Abstract:
A method for measuring shaft flex comprises capturing at least one image of a shaft during movement of the shaft through a swing plane and examining the at least one image to determine the flex of the shaft.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of U.S. Provisional Application No. 61/311,127 to Dawe et al. filed on Mar. 5, 2010 entitled “Apparatus and Method for Measuring Golf Club Shaft Flex and Golf Simulation System Incorporating The Same”, the content of which is incorporated herein by reference in its entirety. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention relates generally to sports measurement systems and in particular, to an apparatus and method for measuring golf club shaft flex and to a golf simulation system incorporating the same. 
       BACKGROUND OF THE INVENTION 
       [0003]    The goal of all sports equipment is to provide athletes with a piece of equipment that will enable the athletes to perform at their best. Many parameters factor into the design of sports equipment, such as weight, length, torque, flex, etc. For example, hockey sticks are sold in a variety of flexes and weights tailored towards specific sizes of hockey players. A young child learning to play hockey is typically best suited to use a short, light weight, soft flex hockey stick, while a professional hockey player is typically best suited to use a long, heavy, stiff flex hockey stick. Other types of sports equipment such as baseball bats, golf clubs, tennis racquets etc. are similarly sold in a variety of forms tailored to fit certain “types” of athletes. 
         [0004]    Certain types of sports equipment rely on the flex of a shaft to help an athlete perform their best. For example, golf club manufactures produce golf club shafts of different lengths and flexes for selection by individual golfers. Most golfers rely on the expertise of golf club fitters to recommend the best type of golf club shaft for their particular size and skill. In the past, golf club fitters would measure the swing speed of a golfer and from this measurement select a golf club shaft type for the golfer. Unfortunately, selecting a golf club shaft type based on a swing speed measurement is highly speculative resulting in inaccurate golf club shaft fitting. 
         [0005]    To address this problem, techniques to measure golf club shaft flex have been considered. For example, U.S. Pat. No. 7,292,070 to Ashida et al. describes a golf club shaft selecting system including a head speed detecting unit for detecting club head speed at impact in a swing of a golfer, a swing tempo detecting unit for detecting the swing tempo of the golfer, a chart indicative of a shaft mass and a shaft flex point corresponding to the swing characteristics of the golfer, a selecting unit for selecting a golf club shaft suitable for the golfer referring to the chart and based on the club head speed and the swing tempo detected by the head speed detecting unit and the swing tempo detecting unit respectively, and a displaying apparatus for displaying the golf club shaft selected by the selecting unit. 
         [0006]    U.S. Pat. No. 7,041,014 to Wright et al. describes a method for matching a test golfer with a particular golf club selected from a group of golf clubs having a plurality of styles. The method utilizes a data set derived in an initial procedure in which the club style preferences for each of a large number of pre-test golfers is recorded and correlated with a set of performance parameters for the golf swings of such pre-test golfers. The data set enables the pre-test golfers to be classified into subgroups, in which golfers within the same subgroup generally prefer the same club style and golfers in different subgroups generally prefer different club styles. During the method, while a golfer takes a golf swing with a golf club, performance parameters for the swing are measured. Based on the measured performance parameters and the previously established data set, the test golfer is classified according to swing type, and the optimum golf club is then selected from the plurality of styles of golf clubs. 
         [0007]    U.S. Pat. No. 5,616,832 to Nauck describes a system and method for the evaluation of dynamics of a golf club comprising a microphone inserted inside the golf club shaft which detects vibrations as sound waves and transmits signals indicative of the vibration&#39;s frequencies and amplitudes to a data acquisition system for processing, display and analysis. The apparatus may also be used for measuring natural frequency of flex through use of a rattler or a micro-switch actuator. 
         [0008]    Although the above references describe techniques to measure a golf swing and select a golf club shaft, improvements are desired. It is therefore an object of the present invention at least to provide an apparatus and method for measuring golf club shaft flex and a golf simulation system incorporating the same. 
       SUMMARY OF THE INVENTION 
       [0009]    Accordingly in one aspect there is provided a method for measuring shaft flex comprising capturing at least one image of a shaft during movement of the shaft through a swing plane; and examining the at least one image to determine the flex of the shaft. 
         [0010]    In one embodiment, the capturing comprises capturing a series of images during movement of the shaft through the swing plane and the examining comprises examining multiple images to determine the flex of the shaft at multiple positions along the swing plane. The examining may comprise determining a flex profile for the shaft over the movement of the shaft through the swing plane. The examining may also comprise measuring a deviation of at least one discrete point along the shaft from a fixed reference to determine shaft flex. The fixed reference may be a straight line extending between a pair of reference points adjacent opposite ends of the shaft. The at least one discrete point and the pair of reference points may be defined by reflective markings on the shaft. The shaft may be the shaft of a golf club. 
         [0011]    According to another aspect there is provided an apparatus for measuring shaft flex comprising at least one imaging device capturing images of a shaft during movement of the shaft through a swing plane; and a processing unit receiving images from the at least one imaging device, and processing received images to determine the flex of the shaft. 
         [0012]    In one embodiment, the optical axis of the at least one imaging device is generally perpendicular to the swing plane. The apparatus may further comprise an illumination source. The at least one imaging device captures a series of images of the shaft during movement of the shaft through the swing plane and the processing structure is configured to process multiple images to determine the flex of the shaft at multiple positions along the swing plane. 
         [0013]    According to yet another aspect there is provided a golf simulation system comprising an apparatus for measuring golf club shaft flex as described above: a golf ball tracking apparatus comprising at least two imaging devices capturing images of a golf ball tracking region disposed in front of a display surface from different vantages to detect a launched golf ball traveling through the golf ball tracking region towards the display surface; a golf ball spin sensing unit capturing images of a region at least partially overlapping with the golf ball tracking region, each captured image comprising a golf ball trail representing a travel path of the golf ball when a golf ball is present in the region during image capture; and at least one processing unit receiving data from the imaging devices and the golf ball spin sensing unit and determining the three-dimensional positions, velocity, acceleration and spin of a detected launched golf ball traveling through the golf ball tracking region, the three-dimensional positions, velocity, acceleration and spin being used by the at least one processing unit to calculate a trajectory of the launched golf ball into a three-dimensional golf scene. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]    Embodiments will now be described more fully with reference to the accompanying drawings in which: 
           [0015]      FIG. 1  is a schematic, partial side elevational view of an apparatus for measuring golf club shaft flex; 
           [0016]      FIG. 2  is a schematic perspective view of a golf club for use with the apparatus of  FIG. 1 ; 
           [0017]      FIGS. 3   a  to  3   h  are front elevational views of a user swinging the golf club of  FIG. 2 ; 
           [0018]      FIGS. 4   a  and  4   b  show images of the golf club shaft during a golf swing captured by an imaging device forming part of the apparatus of  FIG. 1 ; 
           [0019]      FIG. 5  is a side elevational view of the golf club of  FIG. 2  at the top of a golf swing; 
           [0020]      FIG. 6  is a graph showing the flex ratio at three points along the golf club of  FIG. 2  during a golf swing: 
           [0021]      FIG. 7  is a graph showing the shaft angle of the golf club during a golf swing; 
           [0022]      FIG. 8  is a graph showing the maximum flex ratio and the shaft angle of the golf club of  FIG. 2  during a golf swing; 
           [0023]      FIG. 9  is a graph showing the angular velocity and acceleration of the golf club of  FIG. 2  during a golf swing; 
           [0024]      FIG. 10  is a perspective view of a golf simulation system incorporating the apparatus of  FIG. 1 ; 
           [0025]      FIG. 11  is a side elevational view of the golf simulation system of  FIG. 10 ; 
           [0026]      FIG. 12  is a top plan view of the golf simulation system of  FIG. 10 ; 
           [0027]      FIG. 13  is a front elevational view of a golf ball tracking apparatus forming part of the golf simulation system of  FIG. 10 ; 
           [0028]      FIG. 14  is an enlarged front elevational view, partly in section, of a portion of the golf ball tracking apparatus of  FIG. 13 ; 
           [0029]      FIG. 15  is a side schematic view of a golf ball launch area sensing unit forming part of the golf simulation system of  FIG. 10 ; 
           [0030]      FIG. 16  is a schematic perspective view of a golf ball spin sensing unit forming part of the golf simulation system of  FIG. 10 ; 
           [0031]      FIG. 17  is a schematic block diagram of an area-scan digital camera forming part of the golf ball spin sensing unit of  FIG. 16 ; 
           [0032]      FIG. 18  is a schematic block diagram of an illumination board driver and illumination boards forming part of the golf ball spin sensing unit of  FIG. 16 ; 
           [0033]      FIG. 19  shows a backward spinning launched golf ball; 
           [0034]      FIGS. 20 to 23  are flowcharts showing steps performed during player interaction with the golf simulation system of  FIG. 10 ; 
           [0035]      FIG. 24  is an overhead view of a golf club making impact with a golf ball within the launch area of the golf simulation system of  FIG. 10 ; and 
           [0036]      FIG. 25  shows processing of captured images to determine golf ball spin and golf ball spin tilt axis. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0037]    Turning now to  FIG. 1 , an apparatus for measuring golf club shaft flex is shown and is generally identified by reference numeral  100 . As can be seen, the apparatus  100  comprises an imaging device  102  positioned to capture images of a golf ball launch or hitting area in which a player P swinging a golf club  112  stands. The optical axis of the imaging device  102  is positioned to be generally perpendicular an anticipated swing plane SP of the player P. A light source  106  is positioned adjacent the imaging device  102  to illuminate generally evenly the launch area. The hitting area has a non-reflective floor  108  and a non-reflective background  110 . A computing device  128  such as for example, a personal computer or other suitable processing unit or structure is coupled to the imaging device  102 . The computing device  128  processes image frames received from the imaging device  102  to determine the shaft flex of the golf club  112  throughout the swing of the golf club and to display the results as will be described. 
         [0038]    In this embodiment, the non-reflective background  110  is in the form of a curtain or wall covering formed of a non-reflective material that is coated with an acrylic. Similarly, the non-reflective floor  108  comprises a carpet or floor covering formed of a similar non-reflective material. In this embodiment, imaging device  102  is a digital camera that has at least a 640 by 480 pixel array and an electronically controlled shutter and that captures image frames at a frame rate of at least sixty (60) frames per second. As mentioned above, light source  106  evenly illuminates the launch area providing suitable light for the player P to swing the golf club  112  and hit a golf ball GB and for the imaging device  102  to capture image frames that include image data that can be processed to determine shaft flex. In this embodiment, light source  106  comprises a plurality of halogen lights mounted on a track lighting fixture. 
         [0039]    Turning now to  FIG. 2 , the golf club  112  is better illustrated. As can be seen, the golf club  112  comprises a flexible shaft  114  having a club head  116  at one end of the shaft  114 . To facilitate imaging of the golf club  112  and in particular the shaft  114  during a golf swing, reflective markers are provided on the shaft at spaced locations. In this embodiment, five (5) reflective markers  118  to  126  are provided on the shaft  114 . The reflective markers in this embodiment are pieces of retroreflective tape surrounding the shaft  114  at discrete points or locations along the length of the shaft. The dimensions of the retroreflective tape pieces can vary but are selected so that the retroreflective tape pieces can be easily identified in image frames captured by the imaging device  102 . In this example, each piece of retroreflective tape has a length equal to about one (1) inch. 
         [0040]    The positions of the reflective markers  118  to  126  along the shaft  114  are selected to facilitate detection and measurement of the flex of the golf club shaft during a golf swing. In this embodiment, the reflective marker  118  is placed near the top of the shaft  114  adjacent the golf club grip and the reflective marker  126  is placed near the bottom of the shaft  114  adjacent the hozel and club head  116 . The reflective marker  122  is placed adjacent the mid-point of the shaft  114 . The reflective marker  120  is positioned intermediate the reflective markers  118  and  122  and the reflective marker  124  is positioned intermediate the reflective markers  122  and  126 . The reflective markers  118  and  126  are used to determine reference points on the shaft  114  during shaft flex measurement as will be described. 
         [0041]    During operation, when it is desired to measure the flex of a golf club shaft  114  during a golf swing, the player P with the golf club  112  in hand stands in the launch area. The light source  106  is operated to provide generally even illumination to the launch area so that the player P has no or little difficulty completing a golf swing and hitting the golf ball GB. When the player P is ready to make a golf swing, the imaging device  102  is conditioned to capture image frames. As a result, when the player P makes a golf swing, substantially the entire golf swing is captured in image frames. 
         [0042]      FIGS. 3   a  to  3   h  show the golf swing of player P. As can be seen, the golf swing comprises an up-swing component illustrated in  FIGS. 3   a  to  3   d  and a down-swing component illustrated in  FIGS. 3   e  to  3   h . As will be appreciated, the shaft  114  flexes by different amounts over the golf swing depending on the component of the golf swing and the speed of the club head  116  at a particular point of time during the golf swing. For example, as shown in  FIG. 3   d , the shaft  114  flexes towards player P as the momentum of the club head  116  is still in the up-swing direction while the player&#39;s hands begin to move in the down-swing direction. 
         [0043]    The reflective markers  118  to  126  reflect light towards the imaging device  102  throughout the golf swing while the non-reflective background  110  and non-reflective floor  108  inhibit light from reflecting off of these surfaces towards the imaging device. As a result, the reflective markers  118  to  126  appear as bright spots on an otherwise relatively dark background in captured image frames allowing the reflective markers  118  to  126  to be easily discerned.  FIG. 4   a  shows a sequence of image frames captured by the imaging device  102  during the up-swing component of the player&#39;s golf swing while  FIG. 4   b  shows a sequence of image frames captured by the imaging device  102  during the down-swing component of the player&#39;s golf swing. As can be seen, the points along the shaft  114  corresponding to the reflective marker locations are easily identified in the captured image frames. The distance the shaft  114  of the golf club  112  travels between each captured image frame is indicative of the acceleration of the club head  116 . As can be seen, during the up-swing component of the player&#39;s golf swing as shown in  FIG. 4   a , the distance the shaft  114  of the golf club  112  travels between successive image frames is relatively constant signifying a smooth up-swing. During the down-swing component of the player&#39;s golf swing, the distance the shaft  114  of the golf club  112  travels between each pair of successive image frame increases signifying acceleration of the club head  116  during the down-swing until contact is made with the golf ball GB. 
         [0044]      FIG. 5  shows the golf club  112  at the position along the player&#39;s golf swing shown in  FIG. 3   d . As can be seen, at this position the shaft  114  of the golf club  112  flexes. As a result, the reflective markers  118  to  126  are no longer positioned along a straight line but rather are positioned along an arcuate line. The positions of the reflective markers  118  to  126  in captured image frames are used to determine and measure the golf club shaft flex. As will be appreciated, the amount of flex in the shaft  114  during a golf swing depends on a variety of factors, such as shaft stiffness, shaft weight, club head weight, torque, kick point, club head speed, etc. 
         [0045]    During processing, the computing device  128  processes the captured image frames to measure the flex of the golf shaft  114  at various positions throughout the golf swing. In particular, for each captured image frame, the computing device  128  determines the center point  150  to  158  for each bright spot in the image frame that corresponds to a reflective marker  118  to  126 . Center points  150  and  158  are used as the reference points. Once the center points  150  and  158  are determined, the computing device  128  computes a straight line  160  extending between the reference points  150  and  158 . Following computation of the straight line  160 , the distance between each center point  152 ,  154  and  156  and the straight line  160  along a line perpendicular to the straight line denoted by d1, d2 and d3, respectively, is measured. Distances d1, d2 and d3 are representative of the amount of flex of the shaft  114  at their respective points. The greater the distance d1, d2, d3 from the straight line  160 , the greater the amount of golf club shaft flex. If any of the distances d1, d2, and d3 is equal to zero, there is no flexing of the shaft  114  at that particular point. 
         [0046]    As will be appreciated, golf club shafts come in a variety of stiffness and lengths. To accurately compare different golf club shafts, distances d1, d2 and d3 should be normalized. This is done by measuring the length L along the straight line  160  between the reference points  150  and  158 . Length L defines a constant value which can be used to normalize distances d1, d2 and d3 as a flex ratio percentage f1, f2 and f3 according to: 
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         [0000]    The flex ratio percentage indicates the percentage of flexing at each particular center point  152 ,  154 , and  156 . Again, a calculated zero value indicates that there is no flexing of shaft  114  at that particular point. Comparing the three calculated flex ratios allows the maximum flex of the shaft  114  to be calculated according to: 
         [0000]        f   max =max( f   1   ,f   2   ,f   3 ) 
         [0000]    The maximum flex of the shaft  114  is used to represent the flex of the shaft  114  for that image frame. By determining the maximum flex over a series of captured image frames, a flex profile for the shaft  114  over a golf swing can be determined and displayed. A determination can then be made as to whether the shaft flex characteristics of the golf club  112  suit the player&#39;s golf swing. 
         [0047]      FIG. 6  shows a graphical representation of the flex ratio percentage of the shaft  114  at positions along the shaft corresponding to the reflective markers  120 ,  122 , and  124 . The flex ratio percentage is shown along the y-axis, while time is shown along the x-axis. As will be appreciated, a positive flex ratio indicates the flexing of the shaft  114  in a first direction while a negative flex ratio indicates flexing of the shaft in an opposite direction. For each of the center points  152 ,  154 , and  156 , the flex ratio crosses the y-axis at two instances indicating that there are two instances during the player&#39;s swing in which the flex ratio of the shaft  114  is zero. As can be seen, the maximum flex ratio percentage of shaft  114  almost always corresponds to flex ratio f2. Flex ratio f2 is based on the distance d2 of center point  154  from the straight line  160  and hence, the deviation of the reflective marker  124  that is positioned near the mid-point of the shaft  114  from the straight line  160 . This indicates that the kick point of the shaft  114  is located near its mid-point. 
         [0048]      FIG. 7  shows the shaft angle of the golf club  112  during a golf swing. When player P addresses the golf ball GB as shown in  FIG. 3   a , the shaft  114 , when modeled as a vector extending between reflective markers  118  and  126 , will be at an angle close to 0 degrees. The reference point of zero (0) degrees is defined as the position of the golf club  112  when the club head  116  contacts the golf ball. The arrows indicate the direction of travel of the club head  116  during both the up-swing and down-swing components of the player&#39;s golf swing. As player P takes the club head  116  back, the angle of shaft  114  increases up to a point of approximately 270 degrees, although the maximum angle of the shaft  114  greatly depends upon the golfer making the swing. As player P begins the down-swing, the angle of the shaft  114  begins to decrease. The instant the club head  116  contacts golf ball GB, the angle of the shaft  114  is zero (0) degrees, and through impact, the absolute value of the angle of the golf shaft  114  begins to increase in the negative direction. 
         [0049]      FIG. 8  shows a graphical representation of both the maximum flex ratio (wherein the y-axis has the units of percentage) and the shaft angle (wherein the y-axis has the units of radians). Time is represented along the x-axis. Of particular interest is that the maximum flex ratio occurs approximately when the shaft angle is the greatest. As mentioned previously, the shaft angle is the greatest at the top of the golf swing, where the player P transitions from the up-swing to the down-swing. The first zero-crossing of the maximum flex ratio occurs at approximately 3.5 radians (200 degrees). Turning back to  FIG. 7 , it can be seen that the shaft  114  begins to flex from the first direction to the second direction during the up-swing, just past the point when the shaft  114  is vertical (180 degrees). The second zero-crossing of the maximum flex ratio occurs during the down-swing at approximately 1.7 radians (97 degrees). Again, turning back to  FIG. 7 , shaft  114  begins to flex from the second direction to the first direction at a point prior to the club head  116  contacting the golf ball GB. This represents the whipping action of the shaft  114  that occurs prior to the club head  116  contacting the golf ball GB. As one skilled in the art will appreciate, the key to having a properly fit golf club shaft is to have the correct amount of whipping action at impact to optimize golf ball launch and club head speed. 
         [0050]      FIG. 9  shows a graphical representation of the angular velocity and acceleration of the golf club shaft  114 . Angular velocity is defined as the ratio of the change of angle of the shaft  114  to the time interval between consecutive captured image frames. Angular acceleration is defined as the ratio of change of angular velocity of the shaft  114  to the image frame time interval. The first zero crossing of the angular velocity occurs at the top of the up-swing, at the instant when the club head  116  transitions from the up-swing to the down-swing. The angular velocity transitions from a positive value to a negative value at the top of the up-swing, as the club head  116  begins to travel in the negative direction. The peak acceleration occurs during the down-swing when the shaft  114  is in a generally horizontal position. Referring back to  FIG. 7 , this corresponds to a shaft angle of approximately 90 degrees. It is interesting to note that the maximum angular velocity occurs after the maximum acceleration occurs, that is, when the club head  116  contacts the golf ball GB. This is because the golf club shaft keeps accelerating during the downswing for a good golf swing. Since the club head  116  is attached to the shaft  114 , a maximum angular velocity of shaft at impact generally means a maximum velocity of golf club head at impact. Shaft angle, angular velocity, and angular acceleration of golf club shaft are measured and correlated with measurements of shaft flex. Angular velocity and angular acceleration are good indicators of golf swing tempo and can be used together with shaft flex measurements to provide an enhanced dynamic measurement of golf club shaft flex. 
         [0051]    As will be appreciated, the apparatus  100  allows the shaft  114  of the golf club  112  to be determined at various points along the player&#39;s golf swing allowing the shaft flex characteristics to be determined and displayed so that a determination can be made as to whether the shaft flex characteristics suit the golfer&#39;s swing. This is done without requiring the golf club to be modified to a point where its characteristics change. In this embodiment, the only golf club modification that is made is the placement of retroreflective markers in the form of tape pieces on the shaft  114  at spaced locations. As the rectangular tape pieces are light weight, they have virtually no impact on the golf club  112 . 
         [0052]    Apparatus  100  as described above with reference to  FIGS. 1 to 9  can be used as a stand alone system for club-fitting purposes or can be used in conjunction with a golf simulation system such as those described in U.S. Pat. No. 7,544,137, issued on Jun. 9, 2009 to Richardson; U.S. patent application Ser. No. 11/195,017, filed on Aug. 2, 2005, to Richardson et al.; U.S. patent application Ser. No. 11/394,004, filed on Mar. 30, 2006 to Dawe et al.; and PCT Application No. PCT/CA2009/001424 filed on Oct. 7, 2009 to Dawe et al, the contents of which are incorporated in their entirety herein by reference. 
         [0053]    Turning now to  FIG. 10 , the apparatus  100  is shown in conjunction with the golf simulation system described in above-incorporated PCT Application No. PCT/CA2009/001424. As can be seen, sports simulation system  200  includes a golf ball tracking apparatus  202  disposed in front of a golf ball launch or hitting area A in which a player P stands. The launch area has a non-reflective floor  108  and a non-reflective background  110 . In this embodiment, the separation distance between the launch area A and the golf ball tracking apparatus is approximately ten (10) feet. An overhead golf ball launch area sensing unit  203  is disposed above the launch area A. An overhead golf ball spin sensing unit  205  is positioned between the launch area A and the golf ball tracking apparatus  202 . Imaging device  102  of the apparatus  100  is positioned in front of and above player P such that the optical axis of the imaging device  102  is generally perpendicular to the anticipated swing plane SP of the player P. Light source  106  is positioned adjacent imaging device  102  to provide an even distribution of illumination for both the player P and the imaging device  102 . A host computer  204  is coupled to the imaging device  102 , golf ball tracking apparatus  202 , the golf ball launch area sensing unit  203  and the golf ball spin sensing unit  205  via a high-speed serial data link and to a ceiling mounted front video projector  206  that is aimed at the golf ball tracking apparatus  202 . The host computer  204  outputs video image data to the projector  206 , which in turn projects a video sequence on the golf ball tracking apparatus  202 . The video sequence portrays a three-dimensional golf scene that comprises an image of a golf course hole, practice range etc. 
         [0054]    In this embodiment, player P uses golf club  112  to launch the golf ball GB towards the golf ball tracking apparatus. The imaging device  102  captures image frames as the player P swings the golf club  112  to launch golf ball GB. Imaging device  102  outputs the image frames to the host computer  204 , which functions as computing device  120 , for processing. 
         [0055]    The golf ball tracking apparatus  202  outputs two-dimensional golf ball position data to the host computer  204  when the launched golf ball GB travels through a golf ball tracking region monitored by the golf ball tracking apparatus. The golf ball launch area sensing unit  203  outputs image data representing the motion of the golf club  112  through the launch area A before, during and after impact with the golf ball to host computer  204 . The golf ball spin sensing unit  205  outputs image data to the host computer  204  that allows the host computer  204  to determine the spin and the spin tilt axis of the golf ball GB as the golf ball travels through the golf ball tracking region. The host computer  204  in turn processes the two-dimensional golf ball position data, the golf ball launch area sensing unit image data and the golf ball spin sensing unit image data to determine the three-dimensional positions, launch velocity, acceleration, side spin, backspin, spin tilt axis and launch angle of the golf ball so that the trajectory of the golf ball can be accurately calculated. The calculated trajectory is then used to determine a sports result and to update the image data conveyed to the projector  206  so that the presented video sequence shows a simulation of the golf ball travel into the three-dimensional scene as well as the determined sports result. 
         [0056]      FIGS. 11 to 14  better illustrate the golf ball tracking apparatus  202 . As can be seen, the golf ball tracking apparatus  202  comprises an upright, inverted U-shaped frame  210  having a pair of side posts  212  and a crossbar  214  extending between the upper ends of the posts  212 . A screen  222  is supported by the frame  210 . In this embodiment, the screen  222  has a 4:3 aspect ratio making it particularly suited for displaying conventional television images. Those of skill in the art will however, appreciate that other image formats can be used. The screen  222  is loosely fastened to the back of the frame  210  at spaced locations. 
         [0057]    The screen  222  includes multiple layers and is designed to reduce golf ball bounce as well as enhance protection behind the screen. The first or front layer of the screen  222  is formed of highly reflective nylon having some elasticity to resist permanent stretching/pocketing and abrasion. As a result, the front layer provides an excellent display surface  224  on which images projected by the projector  206  are presented. The second or intermediate layer of the screen  222  is formed of soft and thick material and is designed to absorb golf ball energy with reduced elastic effect thereby to inhibit stretching and or damage to the front layer. The third or back layer of the screen  222  is formed of a tough heavy canvas to which the intermediate layer can transfer energy. The back layer also inhibits excess deformation of the intermediate layer when contacted by a launched golf ball. As a result, if the golf ball tracking apparatus  202  is placed adjacent a wall surface or the like, the back layer protects the surface behind the screen  222  from golf ball strike thereby to inhibit damage to the surface and/or significant golf ball rebound. If a space is provided behind the golf ball tracking apparatus  202 , the back layer provides ample protection for the space. 
         [0058]    Imaging devices, in this embodiment a pair of high speed digital cameras  228 , are accommodated within the frame  210  with each camera being positioned adjacent a different top corner of the frame. Thus, the digital cameras  228  are positioned in front of the player P and to the left side and right side of the anticipated golf ball path. The digital cameras  228  are also angled to point downwardly and towards the player position so that the fields of view of the digital cameras are generally perpendicular and overlap in the golf ball tracking region which extends at least from the golf ball launch point to the screen  222 . In this manner, the path of the golf ball can be tracked generally continuously from its launch point until it impacts the screen  222  and then as it rebounds from the screen  222 . 
         [0059]    In this embodiment, each digital camera  228  has at least a 640 by 480 pixel array and includes built-in processing capabilities comprising field programmable gate arrays, a high performance 32-bit microprocessor and high speed memory. The distributed processing capabilities achieved by using the digital cameras  228  and the host computer  204  allow the digital cameras to be operated at very high frame rates thereby allowing multiple images of a fast moving golf ball to be captured as the golf ball travels through the golf ball tracking region  220 . This is due to the fact that the digital cameras  228  need only send data to the host computer  204  relating to images in which golf ball motion has been detected allowing high speed golf balls to be tracked without excessive bandwidth between the host computer  204  and the digital cameras  228  being needed. For example, in the case of a golf ball travelling through the golf ball tracking region  220  at a speed of 200 miles per hour, the frame rates of the digital cameras  228  are selected such that at least four images of the golf ball are captured by each digital camera  228 . The viewing angles of the digital cameras  228  and the dimensions of the frame  210  are selected to provide the digital cameras  228  with a resolving accuracy of approximately 1 mm per pixel. As a result, a small golf ball such as a golf ball will activate approximately 12 pixels per image. This resolving accuracy enables even small, very fast moving launched golf balls to be readily determined in captured images and as a result, reduces false golf ball detection. 
         [0060]    The on-board microprocessor of each digital camera  228  executes a motion detection routine to determine if a golf ball exists in the captured images and if so, whether the golf ball satisfies specified motion detection parameters defining a golf ball characteristic signature. The golf ball characteristic signature is used to ensure the detected golf ball has characteristics matching a struck golf ball. The golf ball can therefore be distinguished from other objects captured in the images such as for example, the golf club head. In this example, the golf ball characteristic signature specifies allowable golf ball size, shape, reflectivity and speed. 
         [0061]    Infrared (IR) light emitting diode (LED) arrays (not shown) are also positioned within the posts  212  beside the digital cameras  228 . The illumination axes of the IR LED arrays are generally coincident with the optical axes OA of the digital cameras. Each IR LED array emits IR radiation that is directed into the golf ball tracking region  220 . As the digital cameras  228  are responsive to both visible and infrared light, providing the background IR illumination allows the golf ball tracking apparatus  202  to work well in a variety of ambient lighting conditions. In situations where a small fast moving golf ball is launched, the IR illumination allows for detection of the golf ball without interfering with the visual quality of the displayed image presented on the screen  222 . 
         [0062]    Audio speakers  240  are provided on the posts  212  and are aimed forwardly toward the launch area A. The audio speakers  240  are driven by an audio amplifier (not shown) accommodated within the frame  210 . The audio amplifier receives audio input from the host computer  204  during play that is conveyed to the audio speakers  240  for broadcast thereby to enhance the sports experience. 
         [0063]    The golf ball launch area sensing unit  203  is disposed directly over the launch area A and comprises an area-scan digital camera  260 , an angled mirror  262 , a plurality of illuminators  264  in the form of halogen spotlights and a power supply (not shown) for the spotlights  264  as shown in  FIG. 15 . The spotlights  264  are aimed to provide sufficient illumination in the launch area A to permit image capture without adversely affecting visibility of the image projected on the screen  222 . The area-scan digital camera  260  is ceiling mounted in a horizontal orientation approximately ten (10) feet above the launch area A. The optical axis of the digital camera  260  is generally in line with the center of the mirror  262  so that the field of view of the area-scan digital camera  260  is re-directed downwardly and centered over the launch area A. In this embodiment, the field of view of the area-scan digital camera  260  encompasses a three (3) foot by three (3) foot region. 
         [0064]    Similar to the digital cameras  228  in the golf ball tracking apparatus  202 , the area-scan digital camera  260  comprises an on-board processor that executes a motion detection routine. During execution of the motion detection routine, as images are captured by the area-scan digital camera  260 , the images are examined to determine if one or more moving objects exist therein that satisfy specified motion parameters. In this example, the motion parameters are selected to allow the on-board processor of the area-scan digital camera  260  to detect when either a moving golf club or moving golf ball or both is in captured images. Captured images including one or more moving objects satisfying the specified motion parameters are sent to the host computer  204  for further processing. 
         [0065]    The golf ball spin sensing unit  205  comprises a ceiling mounted, horizontally oriented area-scan digital camera  270 , an angled mirror  272 , a plurality of infrared (IR) illuminator boards  274  and a driver  276  for the illuminator boards  274  as shown in  FIG. 16 . The optical axis of the digital camera  270  is generally in line with the center of the mirror  272  so that the field of view of the digital camera  270  is re-directed and centered over a region that at least partially overlaps with the golf ball tracking region. In this embodiment, the region extends from the front of the launch area A towards the golf ball tracking apparatus  202  and encompasses a three (3) foot by six (6) foot region. 
         [0066]      FIG. 17  better illustrates the area-scan digital camera  270 . In this embodiment, the digital camera  270  comprises a CMOS image sensor  280  having a 640 by 480 pixel array and a pixel size equal to about 9.9 microns. The image sensor  280  looks through a lens  282  having a focus distance of about twelve (12) millimeters. Such a lens has been found to provide good area coverage while maintaining sufficient resolution. The digital camera  270  includes built-in processing capabilities comprising a field programmable gate array (FPGA)  284 , a high performance microprocessor  286  and a high speed memory buffer  288 . 
         [0067]    In this embodiment, the golf ball spin sensing unit  205  comprises four (4) illuminator boards  274 , with each illuminator board comprising an array of light emitting diodes (LEDs). The illuminator boards  274  are arranged in a manner so that the region within the field of view of the digital camera  270  is generally evenly illuminated when the LEDs of the illuminator boards  274  are on. The driver  276  comprises a pulse generator that drives each of the illuminator boards  274  simultaneously so that the LEDs of the illuminator boards  274  turn on and off in unison at regular intervals. In this embodiment, the LEDs of the illuminator boards  274  remain in the on state for a 0.1 millisecond duration and remain in the off state for a 1 millisecond duration. 
         [0068]    The projector  206  preferably has a resolution of at least 800×600, at least 1200 ANSI Lumens brightness, a short throw lens, vertical ‘keystone’ correction, and the capacity to accept digital RGB computer video signals, and NTSC/PAL baseband television video signals. Projectors having this set of features include the Epson Powerlite 820P, the Toshiba TDP-DI-US, the InFocus LP650 and the Sanyo XP30 for example. 
         [0069]    The host computer  204  is a general purpose computing device. In this embodiment, host computer is an IBM compatible personal computer including an Intel Pentium® processor, at least 128 MB SDRAM, a high-speed hard drive, and a DVD player. The host computer  204  also includes a display adapter assembly including a reconfigurable 32-bit video memory buffer partitioned into three separate buffers. One of the buffers is used to store primary foreground image data representing one or more independent foreground action elements if appropriate for the sports scene being displayed. A second of the buffers is used to store background image data and the third buffer is used to store golf ball trajectory image data. The display adapter assembly treats the foreground action, background and golf ball trajectory image data as overlay image planes that are combined seamlessly to generate the video image data that is output to the projector  206 . The overlay image planes are non-destructive so that when a foreground action element and/or golf ball moves over an underlying image plane it is not necessary to redraw the underlying image plane. To reduce peak processing requirements, the host computer  204  updates the background image data less frequently than the foreground image data. The host computer  204  provides the output video image data to the projector  206  on a video output channel. The host computer  204  receives external video feeds on a television/satellite/cable input channel, a video game input channel and an Internet input channel. 
         [0070]    The host computer  204  is mounted within a protective enclosure (not shown) having external connectors to enable the host computer  204  to be coupled to the projector  206 , the golf ball tracking apparatus  202 , the golf ball launch area sensing unit  203  and the golf ball spin sensing unit  205 . The enclosure also includes external connectors to allow the host computer  204  to receive the television/satellite/cable, external video game and Internet feeds. An interactive touch screen is also provided on the enclosure to allow a player to interact with the host computer  204 . 
         [0071]    A high speed digital serial interface, such as for example IEEE 1394, is used for communications between the host computer  104 , the golf ball tracking apparatus  102 , the golf ball launch area sensing unit  103  and the golf ball spin sensing unit  105 . Using this standard interface provides a low cost, high performance solution while avoiding use of expensive analog frame grabbers. The interface also simplifies wiring as the digital cameras  128  can be daisy-chained without loss of signal integrity. 
         [0072]    The host computer  204  executes sports simulation software stored in the SDRAM. In this example, the sports simulation software includes a golf simulation module that requires a player to hit the golf ball GB at the screen  222  of the golf ball tracking apparatus  202  in response to the video sequence displayed on the screen  222 . 
         [0073]    To provide a realistic playing experience, a high resolution elevation map of the golf course terrain is used. The course terrain elevation map is constructed from a combination of two-dimensional images that include overhead satellite and/or aerial photographs used in conjunction with digital photographs taken from ground level. Using photogrammetry techniques, these orthogonal views are combined together. Using common points in the images i.e. edges of sand hazards, trees etc., a three-dimensional model is synthesized without requiring reference targets to be applied to the terrain of interest. 
         [0074]    During training, practice or game play, the host computer  204  outputs video image data to the projector  206  causing the projector  206  to project a video sequence portraying a three-dimensional sports scene on the display surface  224  that includes a target at which the golf ball is to be launched (see step  500  in  FIG. 20 ). The host computer  204  also conditions the digital cameras  228  to capture a background image of the golf ball tracking region  220  devoid of a golf ball (step  502 ) and then scan the golf ball tracking region to look for the presence of a launched golf ball at a very high frame rate (step  504 ). The player is then prompted to launch the golf ball GB at the screen  222  (step  506 ). At this stage, the digital cameras  228 , the area-scan digital camera  160  and the area-scan digital cameral  270  are conditioned to capture and process images. 
         [0075]    To facilitate detection of golf ball spin, an elongate reflective or retroreflective marker  290  is provided on the golf ball GB (see  FIG. 19 ). In this embodiment, the marker is a 45 mm by 5 mm piece of reflective tape adhered or otherwise secured to the golf ball GB. Prior to launch, the golf ball GB is preferably oriented so that the long dimension of the reflective tape  290  is parallel to the width of the screen  222 . As a result, after launch and while the golf ball backspins as it travels through the field of view of the area-scan digital camera  270 , when the driver  276  turns the LED arrays of the illuminator boards  274  on, the reflective tape  290  is clearly visible to the area-scan digital camera  270  at intervals. 
         [0076]    When the player launches the golf ball at the golf ball tracking apparatus  202  by striking the golf ball with a golf club  112  and the golf ball enters the golf ball tracking region  220 , the golf ball appears in the images captured by the digital cameras  228 . Thus, the digital cameras  228  generally synchronously capture a series of images of the golf ball as it travels from its launch point through the golf ball tracking region  220  to its contact point with the screen  222  and then as the golf ball rebounds off of the screen (step  508 ). The captured images are in turn processed by the on-board processors of the digital cameras  228  to determine if the captured images include a detected golf ball satisfying the golf ball characteristic signature. 
         [0077]    If the detected golf ball satisfies the golf ball characteristic signature, the images are further processed to determine the center of mass of the golf ball in each image and its position in rectangular coordinates (step  510 ). As a result, a series of two-dimensional rectangular coordinates representing the two-dimensional positions of the golf ball as it travels through the golf ball tracking region  220  relative to each digital camera  228  is generated. The two-dimensional rectangular coordinates generated by the digital cameras  228  are in turn conveyed to the host computer  204 . 
         [0078]    The area-scan digital camera  260  of the golf ball launch area sensing unit  203  captures and processes images to look for the existence of a swinging golf club  112  passing through the launch area A and the launched golf ball exiting the launch area A. When a swinging golf club and launched golf ball are detected, the area-scan digital camera  260  outputs the captured images to the host computer  204 . 
         [0079]    The area-scan digital camera  270  of the golf ball spin sensing unit  205  captures images at a frame rate equal to about 100 frames per second (fps) and processes consecutive images to determine if the difference between consecutive images exceeds a threshold signifying the existence of an object in motion. When the difference between consecutive images exceeds the threshold, images are further processed to determine if the object in motion resembles a golf ball. If the object in motion resembles a golf ball, the images are sent to the host computer  204  for further processing. 
         [0080]    Upon receipt of the golf ball coordinates from the golf ball tracking apparatus  202 , the host computer  204  calculates the positions of the golf ball&#39;s center of mass in three-dimensional space throughout its travel through the golf ball tracking region  220  including its collision and rebound with the screen  222  using triangulation techniques (see step  520  in  FIG. 21 ). With the position of the golf ball in three-dimensional space known during its travel through the golf ball tracking region  220  and knowing the frame rates of the digital cameras  228 , the host computer  204  calculates the launch velocity of the golf ball and the velocity of the golf ball over each image frame (step  522 ). The host computer  204  then compares each calculated velocity with the previously calculated velocity to determine the acceleration of the golf ball (step  524 ). 
         [0081]    Upon receipt of the image data from the golf ball launch area sensing unit  203 , the host computer  204  analyzes the club head swing path  300  (see  FIG. 23 ) to determine where the club head hits the golf ball GB and to determine the initial golf ball trajectory or launch angle after being hit. The host computer  204  also defines a club head motion vector  302  as the tangent line along the club head swing path  300 . By estimating the initial golf ball trajectory, a golf ball motion vector  306  is measured. Using this vector, a club face vector  308  can be determined as the line perpendicular to the tangent  310  of the club face at the impact point of the golf ball and the club face. By comparing the club head motion vector  302  and the club face vector  308 , a determination can be made as to whether the club face is open or closed upon impact with the golf ball. The degree to which the club head motion vector  302  is not parallel to the club face vector  308  at the point of impact determines the amount of side spin that the golf ball will have. This enables the host computer  204  to calculate the side spin of the golf ball based on the angle of the club face at the point of contact with the golf ball as well as on the impact and rebound angles of the golf ball with and from the screen  222  (also step  524 ). 
         [0082]    Upon receipt of the images from the golf ball spin sensing unit  205 , the host computer  204  selects the first image (see step  600  in  FIG. 22   a ) and analyses the image to determine if the image includes a golf ball trail  292  (step  602 ) as shown in  FIG. 24 . The golf ball trail  292  appears in images due to the fact that velocity of the golf ball GB exceeds the frame rate of the digital camera  270 . If the image does not include a golf ball trail, the image is discarded and the next image is selected at step  600 . If the selected image includes a golf ball trail  292 , the golf ball trail in the image is located (step  604 ) and is then examined to determine if it is valid (step  606 ). In particular, the length and width of the golf ball trail are compared with the threshold ranges. If the golf ball trail is not valid, the selected image is discarded and the next image is selected at step  600 . If the golf ball trail  292  is validated at step  606 , the image with the valid golf ball trail is designated for further processing (step  608 ) and the process reverts back to step  600  where the next image is selected. 
         [0083]    Once all of the images from the golf ball spin sensing unit  205  have been selected and processed, the images designated for further processing at step  608  are subjected to an image intensity profile analysis (step  610  in  FIG. 22   b ) thereby to generate a combined profile of the golf ball trail over consecutive images as shown in  FIG. 24 . The golf ball trail length L c  per image is determined by the cross points of the combined profile (step  612 ). The images are subjected to adaptive thresholding to identify high intensity regions  296  in the images corresponding to the illuminated reflective tape  290  (step  614 ). A group of high intensity regions  296  corresponding to the reflective tape  290  appears in each image due to the golf ball spin and the pulsed illumination provided by the illuminator boards  274 . The distance between the group of high intensity regions  296  in each consecutive image is then determined and is represented by L t  in  FIG. 24  (step  616 ). The time T p  taken for the golf ball GB to make a single revolution is expressed as: 
         [0000]    
       
         
           
             
               T 
               p 
             
             = 
             
               
                 
                   L 
                   t 
                 
                 
                   L 
                   c 
                 
               
               · 
               
                 T 
                 f 
               
             
           
         
       
     
         [0000]    where T f  is the frame rate of the digital camera  170 . 
         [0084]    The time T p  is calculated for each consecutive image designated for further processing at step  608  and the average single rotation time for the golf ball GB to make a signal revolution is determined (step  618 ). The average single rotation time is then converted into convenient units such as for example rotations per minute (rpms). 
         [0085]    The ball spin tilt axis is then estimated for each image using the orientation of the high intensity regions  296  in each group and the relative angle between the longitudinal axis of the high intensity regions  296  and the longitudinal axis of the golf ball trail  292 . The average ball spin tilt axis over the consecutive images designated for further processing at step  608  is then determined (step  620 ). 
         [0086]    With the three-dimensional positions, launch velocity, acceleration, side spin, launch angle, backspin and spin tilt axis of the golf ball known, the host computer  204  extrapolates an accurate trajectory for the golf ball allowing a realistic simulation of curved and/or arcing golf balls to be generated (step  526 ). The computed golf ball trajectory is then used to determine a sports result by computing the intersection of the calculated golf ball trajectory with the displayed video image (step  528 ). With the golf ball trajectory computed and the sports result determined, the host computer  204  updates the image data that is conveyed to the projector  206  so that the video sequence displayed on the display surface  224  of the screen  222  shows the simulated flight of the golf ball and the sports result (step  530 ). 
         [0087]    During video sequence display, when a simulation of the golf ball flight is shown a graphical duplicate of the golf ball is projected onto the display surface  224  of the screen  222  that begins its flight from the impact point of the golf ball with the screen  222 . In this manner, the golf ball appears to continue its trajectory into the video scene thereby to achieve a realistic video effect. The three-dimensional scene is then updated in accordance with the sports result, allowing game play or practice to continue. 
         [0088]    Although the apparatus  100  has been described as using a single imaging device  102 , multiple imaging devices may be used. If two imaging devices are employed, the imaging devices are preferably positioned at a distance apart from one another and configured to form a stereo pair. In this case, the image frames captured by the imaging devices provide a third dimension for image processing. 
         [0089]    Although the apparatus  100  has been described as utilizing two reference points (tape pieces  118  and  126 ), and three intermediate markers (tape pieces  120 ,  122  and  124 ), more or fewer markers may be used. For example, the apparatus may determine the flex ratio based on only one marker. Alternatively the entire shaft  114  may be covered with a single marker (e.g. a long piece of retroreflective tape) allowing the entire curvature of the shaft to appear in captured image frames during a golf swing. 
         [0090]    Although the image processing used by apparatus  100  has been described as taking reference points along the shaft, and measuring the distance from those reference points to a straight line, the reference points can be used to find the shaft location of non-marked shaft sections by means of interpolation and/or extrapolation. In this way, the flex ratio at any point on the shaft can be determined. 
         [0091]    In the embodiment described above, the imaging device  102  is a digital camera utilized to capture images of player&#39;s golf swing. As one of ordinary skill in the art would appreciate, there is typically an upper limit to the number of image frames that the digital video camera can capture. This does not limit the ability to interpolate and extrapolate data. Similar to interpolating data for shaft flex, the computing device can be configured to interpolate data between any two consecutive image frames captured by the imaging device. At impact the club head  116  slows down and transfers energy to the golf ball. The data obtained by processing the image frames can be extrapolated to predict the shaft flex up to the point of impact. Combining the data obtained from interpolating/extrapolating the reference points on the shaft with the data obtained from interpolating/extrapolating image frames, results in a complete measurement for shaft flex at any point on the shaft and at any time during the up-swing and the down-swing components of the golf swing. 
         [0092]    Although the markers on the shaft have been described as being pieces of retroreflective tape, other markers such as reflective tape, retroreflective paint or reflective paint may be utilized. Alternatively, the shaft may have reference markers incorporated into the material in which the shaft is made, providing a club-fitting shaft for use by club-fitters when fitting a customer for a potential order. 
         [0093]    While the apparatus has been described as determining the flex of a golf club shaft, the apparatus may be utilized to determine the flex of other types of sports equipment, such as tennis racquets and hockey sticks. 
         [0094]    Although the golf simulation system  200  has been described as including a ceiling mounted front projector  206  in combination with a screen  222 , those of skill in the art will appreciate that alternative projection devices may be used. For example, a rear video projector may be used to project images onto the rear surface of the display screen  222 . 
         [0095]    Those of skill in the art will appreciate that the golf ball tracking apparatus  202  may include imaging devices at different locations to view the golf ball tracking region and detect the existence of a launched golf ball. Those of skill in the art will also appreciate that the number of processing stages may be increased or decreased as desired to handle processing of the digital camera image data effectively in real-time and provide a realistic golf ball simulation. 
         [0096]    If desired, the golf ball launch area sensing unit  203  and the golf ball spin sensing unit  205  may include additional camera devices. The golf ball launch area sensing unit  203  and golf ball spin sensing unit  105  may include any number of illuminators or none at all if the ambient light conditions are sufficient to provide for adequate image capture. Further, although the golf ball launch area sensing unit  203  and golf ball spin sensing unit  205  are shown to include mirrors to re-direct the fields of view of the area-scan digital cameras  260  and  270 , those of skill in the art will appreciate that the area-scan digital cameras may be oriented to look directly at the regions of interest. The golf ball launch area sensing unit  203  and golf ball spin sensing unit  205  may also be positioned at any convenient location. 
         [0097]    While the sports simulation system is described as simulating golf, it will be appreciated that the sports simulation system may be used to simulate other sports where a projectile is launched. In such cases, the projectile characteristic signatures are updated to enable launched projectiles to be accurately tracked. 
         [0098]    Although embodiments have been described above with reference to the drawings, those of skill in the art will appreciate that variations and modifications may be made without departing from the spirit and scope thereof as defined by the appended claims.