300  via guides  302 . Vertical motion platform  306  connects with vertical drive belt  307  (also shown at  213  in  FIG. 2B ). Vertical drive belt may be connected with the side of vertical motion platform  306  that faces the vertical drive motor (shown at  212  in  FIGS. 2A and 2B ). Alternatively, a second vertical drive belt may be attached in line with vertical drive belt  307  on the underside of vertical motion platform  306 , such that it moves about the vertical track reel (shown at  208  in  FIG. 2A ). Vertical motion platform  306  contains a recessed portion for receiving vertical drive track  308 , such that host device moves in a straight vertical line along vertical drive track  308 , when the vertical drive motor (shown at  212  in  FIG. 2A ) retracts or extends vertical drive belt  307 . 
     The host device also comprises a horizontal motion platform  309 , which moves across guiderails  303 . Guiderails  303  are parallel and connected with the corners of housing  300  as shown. Guiderails  303  enable horizontal motion platform  309  to move horizontally along them to reach areas of the painting or printing surface that are unreachable due to the position of the vertical drive assembly. For instance, when horizontal movement of the vertical drive assembly is prevented by either vertical tower, guiderails  303  allow the print head to continue moving horizontally. This prevents the width of the painting or printing surface from being reduced by the width of the towers or bases of the towers. 
     Head attachment  304  is removably and pivotally attached with horizontal motion platform at corner swivel  305 . As stated, head attachment  304  may comprise a paint head, print head, or mapping device. Mapping devices may comprise an optical sensor, laser sensor, camera or other suitable device for mapping surface topography, and may include illumination devices. Head attachment  304  may be pivoted about swivel  305 , in order to paint, print or map around corners or angles, and continue printing, painting or mapping adjoining surfaces. This is shown and described in further detail with reference to  FIG. 4 . 
     The print or paint heads used in accordance with the present invention may comprise any industrial paint or print head suitable for printing graphics of the scale necessary to cover surfaces such as walls, ceilings or floors. Preferably, the print or paint head should be capable of holding a sufficient amount of colorant to prevent frequent refilling during painting or printing of a single surface. The print head also contains motion control circuitry that receives instructions from a computing device via an electronic drive board, an antenna or other suitable communication means, such that the print or paint head can move about guiderails on the host device, as described herein. The print head may also contain mapping devices, such that it maps a surface entirely without switching devices, or such that it maps the surface on the fly, a certain number of horizontal and vertical lines ahead of printing or painting. The print head may also be separate from the mapping device but have a sensor for verification of the topography during printing or painting. Preferably, the surface is mapped entirely by a separate mapping device, such that degradation of the mapping device or print head will not necessitate replacement of both devices. Preferably, the print head has a sensor for verifying topography on the fly. 
       FIG. 4  illustrates a two-surface embodiment of an apparatus and method for applying graphics to surfaces. The two-surface embodiment employs the same features as the single-surface embodiments described previously, with additional elements. This embodiment will be described for walls that form right angles with each other, though those skilled in the art will appreciate that the embodiment may be used for walls, ceilings and floors that form different angles or which have concave rounded corners. Vertical members  401  are separated from each other by two horizontal braces  402  that are connected at a right angle via midpost  415 . Vertical members  401  and midpost  415  are all connected or integrated with tensioning cams  404  and  416 , respectively, which support horizontal travel bars  403 . Tensioning cams  416  differs from tensioning cams  404  in that they have two arms  409  for supporting tensioning turnbuckles  405  and  418 . Tensioning turnbuckles  418  also differs from tensioning turnbuckles  405 , in that they must be able to extend past tensioning turnbuckles  405  to the opposite arm of tensioning cam  416 , while remaining parallel to horizontal braces  402 . 
       FIG. 4  illustrates head attachment  417  connected with and perpendicular to host device  407 . This is the second-surface position for head attachment  417 . In order to align the image on a first wall or surface with that on the adjoining wall or surface, print head  417  extends into the second-surface position, when it reaches the corner between the surfaces. It prints or paints fiducial marks on the second surface that act as guidemarkers for the continuation of the graphics being painted or printed on the first surface. When the second surface is mapped for painting or printing, the mapping device detects the fiducial marks and communicates them to the computing device that instructs the various motors, as described previously. This allows the computing device to instruct the vertical, horizontal and print head motors to paint or print graphics that are aligned with the image on the first surface. 
     Once printing or painting of the first surface is completed, vertical drive assembly  406  can either be manually replaced onto those travel bars  403  that face the second surface, or vertical drive assembly may automatically transition around the corners. Preferably, vertical drive assembly  406  automatically transitions around the corners. The horizontal drive rods (shown as  214  in  FIG. 2A ) of vertical drive assembly  406  disengage with those travel bars  403  facing the first surface, engage corner guides  419 , which cover the teeth of midpost cams  416 , and then engage those travel bars  403  facing the second surface. 
     Described hereinafter is a computer-implemented method of painting or printing a graphic on surfaces, such as walls, floors or ceilings. As stated previously, the surfaces may be planar or curvilinear where, for example, some bowing, warping or other curvature or inconstancy lies in the shape of the surface.  FIG. 5  illustrates exemplary steps of the computer-implemented method. In accordance with step  501 , a portable scaffolding system of any type disclosed herein is assembled such that a head attachment will face the surface to be painted or printed when it is attached to the host device. In accordance with step  502 , the scaffolding system is aligned and planed, such that it will paint or print a graphic level with the plane occupied by the surface. Alternatively, the scaffolding system may be aligned with the surface but planed at an angle with the surface, such that the graphic is printed or painted on the surface at a constant angle. If a second wall is to be painted or printed, then the two-surface embodiment of the current invention may be aligned or planed with each surface. 
     In accordance with step  503 , at least one graphic is received into random access memory of a computing device. The graphics may be selected from a database of graphics that is stored on the computing device or on a remote computing device that communicates with the computer via a local area network, a wide area network, or via the Internet. The selected graphics may be edited via the computing device, if necessary. Where two walls are painted or printed, the selected graphics may the same, different or continuations of each other. 
     In accordance with step  504 , the topography of the surface to be painted or printed is mapped. A wall mapping device is attached to the host device of the scaffolding system, as described herein. The host device then steps across the surface to be painted or printed in horizontal or vertical lines and communicates the presence of obstacles and varying thicknesses on the surface. Where the host device is prevented from further movement, the host device moves across guiderails on the host device to access the full width of the surface, as described herein. The wall mapping device communicates data to the computing device for mapping the surface. 
     In accordance with step  505 , a selected graphic is painted or printed onto the first surface. A print or paint head is attached with the host device of the scaffolding system, as described herein. The computing device communicates with the print or paint head and instructs it to emit colorants of varying colors, while communicating with motors that control the horizontal and vertical motion of the host device and the distance of the host device from the surface. It also communicates with the paint or print head to move along the disclosed guiderails when the movement of the host device is obstructed by the vertical members of the scaffolding system or other obstacles. Where two surfaces are being painted or printed, fiducials are painted or printed onto the second surface, in accordance with step  506 . These fiducials may be painted or printed periodically, after each line or a number of lines has been printed on the first surface, or they may be printed or painted after the graphic is completed on the first surface. Alternatively, they may all be printed before the first surface is printed. Preferably, they are painted or printed periodically, after each of a certain number of lines are printed on the first surface. 
     In accordance with step  507 , the topography of the next surface is mapped. A wall mapping device is attached with the host device and steps across the length and height of the next surface. In addition to communicating obstacles along the next surface to the computing device, it communicates the position of the fiducials painted or printed in step  506  to the computing device. In this way, the computing device may produce motions in the host device and print head that will yield alignment of the graphics on each surface. In accordance with step  508 , the next surface is painted or printed in like manner to the first surface. 
       FIG. 6  is a high-level logical block diagram of another embodiment of a system  600  using a portable coordinate measurement machine (PCMM)  601  in the form of a multi-axial articulated arm  602  for applying graphics to surfaces, such as a vertically-oriented wall or substrate  604 . Substrate  604  can be any surface upon which a graphics image is to be applied, and can be planar, non-planar or irregular in shape or orientation. Therefore, the substrate surface may be walls, ceilings, floors, the wings of an airplane, the side panels of a vehicle, for example. The system and method described herein can precisely place colorants to form the desired graphics and image on these surfaces or a portion of these surfaces. PCMM  602  is a piece of equipment traditionally used in the automotive, aerospace, and other industries for inspection and measurement tasks on the shop floor or in the metrology lab. An example of a PCMM that may be used in system  600  is one manufactured by Romer, Inc. of Wixom, Mich. As described in more detail below, PCMM  601  is required to generate geometry data of the multi-axial arm at a very high rate as the free end of the arm is advanced along the contours of the substrate surface. PCMM arm  602  includes a first, second and third articulated joints  605 - 607  connecting first, second and third arm members  608 - 610 . Each articulated joint has multiple axes of movement. For example, first and second joints  605  and  606  each has two axes of movement, and third joint  607  has three axes of movement. The three axes of movement of third joint  607  enables a print head array  612  held at the free-end of PCMM arm  602  to be suitably oriented relative to the print substrate. 
     PCMM  601  additionally includes a coordinate processor and suitable software that are operable to determine, in real-time, the three-dimensional (3D) geometry of the free-end of the arm where the print head array is held. In one embodiment, real-time geometry data  614  includes the X, Y, and Z coordinate of the free-end of the PCMM arm, and angles A, B, and C, representing the angles relative to the X, Y, and Z axes, respectively. This set of real-time geometry data  614  represents the print head array&#39;s position and orientation relative to space, and is provided to a print processor and software  616  that use the received real-time PCMM arm geometry data to determine, also in real-time, which color colorants are to be applied by which print heads  701 - 704  in print head array  612 , shown in  FIG. 7 . Each print head  701 - 704  is assigned a particular colorant, such as cyan, magenta, yellow, and black, and is operable to eject or apply a measured amount of colorant in the assigned color via a plurality of print nozzles. Using interchangeable print heads in the print head array, the system and method described herein can be used for applications in which textures or electro conductive materials are applied to the substrate surfaces. It may be seen that the nozzles are arranged in a predetermined configuration or pattern on each print head. Although print head array  612  is shown with four color print heads  701 - 704 , other printing systems with any number of colors can also be implemented in this manner. Print processor and software  616  includes, but are not limited to, an image processing module  618  which receives the real-time geometry data  614  from PCMM  601  and determine the print head array position and orientation relative to a print region  620  defined on substrate surface  604 . Print region  620  is a work area on substrate surface  604  that the current position of PCMM arm  602  can effectively reach and apply the colorant without moving the temporarily fixed-end or base of the arm. Therefore, a substrate surface  604  to be printed is composed of one or more print regions  620  that may or may not overlap. 
     Because the precise real-time location and orientation of the print head array can be determined, the operator is not required to heed to a particular application format, such as only left-to-right and top-to-bottom. However, the operator&#39;s manual positioning and movement of the print head array attached to the PCMM arm does require a degree of accuracy to achieve complete surface coverage. A small band or gap of unprinted surface would require additional passes by the operator. Further, it may be desirable that the operator moves the print head array smoothly and at a relatively steady rate. In an alternate embodiment, PCMM arm  602  may include actuators that automatically advance, at a prescribed rate and direction, the print head array along a projected path following the contours of the target substrate surface. This embodiment employs a closed loop system in which the real-time geometry data are used to instruct the firing of the print head nozzles as well as advance the print head array. 
     Print processor and software  616  also includes a memory that stores a local copy of a set of color matrix maps  622  of print regions  620 . The local copy of color matrix maps represents a subset of a set of color matrix overlay maps  800  of the entire image, such as shown representatively in  FIG. 8 . Because real-time processing is required, the smaller set of data in the local copy of color matrix maps enables data to be computed and manipulated in an efficient manner. Nevertheless, in some embodiments a larger portion of the image than a single print swath will be pre-processed into the local copy and the exact data that is printed for each encoder pulse will be selected from all of the data pre-processed, by using the coordinate position of the print head. The image is split into horizontal swaths by a Raster Image Processing engine but each swath of the image is now actually wider than the printable width of the print head. For instance, the print head width may be 300 pixels and the pre-processed swath is made up of the print head width plus a margin both above and below that e.g. 300+100+100 pixels. The size of the margins can be chosen during development to determine the optimum balance of typical operator ‘wobble’ with the quantity of data to be manipulated. This technique is put in place as it is assumed that a human operator will not be able to draw the arm across the wall in a sufficiently straight line for accurate printing (˜25 um accuracy). Using this technique, a row of image data is clocked serially into the head driver for each stroke of the image. A head positioned with no vertical offset will have the data starting from the bottom margin of the swath clocked into the head. When the head is offset vertically, then the data clocked into the head is modified. Even using this technique, it is of course possible for the operator to stray beyond the limits of the pre-processed data occasionally and so this occurrence must be planned for and dealt with by the system. In such a situation, the system simply uses blank data to fill the extra pixels and so no image is printed; any missing print can then be filled in on a subsequent print pass. 
     Color matrix maps  800  include multiple color matrix maps  801 - 804 , where each color matrix map corresponds to a color to be applied and indicates the locations where the particular colorants are to be applied. Therefore, in the example shown in  FIG. 8  for a four-color printing system, four color matrix overlay maps are used to represent the graphics image to be applied to the substrate. Because the PCMM arm can be configured to accept a number of print head arrays, it is possible to have an image with more color layers than the number of simultaneously configurable print heads. 
     As areas of the print region are printed, the local color matrix maps are updated to so indicate. A database or another form of suitable memory  624  is used to store the color matrix maps of the entire image, as well as other data. As described in more detail below, print head array firing instructions  626  are determined based on the real-time geometry data and the color matrix maps. In other words, knowing the precise location of the print head array relative to the target substrate surface, instructions for applying specific pixels to specific locations are generated and provided to the print head array. Applied in the right location and sequence, the color pixels applied to the substrate surface make up the desired color, and the desired graphical image is achieved. 
     Print processor and software  616  further includes additional hardware and/or software such as hardware and software  628  for the print head array, for example. A monitor and keyboard, laptop computer, desktop computer, or other computing and user interface devices  630  may be coupled to print processor  616  to enable the operator to study data, receive status feedback, provide operational parameters and other input. It is desirable to have high-speed communication between the various components of system  600 , where suitable data protocols may be used in communication media that may be wired or wireless. The processing platforms for both coordinate and print processors may be any suitable device, including, for example, a processor chip, a digital signal processor, a field programmable gate array. 
     In another embodiment, print processor and software  616  may be resident in a suitable computer  630 . In yet another alternative embodiment, the coordinate processor and accompanying software and print processor and software  616  may reside in the same computing platform and be incorporated into the physical configuration of the PCMM arm. Alternatively, the coordinate software and print software may reside on and execute in computer  630  coupled to PCMM arm  602 . 
       FIG. 9  is a flowchart of an embodiment of a method  900  for applying graphics to surfaces. In step  901 , the image or images to be applied to the target substrate is prepared, edited and finalized. In step  902 , the prepared image or images are stored in a database or memory in a suitable format. Steps  901  and  902  are typically performed off-site in advance of image application. Further, the database may store several graphical images that can be selected by an operator on-site when ready to apply the image to the target substrate. 
     In step  903 , the operator calibrates PCMM arm  602  for mapping the target substrate. A mapping probe (not shown) is used with the PCMM arm to capture the geometry of the substrate surface that is to receive the graphical image. The substrate surface may be planar or non-planar, and can be oriented in any direction. During this step, the position of the arm relative to the target surface is determined so that the two share the same coordinate system. In step  904 , the selected image is processed so that a set of color matrix maps representing the precise placement of all the color pixels is generated. The set of color matrix maps include a color matrix map for each colorant to be applied for the image with respect to the substrate surface. In step  905 , the color matrix maps are further divided into print regions  620 . As described above, each print region represents the work area on the substrate surface that can be reached by the PCMM arm without moving its base or temporarily fixed-end. A suitable algorithm may be used to determine the size and location of the print regions that make up the image, so that the number of times that the PCMM arm has to be positioned and repositioned is minimized. 
     In step  906 , the arm is again calibrated but with the print head array installed on the free-end of the PCMM arm. In step  907 , the operator positions the print head array at a starting location of a print region and provides input, via device  628 , to initiate image application. In step  908 , real-time geometry data is determined by PCMM  601  and received by print processor and software  616 . The coordinate processor and software may make the computation in one of two ways: empirically or by interpolation. In an empirical computation cycle, the real-time geometry data are computed from the axes of rotation at the joints of the PCMM arm. In an interpolated cycle, the real-time geometry data are determined based on one or more sets of prior geometry data. For example, in an interpolated cycle, the six data values (X, Y, Z, A, B, C) are based on the results of an immediately prior empirical cycle and predicted delta values. The predicted delta values may be determined based on a vector representing the direction and speed of movement by the print head array. 
     In step  909 , the print head array position and orientation relative to the target substrate surface are determined based on the real-time geometry data. The determination made in this step includes the determination of each nozzle&#39;s position. The nozzle&#39;s position can be computed using a number of methods, including a vector travel method, in which the nozzle position is updated when the X and Y values change by a predefined amount. Another method computes the new nozzle positions based on any change in the six data values. Yet another method uses a table storing a plurality of pre-stored values, so that the position of a particular nozzle can be identified from the table based on the six geometry data values. Process  900  may employ a combination of these methods to determine the nozzle position and orientation. As each print head array includes multiple print heads, and each print head includes multiple print nozzles, the position of each nozzle must be determined during this step. 
     Based on the nozzle position and orientation data and the local color matrix maps, the pixels or colorants to be applied are determined and then applied to the substrate surface in steps  910  and  911 . In step  910 , the unprinted pixels contained in the color matrix map are matched to specific nozzles on the print heads assigned the same color. Again, this matching process may be done on a real-time computation basis, or by table look-up. When real-time computation method is used, when a nozzle is within a predefined proximity or print target area of a pixel, it is selected for printing or firing. If the nozzle is “out of range,” the pixel is skipped or passed over. Process  900  may include a combination of both and other suitable methods of determining the nozzle position and firing. In step  911 , the distance from the print head array to the substrate surface is verified to ensure that the distance is within tolerance for ideal printing. If the print head is outside of the predetermined distance, then the nozzle would not fire and the pixel is not applied. In step  912 , the local and/or database color matrix maps are updated to indicate which pixels have been applied. The color matrix maps in database  624  are also updated so that the general overall image application process status can be tracked and monitored. In step  913 , a determination is made as to whether the entire image has been completed. An image is completed if the images for all the print regions have been applied to the target substrate surface. If not, execution returns to step  907 , where the operator advances or repositions the print head array. At the completion of each print region, the PCMM arm is repositioned so that the new print region may be easily reached by the print head array. If the entire image has been applied to the substrate surface, as determined in step  913 , then the process ends in step  914 . 
       FIG. 10  is a block diagram of an embodiment of a system  1000  using a PCMM for applying graphics images to a surface. Referring also to  FIG. 6 , PCMM  601  may include seven encoders  1007  coupled to joints  605 - 607  of PCMM arm  602  to provide encoder data used by coordinate processor and software  1008  to determine real-time 3D geometry data  614 . Real-time geometry data  614  are provided to print processor and software  616  via high-speed interfaces or ports  1010  and  1011 . As described above, high-speed interfaces  1010  and  1011  may provide high-speed wired or wireless communication between PCMM  601  and print processor and software  616 . Print processor and software  616  may be controlled by a system console  1012 , which includes a user interface  1014  and database  624  storing images and color matrix maps of one or more of the images. Using the real-time geometry data and color matrix maps, print processor and software determines when nozzles of each print head in the print head array should fire and apply a pixel of colorant. A nozzle will “fire” and apply the colorant of ink or paint only when it is within a predefined area corresponding to an unapplied pixel in a color matrix map. Accordingly, as the operator steadily moves the free-end of the PCMM arm and the print head array following the contours of a print region of the substrate surface, colorants of various colors are applied to form the desired color and the desired image. 
     As print heads fire its nozzles at the rate of 4,000 to 25,000 times per second, and the density of the drop placement is typically 90,000 to 360,000 drops per square inch, PCMM  601  must generate the geometry data fast enough to enable the real-time printing application described herein. For example, generating the geometry data at many thousands or tens of thousands of cycles per second may be needed for the real-time application described herein. 
     It should be noted that while  FIGS. 6 and 10  show logical block diagrams of the system, the implementation of the system may integrate the hardware and software of the geometry processor and software and the print processor and software to minimize the time needed for data exchange between them and improve overall system execution speed. Further, the hardware and at least portions of the software of the geometry and print portions of the system may be incorporated and integrated into the PCMM arm with a user interface on a laptop computer or portable device coupled thereto. 
     While the description herein uses words such as “print,” “print head,” “ink,” and “paint,” it should be understood that the system and method described herein are applicable to apply colorants of any form. For example, the system and method described herein may be used to apply glow-in-the-dark paint or colorant. 
     Those skilled in the art will recognize that various elements of the current invention may be varied without departing from the invention&#39;s scope. For instance, the scaffolding system may be readily adapted to paint or print three or four surfaces, whether by integrating additional sections with the scaffolding system or by positioning the one or two surface embodiments of the invention relative to one another. Additionally, vertical drive assembly may be suited with a cherry-picker type of device that allows printing or painting at a certain distance beyond the height of the fully extended towers. Additionally, the invention may be used for surfaces other than room constructs, such as tables, screens, canvases and other surfaces to which the invention may be sized. Finally, it will be apparent to those skilled in the art that the order of the steps of the method disclosed herein may be varied without departing from the scope of the invention.