JP2001297337A - Amusement device and image processing method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To reduce calculation costs concerning a high-order spline. SOLUTION: When a spline curve is defined with two points P1 and P2 and fine coefficients DP1 and DP2 at these two points on a locus f(t), it is applied by an equality (1). A simple tertiary equality as shown in an equality (2) is previously generated from the algebra calculation of the equality (1) and the locus is found by this tertiary equality. By simplifying an operation expression, the calculation costs are remarkably reduced.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a game machine and an image processing method.

[0002]

2. Description of the Related Art In a game machine, when the movement of a character or other object is set in advance, 3
The movement of the position and posture (angle) in the dimensional space may be defined by a combination of a higher-order spline, for example, a cubic spline.

A cubic spline is given by a cubic polynomial using time as a variable, and its computational cost has conventionally been high.

[0004]

SUMMARY OF THE INVENTION The present invention has been made in order to solve such a conventional problem, and an object of the present invention is to provide an amusement apparatus and an image processing method capable of reducing a calculation cost relating to a higher-order spline. Aim.

[0005]

SUMMARY OF THE INVENTION The present invention relates to a game apparatus and an image processing method for defining the movement of an object in a virtual three-dimensional space by a combination of higher-order spline curves. For the spline curve representing the motion of (1), a simplified formula is obtained by combining the coefficients of the respective degrees of time into one, and the locus is calculated using this formula. This can save computational costs. The higher-order spline is, for example, a cubic spline.

Further, the present invention is a machine-readable recording medium storing a program for causing a computer to execute the image processing method. Here, the “recording medium” is a medium in which information (mainly digital data and programs) is recorded by some physical means, and causes a processing device such as a computer or a dedicated processor to perform a predetermined function. Is what you can do. In short, any method may be used as long as the program is downloaded to the computer by some means and a predetermined function is executed. For example, flexible disk, fixed disk, magnetic tape, magneto-optical disk, CD, CD-RO
M, CD-R, DVD-RAM, DVD-ROM, DV
DR, PD, MD, DCC, ROM cartridge, RAM memory cartridge with battery backup,
Includes flash memory cartridges, nonvolatile RAM cartridges, and the like. This includes the case where data is transferred from a host computer via a wired or wireless communication line (public line, data line, satellite line, etc.). The so-called Internet is also included in the recording medium mentioned here.

[0007]

Next, a preferred embodiment of the present invention will be described with reference to the drawings.

FIG. 1 is a block diagram of a game machine according to the present embodiment. The game device 100 includes a program data storage device or a storage medium (including an optical disk and an optical disk drive) 101 storing a game program and data (including video and music data), a game program execution and control of the entire system. The CPU 102 performs coordinate calculation for image display and the like, a system memory 103 in which programs and data necessary for the CPU 102 to perform processing are stored, and programs and data necessary when the game apparatus 100 is started are stored. BOO
A TROM 104 and a bus arbiter 105 for controlling the flow of programs and data between each block of the game apparatus 100 and devices connected to the outside are provided, and these are connected to a bus (not shown).

A rendering processor 106 is connected to the bus, and the program data storage device or storage medium 1
The video (movie) data read out of the display monitor 01 and the image to be generated according to the operation of the player or the progress of the game are displayed by the rendering processor 106 on the display monitor 1.
10 is displayed. Graphic data and the like necessary for the rendering processor 106 to generate an image are stored in the graphic memory 107.

A sound processor 108 is connected to the bus, and a program data storage device or a storage medium 101 is connected to the bus.
The music data read out from the CPU and sound effects and sounds to be generated in accordance with the operation of the player and the progress of the game are output from the speaker 111 by the sound processor. Sound data and the like necessary for the sound processor 108 to generate sound effects and sounds are stored in the sound memory 109.

A communication interface 112 is connected to the game apparatus 100, and communicates with another game apparatus 100, a network server, a home game machine, a personal computer, and the like through a communication network (not shown). The operation information of the controller, the type, name, position, orientation, vitality, number of times the special abilities can be used by the player and other characters operated by the player, the game execution time, the number of running stages, the number of cleared stages, etc. , Billing information, the number of continuations, the player's name, age, and gender, an identification code attached to the play device, game programs, data, images, videos,
Voice, music, text, and the like can be transmitted and received. Then, the player plays a communication match with another game device 100, and a game device 100 installed in another amusement center, an amusement theme park, or the like,
Investigate the operation status of the amusement device, perform billing calculation, and the like, and relay the game image of the amusement device 100 to a home game machine or a personal computer using a network server or a computer connected to the server. , And so on.

FIG. 2 is a perspective view showing a model of an object according to an embodiment, FIG. 3 is a graph showing the locus of the center of gravity of the object in FIG. 2, and FIG. 4 is an enlarged view showing a method of calculating splines in the graph of FIG. It is.

The objects displayed on the screen of the amusement device create a model as shown in FIG. 2 (FIG. 2 is a human figure), and the movement is defined as the movement of each part. As shown in FIG. 3, this trajectory is a higher-order spline curve such as a cubic spline curve as a temporal change of a position (x, y, z) and a posture (angle) (ξ, η, に お け る) in a three-dimensional space. Is represented by a combination of

In a locus f (t) as shown in FIG. 4, for example, two points P1, P2 and a differential coefficient D at the two points
When a spline curve is defined by P1 and DP2, the points P1,
A spline curve is given by equation (1) using P2 and differential coefficients DP1 and DP2.

[0015] An extremely large number of spline curves have been proposed, and equation (1)
Is an example. Conventionally, since the equation (1) is calculated as it is, an extremely large number of higher-order operations are required.

Therefore, in the fifth embodiment, a simple cubic expression as shown in Expression (2) is generated in advance from the algebraic calculation of Expression (1), and the trajectory is determined by this cubic expression. The simplification of the arithmetic expression greatly reduces the calculation cost.

Note that the calculation of the equation (2) is not performed analytically,
Of course, it is also possible to use an approximate solution method such as the least square method.

Next, a program for simplifying the above-described spline curve will be described using an excerpt of the source list. Here, functions (1) to (5) are shown. Function (1) is a start point time which is a parameter of the spline curve.
Array of TimeS, end time TimeE, and curve properties (time)
Declares the variable type of Knots []. In the function (2), specific numerical values are assigned to these variables and arrays. The function (3) performs a process for simplifying the calculation formula when the spline curve is a Hermite curve, the function (4) performs a process when the spline curve is a straight line, and the function (5) performs a spline curve. If the characteristic of the element is unknown, a process corresponding to the number of elements is performed.

In the function (3), the equation (2), variables A, B, C,
Variables Coeff [SplineBase :: A] and Coeff [Spline corresponding to D
Base :: B], Coeff [SplineBase :: C], Coeff [SplineBase ::
D] is calculated.

In the function (4), the coefficient Coeff [Spli
neBase :: C] and Coeff [SplineBase :: D] are calculated.

In the function (5), when the number of elements is four or more, a cubic curve of least square approximation is calculated (function (5-1)).
When the number of elements is three, a quadratic curve of least square approximation is calculated (function (5-2)), and when the number of elements is two, a linear line of least square approximation is calculated (function (5-3)). ). Otherwise, it is invalid (function (5-4)). [Source list] typedef struct tagSPLINEDEF function (1) {int Type; double TimeS, TimeE; double Knots [SplineBase :: MAX_COEFF];} SPLINEDEF; SplineBase :: SplineBase (double ts, double te, double Knot0, double Knot1, double Knot2, double Knot3) Function (2) {TimeS = ts; TimeE = te; Knots [KNOTO0] = Knot0 Knots [KNOTO1] = Knot1 Knots [KNOTO2] = Knot2 Knots [KNOTO3] = Knot3} void Hermite :: GetGeneralFunctionCoefficient (double Coeff [4]) function (3) {double a, b, c, d; double w, w2, w3; double ts, ts2, ts3; w = TimeE-TimeS; w2 = w * w; w3 = w2 * w ; a = (2.0 * Knots [VAL0] -2.0 * Knots [VAL1] + Knots [SLP0] + Knots [SLP1]) / w3; b = (-3.0 * Knots [VAL0] + 3.0 * Knots [VAL1] -2.0 * Knots [SLP0] -Knots [SLP1]) / w2; c = Knots [SLP0] / w; d = Knots [VAL0]; ts = TimeS; ts2 = ts * ts; ts3 = ts2 * ts; Coeff [SplineBase: : A] = a Coeff [SplineBase :: B] =-3.0 * TimeS * a + b Coeff [SplineBase :: C] = 3.0 * TimeS * TimeS * a-2.0 * TimeS * b + c; Coeff [SplineBase :: D] =-a * ts3 + b * ts2-c * ts + d;} void Linear :: GetGeneralFunctionCoefficients (double Coeff [4]) Function (4) {Coeff [SplineBase :: A] = 0.0; Co eff [SplineBase :: B] = 0.0 Coeff [SplineBase :: C] = (Knots [KNOT1] -Knots [KNOT0]) / (TimeE-TimeS); Coeff [SplineBase :: D] = Knots [KNOT0] -TimeS * Coeff [SplineBase :: C];} void Unknown :: GetGeneralFunctionCoefficients (double Coeff [4]) function (5) {double SumA2, SumB2, SumAB; double SumAC, SumBC; double Determinant; double A, B, C; double Ts , Te, Xs, Xe; double t [3]; int i; Ts = TimeS; Te = TimeE; Xs = pVal [0]; Xe = pVa1 [Size-1]; if (Size> = 4) {function ( 5-1) SumA2 = SumB2 = SumAB = 0.0; SumAC = SumBC = 0.0; for (i = 1; i <Size; i ++) {t [0] = pTime [i]; t [1] = t [0] * t [0]; t [2] = t [1] * t [0]; A = LeastSquare_A (Ts, Te, t); B = LeastSquare_B (Ts, Te, t); C = pVal [i]- LeastSquare_C (Xs, Xe, Ts, Te, t); SumA2 + = A * A; SumB2 + = B * B; SumAB + = A * B; SumAC + = A * C; SumBC + = B * C;} Determinant = SumA2 * SumB2- SumAB * SumAB; Coeff [SplineBase :: A] = (SumB2 * SumAC-SumAB * SumBC) / Determinant; Coeff [SplineBase :: B] = (-SumAB * SumAC + SumA2 * SumBC) / Determinant; Coeff [SplineBase :: C] = (Xs-Xe) / (Ts-Te)-(Ts * Ts + Ts * Te + Te * Te) * Coeff [SplineBase :: A]-(Ts + Te) * Coeff [SplineBase :: B] ; Coeff [SplineBase :: D] = (Ts * Xe-Te * Xs) / (Ts-Te) + Ts * Te + ((Ts + Te) * Coeff [SplineBase :: A] + Coeff [SplineBase :: B]);} else if (Size = 3) {function (5-2) double T, X0, X1, X2; T = Ts + 1.0; X0 = Xs; X1 = pVa [1]; X2 = Xe; Coeff [SplineBase :: A] = 0.0; Coeff [SplineBase :: B] =-0.5 * (-x0 + 2.0 * x1-x2); Coeff [SplineBase :: C] =-0.5 * ((2.0 * T + 1.0) * x0-4.0 * T * x1 + (2.0 * T-1.0) * x2); Coeff [SplineBase :: D] =-0.5 * (-T * (T + 1.0) * x0 + 2.0 * (T * T-1) * x1-T * (T-1.0) * x2); else if (Size = 2) {Function (5-3) Coeff [SplineBase :: A] = Coeff [SplineBase :: B] = 0.0; Coeff [SplineBase :: C] = ( Xs-Xe) / (Ts-Te) Coeff [SplineBase :: D] = Xs-Coeff [SplineBase: C] * Ts;} else {function (5-4) memset (Coeff, 0, sizeof (double) * 4 );} double Unknown :: LeastSquare_A (double Ts, double Te, double t [3]) {return t [2]-(Ts * Ts + Ts * Te + Te * Te) * t [0] + Ts * Te (Ts + Te);} double Unknown :: LeastSquare_B (double Ts, double Te, double t [3]) {return t [1] -t [0] * (Ts + Te) + Ts * Te;} double Unknown :: LeastSquare_C (double Xs, double Xe, double Ts, double Te, double t [3]) {return (t [0] * (Xs-Xe) + Ts * Xe-Te * Xs) / (Ts-Te) ;}}

As described above, according to the present invention, it is possible to reduce the calculation cost related to a higher-order spline.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a hardware configuration of an embodiment of a game device according to the present invention.

FIG. 2 is a perspective view showing a model of the object according to the embodiment;

FIG. 3 is a graph showing a locus of the position and posture (angle) of the object in FIG. 2;

FIG. 4 is an enlarged view showing a method of calculating a spline in the graph of FIG. 3;

[Explanation of symbols]

 x x coordinate y y coordinate z z coordinate 角度 angle around x axis η angle around y axis 角度 angle around z axis t time

Claims (5)

[Claims] 1. An amusement device for defining the movement of an object in a virtual three-dimensional space by a combination of higher-order spline curves. For each coordinate axis, a coefficient of each degree of time is simplified to one for each spline curve. An amusement device characterized in that a calculated formula is obtained and a locus is calculated by the calculated formula. 2. The game device according to claim 1, wherein the higher-order spline is a cubic spline. 3. An image processing method in which the motion of an object in a virtual three-dimensional space is defined by a combination of high-order spline curves, wherein coefficients of each degree of time are combined into one for each spline curve for each coordinate axis. An image processing method comprising: obtaining a simplified calculation formula; and calculating a locus using the calculation formula. 4. The image processing method according to claim 3, wherein the higher-order spline is a cubic spline. 5. A machine-readable recording medium storing a program for executing the image processing method according to claim 3 on a computer.