text: referring to fig1 there is shown a block diagram of the imaging system 100 according to the invention . the imaging system 100 can be a video game system , such as that disclosed in u . s . pat . no . 5 , 513 , 307 ; a personal computer having graphic capabilities or a professional imaging system . the imaging system 100 includes a game memory 63 which can be a device such as a cd player with a cd rom ; a game cartridge which is a rom mounted on a chip for inserting into a slot as is also described in the above referenced patent or even a video player . connected to the game memory is a ram 42 that receives the imaging information from the game memory and stores that information . an input terminal 73 is connected to a processor interface 62 . the input terminal 73 can include multiple player control inputs wherein each player has an input terminal that can be one or more input that includes buttons , keys , mice or joy sticks for controlling the movement of the images that are generated on to a display 55 , from data stored in vcr 55 a or rom 55 b . the buttons on the input terminal 73 initiate the operation and are used to establish a set of targets for moving an image or a portion of an image to the targets . the audio visual interface 45 includes a device such as a video ram ( herein after referred to as “ vram ”) that stores graphic patterns as well as the sound video interface circuits such as those provided in most personal computers . the vram addresses correspond to the locations on the display 55 . as the display 55 is scanned line by line , patterns corresponding to the graphic information are received and video signals are produced which are representative of the graphic patterns . the audio visual interface 45 selects the appropriate signal and if it is a raster scan type of monitor on a dot by dot basis , the image is displayed on the display 55 . the operation of the display 55 is well known in the art . control logic 46 is used to interface a microprocessor 44 output to the audio visual interface 45 and consequently the display 55 . it also is the interface between the input ram 42 and the input terminal 73 which also interfaces to the microprocessor 44 via the processor interface 62 which is controlled by the control logic 46 . x ″ n = kx ( n − 1 ) − δx ′ ( n − 1 ) ; x ′ n = x ′ ( n − 1 ) + x ″ ( n − 1 ) n ; x n = x ( n − 1 )+ x ′ n ψ ″ s = k s ψ s − δ 2 ψ ′ s fig2 a - 2 e represent a time sequence of frames of a display in which an element 21 is joined to a target element 23 at a joint 25 by a representation of a spring 27 . a dash pot 31 provides damping of the movement of element 21 . these figures illustrate the behavior of a single actuator overtime . an appreciation of the invention may be more readily understood by utilizing fig3 in conjunction with equations 1 of the table of equations and fig2 a - 2 e . referring to fig3 at the start 22 , the image displayed on the display 45 will be that of fig1 through 3 . in fig3 at block 26 , the actuators are bound by setting parameters for k and δ . the minimum and maximum values for each actuator are also set . an initial value is chosen for each actuator target and the positions x of each actuator are set equal to their targets , and their velocities ( x 1 ) are set to zero . determined target block 24 represents the setting the target by operator inputs via terminal 73 or by executing movements saved in ram 42 is represented in fig2 b by the relocation of target element 23 . referring back to fig3 the actuators are advanced at block 28 . at block 28 the subroutine that is described in fig9 is initiated . at block 28 , the equations 1 are solved and the position is updated at block 30 . at block 30 , the position of the element 21 is updated by finding the solutions to the equations 1 by executing the flow that is indicated in the flow chart illustrated in fig1 or 11 . after the position is updated , the collision process is executed at block 32 . this process is described in fig1 . following the collision process at block 32 , the frame is incremented at block 38 and the system returns to determine the target at block 24 . referring back at fig2 c ( the third frame ), the element 21 starts to move very rapidly as indicated by force lines 13 towards the target element 23 . at fig2 d ( the fourth frame ) the element 21 has overshot the target position as it reaches position 46 . finally , at fig2 e ( the fifth frame ), the element 21 has come to rest at position 44 which is in the rest state and remains there until the target element 23 is again relocated . the process is repeated until decision block 41 detects that the game is over and exits at block 65 . for a game to be realistic , the movement of the mass 21 must be realistic . the movements must be more than a blur . with the teachings of the current invention , it has been found that by simulating the movement through the use of differential equations such as that of a spring , mass and dash pot represented by equation 1 on the table of equations . the movement can be made to be very realistic . fig4 illustrates a game , a sword fight between players , 101 and 102 . each player has a sword , 103 and 105 respectively , clutched in their hands . the players are positioned to engage in a sword fight . the operator who controls the player 101 , selects as a target , player 102 through the input terminal 73 , initiates a swing to the target player 102 . simultaneously , either a second operator or a program stored in the game memory 63 detects this movement and causes player 102 to position his sword 105 to block the sword 103 . this occurs in fig5 . in fig5 the swords contact each other at point 106 . in the prior art , the reaction of the two swords would have been shown as a blur or a prerendered animation sequence rather than a more realistic , human - like movement . whereas the sequences followed in fig1 provide a reaction to the collision according to physical principals . each figure includes a score keeper such as left score keeper 108 and for player 102 , right score keeper 118 for player 112 . when an injury occurs , then at segments 109 through 117 , the injured portion is deleted from the image . for example , score keeper 118 has lost the lower potion of the arm at segment 112 . in fig6 there is shown an image 2 of a player located at the origin of a cartesian three dimensional space . this allows the image shown on the display 55 to be three - dimensional . there are 3 actuators utilized in the embodiment of fig6 . an actuator is defined as a simulation of the solution of a differential equation for movement in a particular plane or along a ray or line . as discussed earlier , equations 1 , in the table of equations , show the solution for the simulation of a solution in a generic variable x . it has been found that the ratio of k 2 to δ must be roughly constant for a given character of motion . the particular range of values for k and δ are defined by equations 3 and 4 . in the embodiment of fig6 the three actuators are defined by equations 5 , 6 and 7 . in equation 7 , ρ represents the movement of the elbow joint 11 and wrist joint 14 and relates a position of the sword 103 to the shoulder 12 . additionally , there is movement provided in the θ and ψ planes . in particular , ρ is used to define the position of the base 16 of the sword in relation to the shoulder 12 . the position values θ , ψ and ρ and the velocity values θ 1 , ψ 1 and ρ 1 are the input initial values or the values from the preceding frame . what makes the use of actuators unique is that the computer does not actually solve the differential equations but simulates their solution . for example , the differential equation of motion for θ is given by equation 5 and the velocity is provided by equation 9 which is the summation of the velocity of the previous frame and acceleration of the current frame for any given frame . the position is provided by equation 26 which is the summation of the position of the previous frame with the velocity of the current frame . in order to position the elbow joint 11 in the proper position for an elbow , heuristic routine must be used . once the position of the sword base 16 is determined , the position of the elbow joint 11 is constrained to a circle in space centered around the shoulder 12 . the elbow joint 11 position is then defined as the intersection of the circle and the plane formed by the characters &# 39 ; nose 33 , shoulder 12 and base 16 of his sword 103 . the angle of the sword 103 to the forearm 6 is also determined by the following heuristic . if the base 16 of the sword 103 or hand 9 has reached its target position , it is aligned with the vector sum of the vector from the elbow joint 11 to the hand or , in the case of fig6 the base 16 of sword 103 and one half the vector from the elbow joint 11 to the shoulder 12 . if the base 16 of the sword 103 is en route to its target , it attempts to align its blade edge 19 with its direction of motion . fig7 illustrates an alternate embodiment of the invention wherein there are three different planes of movement that are used in the implementation of this invention . an image is centered around the xyz coordinates of fig7 . the three planes are identified by the following coordinates : a φ coordinate in the xy plane , a ψ coordinate in the zy plane and a θ coordinate in the xz plane . fig8 is an example of the alternate embodiment of the invention wherein a more realistic movement is achieved over that illustrated in fig6 by the additions of more actuators thereby eliminating the need to use elbow - heuristic to position the elbow . for example , the image 3 of fig8 has a shoulder joint 5 , an elbow joint 6 and a wrist joint 7 . the shoulder joint 5 is capable of moving in all three planes defined in fig7 whereas the joint 6 can only move in the φ plane and the joint 7 can move in the ψ and φ planes . it is obvious that joint 5 is used to represent the shoulder of an image whereas joint 6 is represented as the elbow and joint 7 is used to represent the wrist . equations 13 , 14 and 15 represent the equations of motion for the joint 5 . equation 16 represents the equation of motion for joint 6 . equations 17 and 18 represent the equations of motion for the joint 7 . the velocity value for each one of these joints is provided by equations 20 through 25 . the positions by equations 30 through 35 . in equations 13 through 18 , the values for velocity and position are values from the previous frame or input initial values . in the embodiment of fig8 the image 3 has a sword 103 and as was discussed earlier , there are 6 actuators φ s , ψ s , θ s ( which are associated with the joint 5 ), φ c ( which is associated with joint 6 ) and φw and ψ w ( which are associated with the joint 7 ) controlling the movement of the sword 103 . the execution of the program for fig8 is discussed in conjunction with fig9 . referring to fig9 which should be used in conjunction with fig3 and 5 , the imaging system 100 of fig1 is designed to cause the display 55 to display a sequence of frames . the sequence of frames begins with frame 1 and runs on as long as the computer is operating the program display of fig5 . in the case of fig3 and 9 , the first task at block 22 is to start the process followed by the loading of the actuators at block 26 and the placement of the target for the first frame at block 24 . this process is begun by an operator initiating of a game in the game memory at block 22 . following the determination of the target at block 24 , the actuators are advanced at block 28 after which the position of an image such as that shown in fig4 and 5 is updated at block 30 . the advancing of the actuators at block 28 is illustrated in fig9 to which reference should now be made . following the determination of the targets at block 24 , the execution of the program will proceed to the start 200 where for each actuator , this routine is executed . at block 230 , the acceleration is computed by equations 13 , 14 , 15 , 16 , 17 or 18 depending on which actuator the acceleration is being determined . following the computation of the acceleration , then the modification of the velocity occurs at block 231 . the modification of the velocity is performed by the execution of one of the following equations from the table of equations — equations 20 , 21 , 22 , 23 , 24 or 25 . after the modification of the velocity has occurred , there is enough data available to modify the position of the base of the sword 16 . modification of the position of the joint to which the particular actuator is associated with and the program is being executed occurs at block 201 wherein one of the following equations from the table of equations is executed . these equations are equations 30 , 31 , 32 , 33 , 34 or 35 . at decision block 202 , a check is made to make sure that the particular joint that is being executed is in bounds . if it is not , then at block 232 the position is set to the closest extreme that was part of the parameters that were set during the load of the actuator at block 203 . at block 204 , the velocity is then set to zero and the routine proceeds to block 302 . there is an impulse representing the force of the actuator lifting one of the extreme bounds on its motion applied to the parent object . by parent object , we mean the actuator controlling the joint which governs the movement of the next closer element of the arm to the body has an actuator . for example , referring to fig8 the hand 7 parent is the elbow 6 and the parent to the elbow 6 is the shoulder 5 . following the application of the impulse to the parent object at block 236 ; we proceed to verity that all of the actuators have been advanced at decision block 205 . if not , the routine goes to block 207 which increments to the next actuator . for example , if the previous set of executions had been to sequentially execute equation 13 , 20 and 30 , at the move to the next actuator , then equations 14 , 21 and 31 would be executed until all of the equations have been executed or solved . when the final actuator needed to apply an impulse to its parent has no parent so it applies that impulse directly to the body of the character 3 and the final parent in this case is the shoulder 5 . it is obvious in the case of fig6 that the same program can be used except the equations that are to be solved are equations 5 , 6 and 7 for acceleration ; equations 9 , 10 and 11 are used to modify the velocity ; equations 26 , 27 and 28 would be used to modify positions . fig1 is a flow diagram that illustrates the execution of the block 30 of fig3 which is to update the positions of the arm segments based upon the actuator values . at start block 300 , the update positions are begun and the position of the base of the sword 16 is determined from θ , ψ and ρ at block 301 . at block 302 , the computer heuristically computes the elbow and sword tips &# 39 ; position as was previous discussed and then proceeds to compute the bicep orientation at block 303 following which the forearm orientation is computed at block 304 and following which the sword orientation is computed at block 303 and then returned to execute block 32 at return segment 300 . the embodiment of fig8 when implemented , follows a flow chart described in fig1 to which reference should now be made . following the start position 120 , the orientation of the shoulder 5 relative to the body is computed from the θ s , φ s and ψ s . it is computed in the following manner . first the shoulder is rotated in the x z plane by an angle of θ s whose value is computed from equation 32 of the table of equations . the shoulder is then rotated in the xy plane by a value of φ s whose value is also computed by equation 31 of the table of equations . then the shoulder is rotated in the yz plane by a value of ψ s whose value is also computed from equation 27 of the table of equations . we next embark to block 125 to compute the orientation of the elbow relative to the upper arm from φ e . this orientation is computed by rotating the elbow to an angle of φ e in the xy plane . again , the value of φ e is computed from equation 33 of the table of equations . finally , in block 127 , the orientation of the wrist is computed relative to the lower arm from φ w and ψ w . ψ w represents rotation of the wrist to an angle of the value ψ w in the yz plane . φ w represents rotation of the wrist to the value of φ w in the xy plane . again , these values are computed from equations 34 and 35 of the table of equations . this concludes the process of updating the position of the sword arm in the second implementation . fig1 , illustrates the process collisions subroutine that is executed at block 32 of fig3 . the start position occurs at block 400 where the at the first step it selects the first body segment of the component at block 401 . at block 402 the question is asked “ did my sword collide with this segment on this frame ?” if the answer is “ no ” we proceed to block 404 and if “ yes ” we proceed to mark it as a hit at block 403 . by “ hit ” we mean that the sword intersected the given body segment of the opponent on this frame such as in fig5 wherein the opponents body segments are numbered 110 , 109 , 108 , 117 , etc . then we proceed to the following question in block 404 “ have we checked all of the segment of the opponents body ?” if the answer is “ no ” we proceed to block 405 where we select the next segment of the opponent and then we proceed back up to block 402 and ask again the question “ did my sword collide with this segment on this frame ?” once we arrive at block 404 and the answer to the question “ save we checked all segments ?” is “ yes ”, we then proceed to block 406 . at block 406 we ask the question “ was at least one segment on the opponent &# 39 ; s body struck by the sword ?” if the answer is “ no ”, we exit the collision process . if the answer is “ yes ”, we proceed to block 407 . at block 407 , we go through all of the body of segments of the opponents that were struck by the sword and chose the one closest to the sword &# 39 ; s original starting position . this is the body segment that we will consider the sword to have struck on this frame . we then proceed to block 408 wherein we apply impulses to the segment that was struck and to the sword using conservation of momentum and conservation of energy and then we exit the collision process . in the discussions of the previous embodiment ( block 32 of fig9 ), every time an apply impulse is described , it refers to the following routine of fig1 is executed . the procedure for applying an impulse to an object begins at block 500 . the execution then proceeds to block 501 where the question is asked “ is the object connected to a parent object by an actuator ?” if the answer is “ yes ”, then in block 502 , the impulse is converted into angular velocity . execution then proceeds to block 503 where the proportion of the impulse absorbed by the actuator is computed . then execution proceeds to block 504 where this proportion of the impulse is applied to the angular velocity of the actuator . then in block 505 , the remaining impulse is applied to the parent object of the actuator . this then sends execution back to block 501 where the same question is now asked about the parent object —“ is this object connected to a parent object by an actuator ?” this process is repeated until the answer to the question in block 501 is “ no ”. execution then proceeds to block 506 . in block 506 , again the proportion of the impulse absorbed in angular velocity of the actuator is computed . then in block 507 , the proportion of the impulse is applied to the object &# 39 ; s angular velocity . then execution proceeds to block 508 where the remainder of the impulse is applied to the figure &# 39 ; s body . this concludes the algorithm for applying an impulse to an object . there are situations wherein an weapon or an object is grasped with two hands . in this situation , the embodiment of fig1 is used . the embodiment of fig1 includes an image 716 that has a sword 708 held by his left arm at his hand 718 and by his right arm 705 at the right hand 712 . in order to provide realistic movements , it has been found that the regular arms ought to be used for display of the image only and the actual position of the sword 708 be determined by the use of a third , invisible arm 714 . the invisible arm 714 connects the neck region of the image 716 to the union of the hands 712 and 718 and has , in the preferred embodiments , three joints 720 , 722 and 710 . in this embodiment of fig1 , acceleration is determined by equations 13 through 18 and velocity is determined by equations 20 to 25 and position is determined by equations 30 through 35 . the only difference is that the shoulder is directly under the head of 715 of the image 716 rather than in the usual position as shown in fig4 and 5 . in this two - handed implementation , once the invisible third arm &# 39 ; s position has been determined , the two actual visible arms are now placed so that both of their hands grasp the same location which is where the base of the sword is as attached to the invisible arm . the elbows of the left and right arm are determined in their position by the same elbow heuristic which is used in the first embodiment as previously described . fig1 , to which reference should now be made , shows an illustration of a computer simulated playback system of two players 511 and 512 . player 512 holds a bat and is a target for player 511 to throw a ball 514 . in actuality , the players 501 and 502 represent actual figures that are being videoed by the camera 515 . player 512 has a sensor terminal 516 which monitors the sensors if 517 , 518 and 519 that are related to the video film made by the camera 515 and correspond to joints 5 , 6 and 7 of fig8 . the data and information that result from this procedure is stored and can be read back via the game memory 63 and displayed on the display 55 . an operator , at the terminal 73 , may apply the actuators defined in the table of equations to the image of player 512 that is shown on the display 55 at block 24 of fig3 . in order to adjust and apply the actuators in this manner , the positional data of a baseball player &# 39 ; s swing and pitch must first be converted into target data for the actuators of the joints . this procedure would involve a frame by frame reverse engineering of the positional data of the baseball player and for the pitcher wherein at each frame the computer would determine which targets were necessary for the actuators to produce the movement that was recorded . the advantage by applying actuators to the embodiments of fig1 is that the movement character of player 512 can be modified by varying the constants ( k ) and ( δ ) and the targets through the input terminal 73 , the figure displayed in 512 can be very agile , if ( k ) is large or very lethargic if ( k ) is a small number . the only requirement is that the ratio of the spring constant ( k 2 ) to the drag coefficient ( δ ) be roughly equal to a constant number for a given quality of movement . but by varying these numbers , the display of the figure in the display 55 can be made agile or lethargic simply by varying the size of the constant ( k ). the data can be stored in the memory 42 or recorded 55 a or in a rom 55 b for playback at a later date . other examples of the use of the actuators to create realistic movements on a display 55 are shown in fig1 in which frog 600 is initially shown in a sitting position at point 610 and has three joints defined by 601 , 602 and 603 . at position 620 , the frog is in the midst of a leap represented by the dotted line 604 in which the illustration of a leg 621 is extended showing the joints 601 , 602 and 603 . from this operation the movements at each joint are represented by equations 1 of the table of equations . similarly , the images in fig1 show two kick boxers in which one boxer 701 has been struck on the representation of his chin 702 and , of course , would have similar degrees of movement of that shown in fig7 so that the equations 6 and 8 for θ and ψ can be used to represent the movement of the figure &# 39 ; s 701 head 203 .