JP2005322056A - Program, information storage medium and image generation system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an image generation system capable of generating a realistic and high-quality image such as a water surface object or the like with small amount of data and small processing load, and to provide a program and an information storage medium. <P>SOLUTION: A configuration point calculating part 116 for calculating the coordinates of a configuration point of an object sets sampling points (i, j) on the basis of a coordinate value parameter i in an r direction and a coordinate parameter j in a θ direction about a given section obtained by performing m division of a polar coordinates system in the r direction and n division of the polar coordinates system in the θ direction, calculates first coordinate values and second coordinate values of the sampling point (i, j) on the basis of the coordinate value parameter i in the r direction and the coordinate value parameter j in the θ direction, and defines third coordinate values of the sampling points (i, j) at time t on the basis of a periodic function with the coordinate value parameter i in the r direction, the coordinate value parameter j in the θ direction and a time parameter t as an argument. An image generation part 120 specifies the coordinates of configuration points of the object at the time t constituted of a plurality of sections including the given section as a set on the first, second and third coordinate values of the sampling points. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a program, an information storage medium, and an image generation system.

  Conventionally, an image generation system (game system) that generates an image that can be seen from a virtual camera (a given viewpoint) in an object space that is a virtual three-dimensional space is known. Popular.

Now, in such an image generation system, it is an important issue to generate a more realistic image in order to improve the player's virtual reality. Therefore, it is desired that the water surface wave displayed on the game screen can be expressed more realistically.
JP 2002-216159 A

  As another method for expressing a wave on the water surface, there is a method in which a water surface object composed of a plurality of polygons is prepared and the water surface object is animated based on wave pattern data.

  However, with this method, the animation pattern of the water surface object is limited, so the resulting wave image is monotonous and lacks realism, and expresses vortex waves and rotating waves. It was difficult.

  In addition, in order to realistically represent vortexing waves and rotating waves, a method of performing physical simulation calculations using a water surface model is also conceivable, but the calculation load becomes enormous, and it is limited to limited hardware such as game systems. There is a problem that real-time image generation is difficult.

  An object of the present invention is to provide an image generation system, a program, and an information storage medium capable of generating a real high-quality image such as a water surface object with a small amount of data and a small processing load.

(1) The present invention is an image generation system for generating an image,
A component point calculating means for determining the coordinates of the object's constituent points based on a periodic function having the sampling point coordinates and time set as arguments to determine the object's constituent points;
Image generating means for generating an image of an object whose shape is specified by the obtained constituent points,
The component point calculation means includes
A sampling point (i, j) is set based on a coordinate value parameter i in the r direction and a coordinate parameter j in the θ direction for a given section obtained by dividing the polar coordinate system into m in the r direction and n in the θ direction. And
The first coordinate value and the second coordinate value of the sampling point (i, j) are obtained based on the coordinate value parameter i in the r direction and the coordinate parameter j in the θ direction,
Obtaining a third coordinate value of the sampling point (i, j) at time t based on a coordinate function parameter i in the r direction, a coordinate parameter j in the θ direction, and a time function having the time parameter t as arguments;
The image generating means includes
Based on the first coordinate value, the second coordinate value, and the third coordinate value of the sampling point, the coordinates of the constituent points of the object at time t configured as a set of a plurality of sections including the given section are specified. It is characterized by doing.

  The program according to the present invention is a program usable by a computer (a program embodied in an information storage medium or a carrier wave), and causes the computer to realize the above means (makes the computer function as the above means). And An information storage medium according to the present invention is an information storage medium readable (usable) by a computer, and includes a program for causing the computer to realize the above means (functioning the computer as the above means). And

  The first coordinate value of the sampling point (i, j) is, for example, the coordinate value x in the x-axis direction, the second coordinate value is the coordinate value z in the z-axis direction, and the third coordinate value is This is the coordinate value y in the y-axis direction.

  The periodic function is a function having a parameter for specifying the position of the sampling point and time as arguments, and is, for example, a trigonometric function of a sine wave (sin) or cosine wave (cos), or a synthesis function including these. By using a periodic function, it is possible to obtain a periodically changing height (y) or the like of a sampling point at a given position (x, z).

  Then, based on the coordinate value (for example, (x, y, z)) of the sampling point (i, j), the constituent point (for example, vertex) of the object (for example, wave object) having a periodically varying height at time t is determined. Specify and perform image generation.

  According to the present invention, for a given section obtained by dividing the polar coordinate system by m in the r direction and n by the θ direction, it is set based on the coordinate value parameter i in the r direction and the coordinate parameter j in the θ direction. The third coordinate value (for example, y coordinate, coordinate representing height) of the sampling point (i, j) is used as a parameter indicating the position of the sampling point (coordinate value parameter i in the r direction and coordinate parameter j in the θ direction) The time parameter t is obtained based on a periodic function with an argument.

  Here, as a periodic function, by using a periodic function for obtaining the height y at the time t of the sampling point (i, j) (sampling point in the Cartesian coordinate system) of the wave mesh for generating the plane wave, in the Cartesian coordinate system The y coordinate of the sampling point (i, j) is mapped to the corresponding sampling point (i, j) of a given section (sector) obtained by dividing the polar coordinate system by m in the r direction and n by the θ direction. be able to.

  Here, the sampling point (i, j) of the wave mesh in the polar coordinate system of the Cartesian coordinate system (sampling point in the Cartesian coordinate system) is obtained in each of the sections obtained by dividing the polar coordinate system into m in the r direction and n in the θ direction. By mapping the height y at time t, a wave that varies continuously and periodically in the polar coordinate system can be generated.

  In addition, by setting the phase component and wavelength component of the periodic function of the plane wave to predetermined values, it is possible to generate wave components that continuously and periodically vary between adjacent meshes in the Cartesian coordinate system. The continuity of waves between adjacent sections in the mapped polar coordinate system can also be ensured.

  Therefore, a wave (rotating wave, vortex, etc.) specified in the polar coordinate system can be expressed by performing a calculation using a periodic function. For example, a wave rotating by performing a simulation calculation of a wave specified in the polar coordinate system. It is possible to find the constituent points of the object of the wave (rotating wave, vortex, etc.) specified in the polar coordinate system with a very small calculation load compared to the case of expressing the vortex and the like.

(2) Further, an image generation system, a program, and an information storage medium according to the present invention are:
The component point calculation unit is
For each section obtained by dividing the polar coordinate system into m parts in the r direction and n parts in the θ direction,
A sampling point (i, j) is set based on the coordinate value parameter i in the r direction and the coordinate parameter j in the θ direction,
The first coordinate value and the second coordinate value of the sampling point (i, j) are obtained based on the coordinate value parameter i in the r direction and the coordinate parameter j in the θ direction,
Obtaining a third coordinate value of the sampling point (i, j) at time t based on a coordinate function parameter i in the r direction, a coordinate parameter j in the θ direction, and a time function having the time parameter t as arguments;
The image generation unit
Based on the first coordinate value, the second coordinate value, and the third coordinate value of the sampling point, the coordinates of the constituent point of the object at time t configured as a set of each section are specified.

(3) Further, an image generation system, a program, and an information storage medium according to the present invention are:
The component point calculation unit is
Based on the third coordinate value of each sampling point (i, j) of the given section, the other section obtained by dividing n in the θ direction belonging to the same divided area with respect to the given section and the r direction The third coordinate value of each corresponding sampling point (i, j) is obtained.

  According to the present invention, for each section belonging to each concentric circle of donuts divided in the r direction, the value of the sampling point obtained for one section can be reused (the value of y is unchanged). The values of x and z can be obtained by rotation calculation).

  Therefore, it is possible to determine the constituent points of the object of the wave (rotating wave, vortex, etc.) specified in the polar coordinate system with a small calculation load.

(4) Further, an image generation system, a program, and an information storage medium according to the present invention are:
The component point calculation means includes
At least one of the amplitude parameter and the wavelength parameter of the periodic function is changed according to time and a game event.

  In this way, the wavelength parameter and amplitude parameter of the periodic function can be changed to arbitrary values, and the wavelength and amplitude of the wave shape of the object can be variably controlled. As a result, it is possible to change the shape of the object in various ways with a low-load process of simply changing the parameter setting value.

(5) An image generation system, a program, and an information storage medium according to the present invention include
The component point calculation means includes
When changing the direction of the wave represented by the periodic function, the amplitude parameter of the periodic function is changed so that the amplitude of the wave is small, and then the wavelength parameter of the periodic function is changed, and then The amplitude parameter of the periodic function is changed so that the amplitude of the wave is increased.

  In the present invention, when changing the direction of travel of the wave represented by the periodic function, the wavelength parameter of the periodic function is changed after changing the amplitude parameter of the periodic function so that the amplitude of the wave is reduced. Thereafter, the amplitude parameter of the periodic function can be changed so that the amplitude of the wave becomes large.

  By doing this, the wave image of a wave rotating in a given direction gradually decreases in wave height, and changes to a wave rotating in a different direction from the given direction through the saddle state. Can be generated.

  Here, by changing the amplitude parameter of the wave so that the amplitude of the wave approaches 0 at the moment when the direction of the wave changes, the moment when the direction of the wave changes changes to a state like a cocoon (the amplitude is 0 Alternatively, an image that does not feel unnatural due to a change in the direction of the wave can be generated.

(6) An image generation system, a program, and an information storage medium according to the present invention are:
The component point calculation means includes
Wavelength parameters are set so that the traveling direction of the periodic function is different from that of the first periodic function and the wave generated by the first periodic function, and the amplitude is smaller than the amplitude of the wave generated by the first periodic function. A composite function of a plurality of periodic functions including a second periodic function in which the amplitude parameter is set to have
The amplitude parameter of the first periodic function is changed so that the amplitude of the wave generated by the first periodic function is decreased, and at the same time, the second amplitude is increased so that the amplitude of the wave generated by the second periodic function is increased. The amplitude parameter of the periodic function is changed.

  By doing so, the first periodic function and the second periodic function crossfade, and the wave rotating with the first periodic function and the given direction gradually decreases in height. From this state, it is possible to generate an image of a wave that changes into a wave that rotates in a direction different from a given direction.

(7) An image generation system, a program, and an information storage medium according to the present invention include
The component point calculation means includes
The third coordinate value of the sampling point (i, j) at time t is obtained based on a composite function of the periodic function and an offset function having the r-direction coordinate value parameter i as arguments.

  The offset function may be linked to the amplitude.

  According to the present invention, the wave surface tension and undulation can be expressed by appropriately setting the offset function.

  Hereinafter, this embodiment will be described. In addition, this embodiment demonstrated below does not unduly limit the content of this invention described in the claim. In addition, all the configurations described in the present embodiment are not necessarily essential configuration requirements of the present invention.

1. Configuration FIG. 1 shows an example of a functional block diagram of an image generation system (game system) of the present embodiment. Note that the image generation system of the present embodiment may have a configuration in which some of the components (each unit) in FIG. 1 are omitted.

  The operation unit 160 is for a player to input operation data, and the function can be realized by a lever, a button, a steering, a microphone, a touch panel display, a housing, or the like. The storage unit 170 serves as a work area for the processing unit 100, the communication unit 196, and the like, and its function can be realized by a RAM (VRAM) or the like.

  The information storage medium 180 (computer-readable medium) stores programs, data, and the like, and functions as an optical disk (CD, DVD), magneto-optical disk (MO), magnetic disk, hard disk, and magnetic tape. Alternatively, it can be realized by a memory (ROM). The processing unit 100 performs various processes of the present embodiment based on a program (data) stored in the information storage medium 180. That is, the information storage medium 180 stores a program for causing a computer to function as each unit of the present embodiment (a program for causing a computer to execute processing of each unit).

  The display unit 190 outputs an image generated according to the present embodiment, and its function can be realized by a CRT, LCD, touch panel display, HMD (head mounted display), or the like. The sound output unit 192 outputs the sound generated by the present embodiment, and its function can be realized by a speaker, headphones, or the like.

  The portable information storage device 194 stores player personal data, game save data, and the like. Examples of the portable information storage device 194 include a memory card and a portable game device. The communication unit 196 performs various controls for communicating with the outside (for example, a host device or other image generation system), and functions thereof are hardware such as various processors or communication ASICs, programs, and the like. It can be realized by.

  Note that a program (data) for causing a computer to function as each unit of this embodiment is distributed from the information storage medium of the host device (server) to the information storage medium 180 (storage unit 170) via the network and communication unit 196. May be. Use of the information storage medium of such a host device (server) can also be included in the scope of the present invention.

  The processing unit 100 (processor) performs processing such as game processing, image generation processing, or sound generation processing based on operation data and programs from the operation unit 160. Here, as the game process, a process for starting a game when a game start condition is satisfied, a process for advancing the game, a process for placing an object such as a character or a map, a process for displaying an object, and a game result are calculated. There is a process or a process of ending a game when a game end condition is satisfied. The processing unit 100 performs various processes using the storage unit 170 as a work area. The functions of the processing unit 100 can be realized by hardware such as various processors (CPU, DSP, etc.), ASIC (gate array, etc.), and programs.

  The processing unit 100 includes an object space setting unit 110, a movement / motion processing unit 112, a virtual camera control unit 114, a wave object calculation unit 116, a drawing unit 120, and a sound generation unit 130. Note that some of these may be omitted.

  The object space setting unit 110 includes various objects (primitive surfaces such as polygons, free-form surfaces, and subdivision surfaces) representing display objects such as characters, buildings, stadiums, cars, trees, columns, walls, and maps (terrain). (Object) is set in the object space. That is, the position and rotation angle (synonymous with direction and direction) of the object (model object) in the world coordinate system are determined, and the rotation angle (X, Y, Z axis around the position (X, Y, Z)) is determined. Arrange objects at (rotation angle).

  The movement / motion processing unit 112 performs a movement / motion calculation (movement / motion simulation) of an object (such as a character, a ball, a car, or an airplane). That is, an object (moving object) is moved in the object space or an object is moved based on operation data input by the player through the operation unit 160, a program (movement / motion algorithm), various data (motion data), or the like. Perform processing (motion, animation). Specifically, a simulation process for sequentially obtaining object movement information (position, rotation angle, speed, or acceleration) and motion information (position or rotation angle of each part object) every frame (1/60 second). I do. A frame is a unit of time for performing object movement / motion processing (simulation processing) and image generation processing.

  The virtual camera control unit 114 performs a virtual camera (viewpoint) control process for generating an image viewed from a given (arbitrary) viewpoint in the object space. Specifically, a process for controlling the position (X, Y, Z) or the rotation angle (rotation angle about the X, Y, Z axes) of the virtual camera (process for controlling the viewpoint position and the line-of-sight direction) is performed.

  For example, when an object (eg, character, ball, car) is photographed from behind using a virtual camera, the position or rotation angle of the virtual camera (the direction of the virtual camera is set so that the virtual camera follows changes in the position or rotation of the object. ) To control. In this case, the virtual camera can be controlled based on information such as the position, rotation angle, or speed of the object obtained by the movement / motion processing unit 112. Alternatively, the virtual camera may be controlled to rotate at a predetermined rotation angle or to move along a predetermined movement path. In this case, the virtual camera is controlled based on the virtual camera data for specifying the position (movement path) or rotation angle of the virtual camera.

  The wave object calculation unit 116 functions as a composition point calculation unit that obtains coordinates of a component point of an object based on a periodic function that uses coordinates and time of sampling points set to obtain a component point of the object as arguments. .

  The wave object calculation unit 116 calculates sampling points based on the coordinate value parameter i in the r direction and the coordinate parameter j in the θ direction for a given section obtained by dividing the polar coordinate system in m direction in the r direction and n division in the θ direction. (I, j) is set, the first coordinate value and the second coordinate value of the sampling point (i, j) are obtained based on the coordinate value parameter i in the r direction and the coordinate parameter j in the θ direction, and the time t The third coordinate value of the sampling point (i, j) at the time may be obtained based on a periodic function having the coordinate value parameter i in the r direction, the coordinate parameter j in the θ direction, and the time parameter t as arguments. Good.

  In addition, the wave object calculation unit 116 obtains sampling points (corresponding to the coordinate value parameter i in the r direction and the coordinate parameter j in the θ direction) for each section obtained by dividing the polar coordinate system in the r direction and the n direction. i, j) is set, the first coordinate value and the second coordinate value of the sampling point (i, j) are obtained based on the coordinate value parameter i in the r direction and the coordinate parameter j in the θ direction, and at the time t Processing for obtaining the third coordinate value of the sampling point (i, j) based on a coordinate function parameter i in the r direction, a coordinate parameter j in the θ direction, and a time parameter t as arguments may be performed. .

  Further, the wave object calculation unit 116, based on the third coordinate value of each sampling point (i, j) of the given section (sector), the θ direction belonging to the same divided area with respect to the given section and the r direction. The third coordinate value of each sampling point (i, j) corresponding to the other section obtained by dividing into n may be processed.

  Further, the wave object calculation unit 116 may perform a process of changing at least one of the amplitude parameter and the wavelength parameter of the periodic function according to time and a game event.

  In addition, when changing the direction of the wave expressed by the periodic function, the wave object calculation unit 116 changes the amplitude parameter of the periodic function so that the amplitude of the wave becomes small, and then changes the wavelength of the periodic function. You may make it perform the process which changes the amplitude parameter of the said periodic function so that the parameter may be changed and the amplitude of the said wave may become large after that.

  In addition, the wave object calculation unit 116 sets the wavelength parameter so that the traveling direction of the periodic function is different from that of the first periodic function and the wave generated by the first periodic function, and generates the first periodic function using the first periodic function. A composite function of a plurality of periodic functions including a second periodic function in which an amplitude parameter is set to have an amplitude smaller than the amplitude of the generated wave, and the amplitude of the wave generated by the first periodic function is A process of changing the amplitude parameter of the second periodic function so as to increase the amplitude of the wave generated by the second periodic function at the same time as changing the amplitude parameter of the first periodic function so as to be reduced. It may be.

  In addition, the wave object calculation unit 116 performs processing for obtaining the third coordinate value of the sampling point (i, j) at time t based on a composite function of the offset function having the periodic function and the coordinate value parameter i in the r direction. It may be.

  The drawing unit 120 performs drawing processing based on the results of various processing (game processing) performed by the processing unit 100, thereby generating an image and outputting it to the display unit 190. It functions as an image generation unit that generates an image of an object that is specified. In the case of generating a so-called three-dimensional game image, first, geometric processing such as coordinate transformation (world coordinate transformation, camera coordinate transformation), clipping processing, or perspective transformation is performed, and drawing data ( The position coordinates, texture coordinates, color data, normal vector, α value, etc.) of the vertexes of the primitive surface are created. Based on the drawing data (primitive surface data), the object (one or a plurality of primitive surfaces) after perspective transformation (after geometry processing) is stored as image data in units of pixels such as a drawing buffer 172 (frame buffer, intermediate buffer, etc.) Can be drawn in a VRAM). Thereby, an image that can be seen from the virtual camera (given viewpoint) in the object space is generated.

  The drawing unit 120 includes a texture mapping unit. The texture mapping unit performs processing for mapping the texture (texel value) stored in the texture storage unit 174 to the object. Specifically, the texture (surface properties such as color and α value) is read from the texture storage unit 174 using the texture coordinates set (given) at the vertices of the object (primitive surface). Then, a texture that is a two-dimensional image or pattern is mapped to the object. In this case, processing for associating pixels and texels, bilinear interpolation (texel interpolation), and the like are performed.

  The drawing unit 120 can also perform an α blending process (usually α blending, α addition blending, α subtraction blending, or the like) based on an α value (A value), or a hidden surface removal process using a Z buffer or the like.

  The sound generation unit 130 performs sound processing based on the results of various processes performed by the processing unit 100, generates game sounds such as BGM, sound effects, or sounds, and outputs the game sounds to the sound output unit 192.

  Note that the game system of the present embodiment may be a system dedicated to the single player mode in which only one player can play, or may be a system having a multiplayer mode in which a plurality of players can play. Further, when a plurality of players play, game images and game sounds to be provided to the plurality of players may be generated using one terminal, or connected via a network (transmission line, communication line) or the like. Alternatively, it may be generated by distributed processing using a plurality of terminals (game machine, mobile phone).

2. Features and Processing of the Present Embodiment Next, the method of the present embodiment will be described with reference to the drawings.

  In the present embodiment, the shape of an object of a wave rotating on a vortex using a periodic function used when generating a plane wave (a wave in which the height of a constituent point (for example, a vertex) changes periodically at time t) Is identified.

  If the height at the time t of the sampling point (i, j) of the wave mesh for generating a plane wave is y, it can be expressed by the following equation.

  The periodic function is specified as a composite function of a plurality of periodic functions (for example, trigonometric functions) specified by k = 1 to Kmax. The amplitude parameter Ak represents the wave height of the wave component, the wavelength parameter nk represents the wave number (integer) in the i direction and the traveling direction with respect to the i direction component, and the wavelength parameter mk represents the wave number (integer) in the j direction and the traveling direction with respect to the j direction component. Represents.

  FIG. 2 is a diagram for explaining a wave shape in a Cartesian coordinate system (orthogonal coordinate system) generated by a periodic function.

  For example, if the periodic function is configured as a combined function of three periodic functions, a periodic function W0 (210) with k = 0, a periodic function W1 (220) with k = 1, and a periodic function W2 (230) with k = 2. To do.

  A periodic function W0 (210) of k = 0 is a periodic function of a wavelength parameter nk = 0 and a wavelength parameter mk = 1, and represents a wave having only a j-direction component as indicated by 212.

  A periodic function W1 (220) with k = 1 is a periodic function with a wavelength parameter nk = 2 and a wavelength parameter mk = 0, and represents a wave having only an i-direction component as indicated by 222.

  A periodic function W2 (230) of k = 2 is a periodic function of a wavelength parameter nk = 1 and a wavelength parameter mk = 2, and represents a wave having an i-direction component and an i-direction component as indicated by 232.

  A wave 240 is identified by a combined function of three periodic functions: a periodic function W0 (210) having a periodic function k = 0, a periodic function W1 (220) having k = 1, and a periodic function W2 (230) having k = 2. The shape is shown.

  Reference numeral 250 represents a sampling point (i, j) in a Cartesian coordinate system (orthogonal coordinate system). The y coordinate of each sampling point (i, j) is obtained by the above equation (1), and the shape of the wave object as indicated by 240 is specified.

  In the present embodiment, a given section obtained by dividing the y coordinate of the sampling point (i, j) in the Cartesian coordinate system described in FIG. 2 into m in the r direction and n in the θ direction of the polar coordinate system ( By mapping to the corresponding sampling point (i, j) of the sector), a wave rotating in a vortex shape is expressed.

  FIGS. 3A and 3B are diagrams for explaining sections in the polar coordinate system.

  3A in FIG. 3A is divided into m (r = 0, r = 1,..., R = m−1) in the R direction of the polar coordinate system and n (s = 0, s = 1,... S = n−1), and shows a given section (sector) obtained. FIG. 3B shows a Cartesian coordinate system for generating a plane wave.

  The sampling point P (i, j) of a given section (sector) 300-1 in FIG. 3A corresponds to the sampling point P ′ (i, j) in the Cartesian coordinate system of FIG. Yes.

  Here, the first coordinate value (x) and the second coordinate value (z) of the sampling point P (i, j) of a given section (sector) 300-1 are coordinates in the r direction as shown in the following equation. Is set based on the value parameter i and the coordinate parameter j in the θ direction.

  Further, the third coordinate value (y) of the sampling point (i, j) at time t is expressed by Equation (1) (coordinate value in the r direction) in the same manner as the sampling point P ′ (i, j) in the corresponding Cartesian coordinate system. A periodic function having a parameter i and a coordinate parameter j in the θ direction and a time parameter t as arguments).

  Further, based on the third coordinate value (y) of each sampling point (i, j) of the given section (sector) 300-1, it belongs to the same divided area in the r direction with respect to the given section 300-1. A third coordinate value (y) of each sampling point (i, j) corresponding to another section (for example, 300-2, 300-3,...) obtained by dividing n in the θ direction is obtained. May be.

  Specifically, correspondence between the given section 300-1 and other sections (for example, 300-2, 300-3,...) Obtained by dividing n into the θ direction belonging to the same divided area in the r direction. The third coordinate value (y) of each sampling point (i, j) to be set is the same value.

  Each of the samplings corresponding to the other sections (for example, 300-2, 300-3,...) Obtained by dividing n in the θ direction belonging to the same divided area with respect to the given section 300-1 and the r direction. Regarding the first coordinate value (x) and the second coordinate value (z) of the point (i, j), the given section 300-1 and other sections (for example, 300-2, 300-3,. The value rotated according to the angle to ()) can be used.

  By doing in this way, about each division which belongs to each concentric circle of donut shape divided about r direction, it can ask for by reusing the value of the sampling point calculated about one division (about the value of y) It can be used as it is, and the value of xz can be obtained by rotation calculation).

  FIGS. 4A, 4B to 9A, 9B are diagrams for explaining the relationship between the plane wave to be mapped (plane wave in the Cartesian coordinate system) and the rotation of the generated wave.

  Reference numeral 410 in FIG. 4A represents a traveling direction of a plane wave (a plane wave to be mapped (a plane wave in a Cartesian coordinate system) generated by a periodic function of nk = 1 and mk = 1.

  FIG. 4B shows m division (r = 0, r = 1,..., R = m−1) in the R direction of the polar coordinate system, and n division (s = 0, s = 1) in the θ direction. The plane wave (plane wave generated by a periodic function of nk = 1 and mk = 1) in FIG. 4A is mapped to a given section (sector) 420-1 obtained by s = n−1) The traveling direction 430-1 of the wave of time is shown.

  By mapping the plane wave of FIG. 4A (plane wave generated by a periodic function of nk = 1, mk = 1) for all sections, while rotating counterclockwise as shown in FIG. A wave from the center toward the outside can be expressed.

  Reference numeral 411 in FIG. 5A represents a traveling direction of a plane wave (a plane wave to be mapped (a plane wave in a Cartesian coordinate system) generated by a periodic function of nk = 1 and mk = -1.

  FIG. 5B shows m division (r = 0, r = 1,..., R = m−1) in the R direction of the polar coordinate system, and n division (s = 0, s = 1,. Map the plane wave of FIG. 5A (plane wave generated by a periodic function of nk = 1, mk = −1) to a given section (sector) 421-1 obtained by s = n−1) The wave traveling direction 431-1 is shown.

  For all the sections, by mapping the plane wave of FIG. 5A (plane wave generated by a periodic function of nk = 1, mk = −1), while rotating clockwise as shown in FIG. 5B A wave from the center toward the outside can be expressed.

  Reference numeral 412 in FIG. 6A represents a traveling direction of a plane wave (a plane wave to be mapped (a plane wave in a Cartesian coordinate system) generated by a periodic function of nk = −1 and mk = 1.

  FIG. 6B shows m divisions (r = 0, r = 1,... R = m−1) in the R direction of the polar coordinate system, and n divisions (s = 0, s = 1,. Map the plane wave of FIG. 6A (plane wave generated by a periodic function of nk = −1, mk = 1) to a given section (sector) 422-1 obtained by s = n−1) The wave traveling direction 432-1 is shown.

  By mapping the plane wave of FIG. 6A (plane wave generated by a periodic function of nk = −1, mk = 1) for all the sections, it rotates counterclockwise as shown in FIG. 6B. However, it is possible to express waves from the outside to the center.

  Reference numeral 413 in FIG. 7A represents the traveling direction of a plane wave (plane wave to be mapped (plane wave in the Cartesian coordinate system) generated by a periodic function of nk = −1 and mk = −1.

  FIG. 7B shows m divisions (r = 0, r = 1,..., R = m−1) in the R direction of the polar coordinate system, and n divisions (s = 0, s = 1,. A plane wave (plane wave generated by a periodic function of nk = −1 and mk = −1) in FIG. 7A is given to a given section (sector) 423-1 obtained by s = n−1). The wave traveling direction 433-1 when mapped is shown.

  By mapping the plane wave of FIG. 7A (plane wave generated by a periodic function of nk = −1, mk = −1) for all the sections, it rotates clockwise as shown in FIG. 7B. However, it is possible to express waves from the outside to the center.

  Reference numeral 414 in FIG. 8A represents a traveling direction of a plane wave (a plane wave to be mapped (a plane wave in a Cartesian coordinate system) generated by a periodic function of nk = 1 and mk = 0.

  FIG. 8B shows an m division (r = 0, r = 1,..., R = m−1) in the R direction of the polar coordinate system, and an n division (s = 0, s = 1,. A plane wave (plane wave generated by a periodic function of nk = 1, mk = 0) in FIG. 8A is mapped to a given section (sector) 424-1 obtained by s = n−1) The wave traveling direction 434-1 is shown.

  For all sections, a wave traveling outward from the center as shown in FIG. 8B by mapping the plane wave of FIG. 8A (plane wave generated by a periodic function of nk = 1, mk = 0). Can be expressed.

  Reference numeral 415 in FIG. 9A represents a traveling direction of a plane wave (a plane wave to be mapped (a plane wave in a Cartesian coordinate system) generated by a periodic function of nk = 0 and mk = 1.

  In FIG. 9B, m division (r = 0, r = 1,..., R = m−1) in the R direction of the polar coordinate system, and n division (s = 0, s = 1,. A plane wave (plane wave generated by a periodic function of nk = 0, mk = 1) in FIG. 9A is mapped to a given section (sector) 425-1 obtained by s = n−1). The traveling direction 435-1 of the wave of time is shown.

  For all the sections, the plane wave of FIG. 9A (plane wave generated by a periodic function of nk = 0, mk = 1) is mapped to form a concentric circle counterclockwise as shown in FIG. 9B. A rotating wave can be expressed.

  In the present embodiment, various waves can be expressed by changing at least one of the amplitude parameter and the wavelength parameter of the periodic function to be used according to time and a game event.

  For example, a change in the direction of wave rotation can be expressed by changing the amplitude parameter and wavelength parameter of the periodic function used in conjunction with each other.

  FIG. 10 is a diagram for explaining an example of a technique for expressing a change in the rotation direction of a wave.

  FIG. 10 shows the relationship between the temporal change in the parameters of the periodic function and the change in the direction of the wave.

  That is, at time t0, when a wave is generated using a periodic function of nk = 1, mk = 1, Ak = 1, 0, a wave directed from the center to the outward direction in the counterclockwise direction as indicated by 510-1 is generated. Generated.

  And finally, at the time t3, when changing to a wave traveling from the center to the outward direction (a wave rotating in the opposite direction to 510-1) while rotating clockwise as indicated by 510-3, time t0 to t1 After that, the amplitude parameter Ak of the periodic function is changed so that the amplitude of the wave becomes smaller (from 1.0 to 0) (while nk and mk are not changed during this time), and after the wave amplitude becomes 0 (凪State 510-2) At time t2, mk is changed from 1 to -1.

  Then, the amplitude parameter Ak of the periodic function is changed (changes from 0 to 1.0) so that the amplitude of the wave increases from time t2 to time t3 (while nk and mk are not changed).

  As described above, in the present embodiment, when the direction of travel of the wave represented by the periodic function is changed, the periodic function is changed after the amplitude parameter of the periodic function is changed so that the amplitude of the wave is reduced. Then, the amplitude parameter of the periodic function is changed so that the amplitude of the wave increases.

By doing in this way, the wave height gradually decreases from the wave (510-1) that is opposite to the clockwise direction and goes from the center to the outward direction. It is possible to generate an image of a wave that changes to a wave (510-3) that travels outward from the center while rotating to the center.

  Here, by changing the amplitude parameter of the wave so that the amplitude of the wave approaches 0 at the moment when the direction of the wave changes, the moment when the direction of the wave changes changes to a state like a trap (the amplitude is 0). Or, since it is close to 0, it looks like there is no wave), and an image that does not feel unnaturalness due to a change in the direction of the wave can be generated.

  FIG. 11 is a diagram for explaining another example of a technique for expressing a change in the rotation direction of a wave. Here, an example in which the rotation of a wave is changed using a composite function of two periodic functions of k = 0 (periodic function that generates the wave w1) and k = 1 (periodic function that generates the wave w2) will be described.

  FIG. 11 shows the relationship between the temporal change in the parameters of the two periodic functions and the change in the wave direction.

  That is, at time t1, the parameters of the periodic function of k = 0 are nk = 1, mk = 1, Ak = 1, 0, and the parameters of the periodic function of k = 1 are nk = 1, mk = −1, Ak = 0,0. Here, the wave w1 generated by the periodic function of k = 0 is a wave traveling outward from the center while rotating counterclockwise, and the wave w2 generated by the periodic function of k = 1 rotates clockwise. However, at time t1, the amplitude parameter of the periodic function with k = 1 is 0, so that the height difference of the generated wave w2 is 0 and does not affect the synthesis function. . Therefore, at time t1, the wave w1 generated by the periodic function of k = 0 is displayed (520-1).

  At time t3, the parameters of the periodic function of k = 0 are nk = 1, mk = 1, and Ak = 0, and the parameters of the periodic function of k = 1 are nk = 1, mk = −1, Ak = 1, 0. Here, the wave w1 generated by the periodic function of k = 0 is a wave traveling outward from the center while rotating counterclockwise, and the wave w2 generated by the periodic function of k = 1 rotates clockwise. However, at time t3, the amplitude parameter of the periodic function of k = 0 is 0, so that the height difference of the generated wave w1 is 0 and does not affect the synthesis function. . Therefore, at time t3, the wave w2 generated by the periodic function of k = 1 is displayed (520-3).

  At time t1 to t2, the amplitude parameter of the periodic function of k = 0 is decreased toward 0.1 to 0.5 (the amplitude parameter of the periodic function is changed so that the amplitude of the wave is reduced), and k = 1, the amplitude parameter of the periodic function is increased from 0.0 to 0.5 (the amplitude parameter of the periodic function is changed so that the amplitude of the wave is increased).

  Thus, at time t2, the wave w1 generated by the periodic function of k = 0 and the wave w2 generated by the periodic function of k = 1 cancel each other, and the amplitude of the wave becomes 0 (the state of 凪520-2).

  Then, at time t2 to t3, the amplitude parameter of the periodic function of k = 0 is decreased toward 0.5 to 0.0 (the amplitude parameter of the periodic function is changed so that the amplitude of the wave is reduced), The amplitude parameter of the periodic function with k = 1 is increased from 0.5 to 1.0 (the amplitude parameter of the periodic function is changed so that the amplitude of the wave is increased).

By doing in this way, the wave height gradually decreases from the wave (520-1) traveling in the opposite direction to the clockwise direction from the center to the outward direction, and the ridgeline state (520-2) is turned to the clockwise direction. It is possible to generate an image of a wave that changes to a wave (520-3) that travels outward from the center while rotating to the center.

  12 to 14 are wave images generated by the method of the present embodiment.

  FIG. 12 is an image of a wave traveling outward from the center while rotating clockwise around the object 510.

  FIG. 13 is an image of a wrinkle state in which the difference in height of the waves has disappeared.

  FIG. 14 is an image of a wave traveling outward from the center while rotating counterclockwise around the object 510.

  For example, by using the method of the present embodiment described with reference to FIGS. 10 and 11, it is possible to generate a wave image that changes as shown in FIGS. 12 to 13 as time elapses.

  In this embodiment, as described with reference to FIGS. 3A and 3B, the plane wave of the Cartesian coordinate system is mapped to each section in the polar coordinate system. Here, since the section near the center of the wave has a fan shape, the vortex may become unnatural. However, as shown in FIGS. 12 to 14, the center portion can be made more natural by arranging the object at the center of the wave rotation.

  FIGS. 15A and 15B are diagrams for explaining other features of the present embodiment, and show cross-sectional views in the y-axis direction of generated waves.

  The third coordinate value (y) of the sampling point p (i, j) at time t is obtained based on the synthesis function of the offset function Ofset (r) having the periodic function F and the coordinate value parameter i in the r direction. Also good.

  Here, by configuring the offset function Ofset (r) to increase as the absolute value of r increases, the height of the wave increases away from the center 0 in the r direction as shown in FIG. Waves with y rising above the reference plane 610 can be generated.

  Further, by constructing the offset function Ofset (r) so that the value of the offset function Ofset (r) rapidly decreases when the absolute value of r is near 0, a wave that falls into a hole shape near the center 0 is generated as shown in FIG. can do.

  FIG. 16 is a diagram for explaining calculation of an object normal vector whose shape is specified by a sampling point.

When obtaining the normal vector n (i, j) of P1 (i, j) in this embodiment,
First, a vector Z representing a height difference between a vertex P4 (i + 1, j) and a vertex P5 (i-1, j) adjacent to P1 (i, j), and a vertex P3 (i, j, adjacent to P1 (i, j)). j + 1) and vertex P2 (i, j-1) representing a vector X representing the height difference, X and Z outer product Y (i, j) are obtained, and n = Y / | based on outer product Y (i, j) A normal vector is obtained by Y |.

  FIG. 17 is a flowchart showing the processing flow of the present embodiment.

  First, the game is initialized (step S10), and the time parameter t is set to 0 (step S20).

  Next, the following processing is performed for each frame to generate an image including a moving wave (vortex wave) that periodically changes over time.

  First, game processing is performed (step S30), parameters and object arrangement information in the frame are calculated, and viewpoint setting is performed (step S30).

  Next, wave height data at each sampling point is created (step S50).

  Next, the shape of the wave object in the frame (at time tn) is specified based on the wave height data at each sampling point, and a drawing process of a virtual three-dimensional space including what object is performed (step S60).

  Next, the time parameter t is incremented (step S70).

  If the game has not ended, the process returns to step S30, and image generation processing is performed for the next frame (step S80).

  FIG. 18 is a diagram for explaining a detailed processing example of creation of wave height data at each sampling point.

  First, the index parameter i of each sampling point (i, j) is initialized with i = −1 (step S110).

  Next, the index counter i is initialized with i = −1 (step S120).

  Next, the y coordinate of the sampling point (i, j) at time t is calculated using a periodic function as shown in, for example, Expression (1) and stored in the Z coordinate value storage buffer ydata (i) (j) ( Step S130). The Z coordinate value storage buffer ydata (i) (j) stores y coordinate values corresponding to sampling points (i) (j) for one sector. Further, for the purpose of obtaining the normal line, (actually necessary number of vertices + 2) is calculated and stored.

  Next, the index parameter j is incremented (step S140). If j> M + 1 is not satisfied, the process returns to step S130 (step S150).

  If j> M + 1, the index parameter i is incremented (step S160).

  If i> N + 1 is not true, the process returns to step S120. If i> N + 1, the wave height data creation process is terminated (step S170).

  FIG. 19 is a diagram for explaining a detailed processing example of wave object drawing.

  First, the r direction parameter r of a sector (r, s), which is a given section obtained by m division in the r direction of the polar coordinate system and n division in the θ direction, is initialized to r = 0 (step S210).

  Next, the θ direction parameter s is initialized to s = 0 (step S220).

  The index parameter i at the sampling point (i, j) is initialized with i = −1 (step S230).

  Next, the index counter i is initialized with i = −1 (step S240).

  Next, the x and z coordinates of the (i, j) th sampling point of the sector (r, s) are obtained (step S250).

  Next, the (i, j) -th sampling point y-coordinate is obtained from the Z-coordinate value storage buffer ydata (i) (j) (step S260).

Next, an offset value is added to the y coordinate (step S270). The offset value is obtained by, for example, ofset−y (i, r) = (r + i / N) ² .

  Next, the index parameter j is incremented (step S280). If j> M + 1 is not satisfied, the process returns to step S250 (step S290).

  If j> M + 1, the index parameter i is incremented (step S300).

  If i> N + 1 is not satisfied, the process returns to step S240. If i> N + 1 is satisfied, the process proceeds to the next rendering process.

  First, i = 0 is initially set (step S320).

  Next, i = 0 is initially set (step S330).

  Next, as described with reference to FIG. 16, the normal of the sampling point (i, j) is obtained from the difference in height from the adjacent vertex (step S340).

  Next, the luminance, transparency, and texture UV of the sampling point (i, j) are obtained based on the normal information, light source information, and viewpoint information (step S350).

  Next, the index parameter j is incremented (step S360). If j> M is not satisfied, the process returns to step S340 (step S370).

  If j> M, the index parameter i is incremented (step S380).

  If i> N is not true, the process returns to step S330. If i> N + 1, the sampling point (0, 0) to (N, M) is regarded as the vertex of the wave object, rendering processing is performed, and the object is drawn ( Step S400).

  Next, the θ direction parameter s is incremented to s = s + 1 (step S410).

  If not s> n, the process returns to step S230 (step S420).

  If s> n, the r-direction parameter r is incremented to r = r + 1 (step S440).

  If r> m is not satisfied, the process returns to step S220. If r> m is satisfied, the wave object drawing process is terminated (step S440).

3. Hardware Configuration FIG. 20 shows an example of a hardware configuration capable of realizing this embodiment. The main processor 900 operates based on a program stored in a CD 982 (information storage medium), a program downloaded via the communication interface 990, a program stored in the ROM 950, or the like, and includes game processing, image processing, sound processing, and the like. Execute. The coprocessor 902 assists the processing of the main processor 900, and executes matrix operation (vector operation) at high speed. For example, when a matrix calculation process is required for a physical simulation for moving or moving an object, a program operating on the main processor 900 instructs (requests) the process to the coprocessor 902.

  The geometry processor 904 performs geometry processing such as coordinate conversion, perspective conversion, light source calculation, and curved surface generation based on an instruction from a program operating on the main processor 900, and executes matrix calculation at high speed. The data decompression processor 906 performs decoding processing of compressed image data and sound data, and accelerates the decoding processing of the main processor 900. Thereby, a moving image compressed by the MPEG method or the like can be displayed on the opening screen or the game screen.

  The drawing processor 910 executes drawing (rendering) processing of an object composed of primitive surfaces such as polygons and curved surfaces. When drawing an object, the main processor 900 uses the DMA controller 970 to pass the drawing data to the drawing processor 910 and, if necessary, transfers the texture to the texture storage unit 924. Then, the drawing processor 910 draws the object in the frame buffer 922 while performing hidden surface removal using a Z buffer or the like based on the drawing data and texture. The drawing processor 910 also performs α blending (translucent processing), depth cueing, mip mapping, fog processing, bilinear filtering, trilinear filtering, anti-aliasing, shading processing, and the like. When an image for one frame is written in the frame buffer 922, the image is displayed on the display 912.

  The sound processor 930 includes a multi-channel ADPCM sound source and the like, generates game sounds such as BGM, sound effects, and sounds, and outputs them through the speaker 932. Data from the game controller 942 and the memory card 944 is input via the serial interface 940.

  The ROM 950 stores system programs and the like. In the case of an arcade game system, the ROM 950 functions as an information storage medium, and various programs are stored in the ROM 950. A hard disk may be used instead of the ROM 950. The RAM 960 is a work area for various processors. The DMA controller 970 controls DMA transfer between the processor and the memory. The CD drive 980 accesses a CD 982 in which programs, image data, sound data, and the like are stored. The communication interface 990 performs data transfer with the outside via a network (communication line, high-speed serial bus).

  The processing of each unit (each unit) in this embodiment may be realized entirely by hardware, or may be realized by a program stored in an information storage medium or a program distributed via a communication interface. Also good. Alternatively, it may be realized by both hardware and a program.

  When the processing of each part of this embodiment is realized by both hardware and a program, a program for causing the hardware (computer) to function as each part of this embodiment is stored in the information storage medium. More specifically, the program instructs the processors 902, 904, 906, 910, and 930, which are hardware, and passes data if necessary. Each processor 902, 904, 906, 910, 930 realizes the processing of each unit of the present invention based on the instruction and the passed data.

  The present invention is not limited to that described in the above embodiment, and various modifications can be made.

  In the invention according to the dependent claims of the present invention, a part of the constituent features of the dependent claims can be omitted. Moreover, the principal part of the invention according to one independent claim of the present invention can be made dependent on another independent claim.

  Further, the present invention can be applied to various game systems (image generation systems) such as a business game system, a home game system, a large attraction system in which a large number of players participate, a simulator, a multimedia terminal, and a mobile phone.

An example of a functional block diagram of an image generation system (game system) of this embodiment is shown. It is a figure for demonstrating the wave shape in the Cartesian coordinate system (orthogonal coordinate system) produced | generated by a periodic function. FIGS. 3A and 3B are diagrams for explaining sections in the polar coordinate system. 4A and 4B are diagrams for explaining the relationship between the plane wave to be mapped (plane wave in the Cartesian coordinate system) and the rotation of the generated wave. 5A and 5B are diagrams for explaining the relationship between the plane wave to be mapped (plane wave in the Cartesian coordinate system) and the rotation of the generated wave. 6A and 6B are diagrams for explaining the relationship between the plane wave to be mapped (plane wave in the Cartesian coordinate system) and the rotation of the generated wave. FIGS. 7A and 7B are diagrams for explaining the relationship between the plane wave to be mapped (plane wave in the Cartesian coordinate system) and the rotation of the generated wave. 8A and 8B are diagrams for explaining the relationship between the plane wave to be mapped (plane wave in the Cartesian coordinate system) and the rotation of the generated wave. FIGS. 9A and 9B are diagrams for explaining the relationship between the plane wave to be mapped (plane wave in the Cartesian coordinate system) and the rotation of the generated wave. It is a figure for demonstrating an example of the method of expressing the change of the rotation direction of a wave. It is a figure for demonstrating another example of the method of expressing the change of the rotation direction of a wave. It is the image of the wave produced | generated by the method of this Embodiment. It is the image of the wave produced | generated by the method of this Embodiment. It is the image of the wave produced | generated by the method of this Embodiment. FIGS. 15A and 15B are diagrams for explaining other features of the present embodiment. It is a figure for demonstrating calculation of an object normal vector by which a shape is specified by a sampling point. It is a flowchart figure which shows the flow of the process of this Embodiment. It is a figure for demonstrating the detailed process example of preparation of the wave height data in each sampling point. It is a figure for demonstrating the detailed process example of wave object drawing. The example of the hardware constitutions which can realize this embodiment is shown.

Explanation of symbols

100 processing unit, 110 object space setting unit, 112 movement / motion processing unit,
114 virtual camera control unit, 116 wave object calculation unit, 120 drawing unit, 130 sound generation unit, 160 operation unit, 170 storage unit, 172 drawing buffer, 174 texture storage unit, 180 information storage medium, 190 display unit,
192 sound output unit, 194 portable information storage device, 196 communication unit

Claims (9)

A program for generating images,
A component point calculation unit that obtains the coordinates of the constituent points of the object based on a periodic function that takes the coordinates of the sampling points and the time set to obtain the constituent points of the object as arguments;
Causing the computer to function as an image generation unit that generates an image of an object whose shape is specified by the obtained component points;
The component point calculation unit is
A sampling point (i, j) is set based on a coordinate value parameter i in the r direction and a coordinate parameter j in the θ direction for a given section obtained by dividing the polar coordinate system into m in the r direction and n in the θ direction. And
The first coordinate value and the second coordinate value of the sampling point (i, j) are obtained based on the coordinate value parameter i in the r direction and the coordinate parameter j in the θ direction,
Obtaining a third coordinate value of the sampling point (i, j) at time t based on a coordinate function parameter i in the r direction, a coordinate parameter j in the θ direction, and a time function having the time parameter t as arguments;
The image generation unit
Based on the first coordinate value, the second coordinate value, and the third coordinate value of the sampling point, the coordinates of the constituent points of the object at time t configured as a set of a plurality of sections including the given section are specified. The program characterized by doing. In claim 1,
The component point calculation unit is
For each section obtained by dividing the polar coordinate system into m parts in the r direction and n parts in the θ direction,
A sampling point (i, j) is set based on the coordinate value parameter i in the r direction and the coordinate parameter j in the θ direction,
The first coordinate value and the second coordinate value of the sampling point (i, j) are obtained based on the coordinate value parameter i in the r direction and the coordinate parameter j in the θ direction,
Obtaining a third coordinate value of the sampling point (i, j) at time t based on a coordinate function parameter i in the r direction, a coordinate parameter j in the θ direction, and a time function having the time parameter t as arguments;
The image generation unit
A program for specifying coordinates of a constituent point of an object at time t configured as a set of sections based on a first coordinate value, a second coordinate value, and a third coordinate value of a sampling point. In any one of Claims 1 thru | or 2.
The component point calculation unit is
Based on the third coordinate value of each sampling point (i, j) of the given section, the other section obtained by dividing n in the θ direction belonging to the same divided area with respect to the given section and the r direction A program for obtaining a third coordinate value of each sampling point (i, j) corresponding to. In any one of Claims 1 thru | or 3,
The component point calculation unit is
A program for changing at least one of an amplitude parameter and a wavelength parameter of the periodic function according to time and a game event. In any one of Claims 1 thru | or 4,
The component point calculation unit is
When changing the direction of the wave represented by the periodic function, the amplitude parameter of the periodic function is changed so that the amplitude of the wave is small, and then the wavelength parameter of the periodic function is changed, and then A program characterized by changing the amplitude parameter of the periodic function so that the amplitude of the wave is increased. In any one of Claims 1 thru | or 4,
The component point calculation unit is
Wavelength parameters are set so that the traveling direction of the periodic function is different from that of the first periodic function and the wave generated by the first periodic function, and the amplitude is smaller than the amplitude of the wave generated by the first periodic function. A composite function of a plurality of periodic functions including a second periodic function in which the amplitude parameter is set to have
The amplitude parameter of the first periodic function is changed so that the amplitude of the wave generated by the first periodic function is decreased, and at the same time, the second amplitude is increased so that the amplitude of the wave generated by the second periodic function is increased. A program characterized by changing the amplitude parameter of the periodic function. In any one of Claims 1 thru | or 6.
The component point calculation unit is
A program characterized in that a third coordinate value of a sampling point (i, j) at time t is obtained based on a composite function of the periodic function and an offset function having an argument value i in the r direction as an argument. An information storage medium readable by a computer, comprising the program according to claim 1. An image generation system for generating an image,
A component point calculation unit that obtains the coordinates of the constituent points of the object based on a periodic function that takes the coordinates of the sampling points and the time set to obtain the constituent points of the object as arguments;
An image generation unit that generates an image of an object whose shape is specified at the obtained configuration point,
The component point calculation unit is
A sampling point (i, j) is set based on a coordinate value parameter i in the r direction and a coordinate parameter j in the θ direction for a given section obtained by dividing the polar coordinate system into m in the r direction and n in the θ direction. And
The first coordinate value and the second coordinate value of the sampling point (i, j) are obtained based on the coordinate value parameter i in the r direction and the coordinate parameter j in the θ direction,
Obtaining a third coordinate value of the sampling point (i, j) at time t based on a coordinate function parameter i in the r direction, a coordinate parameter j in the θ direction, and a time function having the time parameter t as arguments;
The image generation unit
Based on the first coordinate value, the second coordinate value, and the third coordinate value of the sampling point, the coordinates of the constituent points of the object at time t configured as a set of a plurality of sections including the given section are specified. An image generation system characterized by:

Images