JP2002032790A - Game system and information storage medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a game system capable of realizing the representation of anisotropic reflection with a small quantity of processing burden, and to provide an information storage medium. SOLUTION: A reflection vector at each configuration point of an object is calculated on the basis of light source information and normal information, the direction of the reflection vector is changed into the direction of anisotropic reflection to obtain a 2nd reflection vector, and the shading processing of the object is performed on the basis of the 2nd reflection vector and line of sight information. The reflection vector R is subjected to coordinate transformation to a UVN coordinate system to calculate an RUVN, the direction of the RUVN is changed in the UVN coordinate system to obtain a 2nd reflection vector RUVN2, and the RUVN2 is returned to a world coordinate system to perform shading operation. The U and V axial components of the RUVN are scaled to change the directions of the RUVN. When the object is represented on a free-form surface, the U and V axes are set in the direction of a tangent vector at each configuration point on the free-form surface. Specular representation texture is mapped onto the object on the basis of texture coordinates calculated from the RUVN2.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

[0001] The present invention relates to a game system and an information storage medium.

[0002]

2. Description of the Related Art Conventionally, there has been known a game system for generating an image which can be viewed from a given viewpoint in an object space which is a virtual three-dimensional space. Popular as something you can do. For example, in the case of a game system in which a racing game can be enjoyed, a player operates a car (object) to run in an object space and competes with another player or a car operated by a computer to perform a three-dimensional game. Enjoy.

In such a game system, it is an important technical problem to generate a more realistic and high-quality image in order to improve the virtual reality of the player. Therefore, it is desirable that specular reflection (specular) on the surface of the object can be expressed more realistically.

[0004] As a technique for realizing such specular reflection,
Conventionally, models such as Phong and Blinn have been known. However, these models are all isotropic reflection models, and the intensity distribution of reflected light is isotropic.

On the other hand, if there is a scratch in a certain direction on the surface of the object, the reflected light is affected by the scratch and a phenomenon occurs in which the reflected light is strongly reflected in a specific direction. For example, a phenomenon in which a light and dark pattern peculiar to a knob of an audio device having a concentric scratch is visible, or an "angel ring" is visible in human hair.

In order to express such a specific light and dark pattern, a so-called anisotropic reflection model is required. And about the conventional example of such an anisotropic reflection model,
For example, it is disclosed in "" A Study on Anisotropic Reflection Model ", Takagi and Yokoi et al., Graphics and CAD, 11-1, 1983.10.17".

[0007] For example, assume that the surface of the object has a flaw as shown in FIG. FIG. 1B shows a local point P in FIG. 1A. here,
A normal vector perpendicular to the surface is N, a vector horizontal to the flaw is U, and a vector perpendicular to the flaw is V. Light source L
Let R be a reflection vector at a point P of a light source vector L from S. At this time, the reflection vector R is as shown in the following equation (1).

R = 2 (NL) NL (1) In a general reflection model, specular reflection light (specular reflection) is obtained based on the angle between the reflection vector R and the line-of-sight vector obtained by the above equation (1). Component) is determined.

The Ohira model shown in FIG. 2A is a model of the specular reflection light itself based on the intensity distribution of a flat ellipsoid. That is, the intensity of specular reflected light is obtained based on the length DE up to the point where the line-of-sight vector E intersects the ellipsoid ELP.

On the other hand, in the Takagi-Yokoi model shown in FIG. 2 (B), the fine plane model of Blin is made to have anisotropy, and the distribution of the fine plane is solved by an ellipsoid model.

However, in such Ohira and Takagi / Yokoi models, since an ellipsoidal model is used, it takes a great deal of processing time to calculate the intensity of specular reflected light. Therefore, this model is not suitable for a game system that requires strong real-time processing.

In the Ohira and Takagi-Yokoi models, the intensity of specular reflected light, which is a scalar quantity, is output as a calculation result. Therefore, specular shape (highlight shape)
Cannot be solved by using a so-called specular mapping technique.

In this case, CG of non-real-time processing
The above problem can be solved by calculating the intensity of specular reflection light in pixel units as in (Computer Graphics), but this causes a problem of further increasing the processing time.

SUMMARY OF THE INVENTION The present invention has been made in view of the above problems, and has as its object to provide a game system and an information storage medium capable of realizing the expression of anisotropic reflection with a small processing load. It is in.

[0015]

In order to solve the above problems, the present invention relates to a game system for generating an image, comprising: a reflection vector at each constituent point of an object based on light source information and normal line information. Means for determining the second reflection vector by changing the direction of the reflection vector to the direction of anisotropic reflection, and shading calculation of the object based on the second reflection vector and the viewpoint information. And means for performing the operation. Further, an information storage medium according to the present invention is an information storage medium that can be used by a computer, and includes a program for executing the above means. Further, the program according to the present invention is a program usable by a computer (including a program embodied in a carrier wave), and includes a processing routine for executing the above means.

According to the present invention, light source information (eg, light source vector, light source position) and normal line information (eg, normal vector,
A reflection vector at each component point (for example, a vertex or a primitive point) of the object is obtained based on the information indicating the direction of the surface. By changing this reflection vector in the direction of anisotropic reflection (for example, in the case where it is assumed that the object has a flaw or the like, the direction perpendicular to the flaw), the second reflection vector is changed. Desired. Then, the shading calculation of the object is performed using the second reflection vector.

In this way, according to the present invention, anisotropic reflection can be expressed by a calculation process with a very small load as compared with the conventional method using an ellipsoid model. Therefore, it is possible to construct an anisotropic reflection model optimal for a game system that requires real-time processing.

Further, the game system, the information storage medium and the program according to the present invention convert the reflection vector into a second coordinate system which defines the direction of anisotropic reflection, and convert the reflection vector in the second coordinate system. The second reflection vector is obtained by changing the direction of the reflection vector, and the second reflection vector in the second coordinate system is coordinate-transformed to the first coordinate system. A shading operation of an object is performed based on the second reflection vector.

In this way, for example, in the second coordinate system set for each constituent point, the direction of the reflection vector can be changed by unified processing, and the processing can be simplified.

Further, in the game system, the information storage medium and the program according to the present invention, the second coordinate system may include a first axis representing a direction of anisotropic reflection and a second axis intersecting the first axis.
Wherein the direction of the reflection vector in the second coordinate system is changed to any one of the first and second axes to obtain the second reflection vector. And

According to this configuration, for example, in the second coordinate system set for each constituent point, the direction of the reflection vector is changed to any one of the first and second axes. Anisotropic reflection can be expressed.

The direction of the flaw assumed on the surface of the object may be any one of the first and second axes.

Further, in the game system, the information storage medium and the program according to the present invention, the second coordinate system may include a first axis representing a direction of anisotropic reflection and a second axis intersecting the first axis.
And the component of the first axis of the reflection vector in the second coordinate system is scaled by a first coefficient, and the second component of the reflection vector in the second coordinate system is The second reflection vector is obtained by scaling a component of the second axis by a second coefficient.

By doing so, the first of the reflection vectors,
The second reflection vector can be obtained by a simple process of simply scaling the component of the second axis by the first and second coefficients, and the processing load can be greatly reduced.

Further, in the game system, the information storage medium and the program according to the present invention, the second coordinate system may include a first axis representing a direction of anisotropic reflection and a second axis intersecting the first axis.
When the object is represented by a free-form surface, the first and second axes are set in the directions of the first and second tangent vectors at the respective constituent points of the free-form surface. Features.

In this way, the second coordinate system can be set only by obtaining the first and second tangent vectors at each of the constituent points of the free-form surface by a given calculation formula. Can be simplified. In addition, a tangent vector that needs to be obtained in order to obtain a normal vector can be effectively used for the setting processing of the second coordinate system, and the processing efficiency can be improved.

In the game system, the information storage medium and the program according to the present invention, a normal vector serving as the normal information is obtained based on the first and second tangent vectors. The third of the second coordinate system
Is set.

In this manner, the reflection vector can be obtained by using the normal vector as the normal information, and the tangent vector obtained to obtain the normal vector is determined by the second coordinate system. Can be effectively used for the setting process, and the efficiency of the process can be improved.

Further, the game system, the information storage medium and the program according to the present invention determine the texture coordinates of the specular expression texture based on the second reflection vector, and convert the specular expression texture into an object based on the determined texture coordinates. Is characterized in that

This makes it possible to effectively solve the problem that the specular shape (highlight shape) becomes unnatural due to the influence of the shape of the primitive surface (polygon or the like).

In the game system, the information storage medium and the program according to the present invention, when the direction of the second reflection vector coincides with the direction of the line-of-sight vector, the center of the highlight image drawn on the specular expression texture is adjusted. The reference transformation is performed on the second reflection vector to obtain the texture coordinates.

In this manner, texture coordinates for referring to the specular expression texture can be obtained by a simple process.

[0033]

Preferred embodiments of the present invention will be described below with reference to the drawings.

1. Configuration FIG. 3 shows an example of a functional block diagram of a game system (image generation system) of the present embodiment. In this figure, in the present embodiment, at least the processing unit 100 may be included (or the processing unit 100 and the storage unit 170 may be included).
The other blocks can be optional components.

The operation section 160 is for the player to input operation data, and its function can be realized by hardware such as a lever, a button, a microphone, or a housing.

The storage unit 170 stores the processing unit 100 and the communication unit 1
A work area such as 96
It can be realized by hardware such as.

An information storage medium (storage medium usable by a computer) 180 stores information such as programs and data.
D, DVD), magneto-optical disk (MO), magnetic disk, hard disk, magnetic tape, or memory (RO
M) and the like. Processing unit 10
0 performs various processes of the present invention (the present embodiment) based on the information stored in the information storage medium 180. That is, the information storage medium 180 stores information (program or data) for executing the means (particularly, the blocks included in the processing unit 100) of the present invention (the present embodiment).

Some or all of the information stored in the information storage medium 180 is transferred to the storage unit 170 when the power to the system is turned on. Information storage medium 1
80 includes a program for performing the processing of the present invention, image data, sound data, shape data of a display object, information for instructing the processing of the present invention, information for performing the processing according to the instruction, and the like. Can be made.

The display unit 190 outputs an image generated according to the present embodiment.
LCD or HMD (Head Mount Display)
It can be realized by hardware such as.

The sound output section 192 outputs the sound generated according to the present embodiment, and its function can be realized by hardware such as a speaker.

The portable information storage device 194 stores personal data of a player, save data of a game, and the like. The portable information storage device 194 may be a memory card, a portable game device, or the like. Can be.

The communication unit 196 performs various controls for performing communication with the outside (for example, a host device or another game system), and has a function of various processors or a communication ASIC. This can be realized by hardware, a program, or the like.

A program or data for executing the means of the present invention (this embodiment) is distributed from the information storage medium of the host device (server) to the information storage medium 180 via the network and the communication unit 196. It may be. Use of the information storage medium of such a host device (server) is also included in the scope of the present invention.

The processing section 100 (processor) includes the operation section 1
Various processes such as a game process, an image generation process, and a sound generation process are performed based on the operation data from 60 or a program. The function of the processing unit 100 can be realized by hardware such as various processors (CPU, DSP, etc.) or ASIC (gate array, etc.), or a given program (game program).

Here, the game processing performed by the processing unit 100 includes coin (price) reception processing, various mode setting processing, game progress processing, selection screen setting processing, and objects (one or more primitive planes). Processing for determining the position and rotation angle (rotation angle about the X, Y or Z axis)
Processing to move objects (motion processing); processing to determine the viewpoint position (virtual camera position) and viewing angle (virtual camera rotation angle); processing to place objects such as map objects in object space; hit check processing; A process for calculating a game result (result, performance), a process for a plurality of players to play in a common game space, a game over process, and the like can be considered.

Further, the processing section 100 generates an image that can be viewed from a given viewpoint (virtual camera) in the object space, for example, based on the result of the game processing, and outputs the generated image to the display section 190.

Further, the processing section 100 performs various kinds of sound processing based on the results of the game processing, and performs BGM, sound effects,
Alternatively, a sound such as voice is generated and output to the sound output unit 192.

Note that all of the functions of the processing unit 100 may be realized by hardware, or all of the functions may be realized by a program. Alternatively, it may be realized by both hardware and a program.

The processing unit 100 includes a reflection vector calculation unit 11
0, a reflection vector changing unit 112, a shading calculation unit 114, and a drawing unit 130.

Here, the reflection vector calculation unit 110 calculates each component point of the object based on light source information (light source position, light source vector, etc.) and normal line information (normal vector, information indicating the direction of a surface, etc.). Find the reflection vector at (vertex, primitive point, etc.).

The reflection vector changing unit 112 changes the direction of the reflection vector obtained by the reflection vector calculation unit 110 to the direction of anisotropic reflection (the direction specified by the direction of the flaw), and performs the second reflection. Find a vector. More specifically, the reflection vector is coordinate-transformed from a first coordinate system (for example, a world coordinate system) to a second coordinate system that defines the direction of anisotropic reflection. Next, a second reflection vector is obtained by changing the direction of the reflection vector in the second coordinate system. Then, the second reflection vector in the second coordinate system is coordinate-converted back to the first coordinate system.

The shading calculation unit 114 calculates the second reflection vector obtained by the reflection vector changing unit 112,
Based on viewpoint information (viewpoint position, gaze vector, etc.)
Performs shading operations on objects. The shading calculation in this case is based on the angle (luminance) of the specular reflected light based on the angle between the second reflection vector and the line-of-sight vector.
May be realized by Phong's model, or Blin, which considers the surface of an object as a set of micro-planes
It may be realized by the model of n). Alternatively, texture coordinates may be obtained based on the second reflection vector, and specular mapping may be realized by mapping a specular expression texture to an object based on the texture coordinates.

The drawing unit 130 performs geometry processing (coordinate conversion, clipping processing, perspective conversion, light source calculation, etc.)
A process of drawing an image of the subsequent object (one or more primitive surfaces) in a drawing area 174 (an area where image information can be stored in pixel units such as a frame buffer and a work buffer) is performed.

The drawing data (position coordinates, texture coordinates, color (luminance) data, normal vector, α value, etc.) given to the constituent points after the geometry processing are stored in the main storage unit 172. The drawing unit 130 performs a drawing process based on the drawing data (polygon data).

The texture mapping unit 132 included in the drawing unit 130 performs a process for mapping the texture stored in the texture storage unit 176 to the object.

For example, when performing specular mapping, texture coordinates are obtained based on the second reflection vector obtained by the reflection vector changing unit 112, and the texture coordinates are determined for each constituent point (vertex) of the object. Granted. Then, the texture mapping unit 132
Reads a specular expression texture (for example, a texture on which a highlight image to be mapped is drawn) specified by texture coordinates assigned to each constituent point from the texture storage unit 176 and maps the texture onto an object.

It should be noted that the game system according to the present embodiment
The system may be a system dedicated to the single player mode in which only one player can play, or a system having not only such a single player mode but also a multi-player mode in which a plurality of players can play.

When a plurality of players play,
The game image and the game sound to be provided to the plurality of players may be generated using one terminal, or may be generated using a plurality of terminals (game machine, mobile phone, etc.) connected via a network (transmission line, communication line) or the like. ) May be generated.

2. 2. Features of the Present Embodiment 2.1 Expression of Anisotropic Reflection by Changing Direction of Reflection Vector The surface of an object having the property of anisotropic reflection is considered to be damaged in a specific direction. Due to the presence of the flaw, much of the light incident on the surface of the object is reflected in a direction perpendicular to the direction of the flaw. Therefore, if the direction of the reflection vector on the surface of the object having no flaw can be changed to a direction considering the flaw on the surface of the object, an anisotropic reflection model can be constructed.

Therefore, in this embodiment, first, FIG.
, The light source vector from the light source LS is L,
Assuming that the normal vector perpendicular to the surface is N, the reflection vector R at each component point (vertex, primitive point, etc.) of the object is obtained as in the following equation (2). That is, the reflection vector R is obtained based on the light source information (L) and the normal line information (N).

R = 2 (NL) NL (2) In FIG. 4A, the scratch on the surface of the object occurs in either the U-axis direction or the V-axis direction. It is assumed that

In this embodiment, the reflection vector R obtained by the above equation (2) is changed in the direction of anisotropic reflection as shown in FIG.
Is obtained.

More specifically, the direction of the wound is U-axis (first,
If it is assumed that the direction is one of the second axes (as one of the second axes), the direction of the reflection vector R is changed toward the V axis (by rotating it) as shown in FIG. ) To obtain a reflection vector R2. This makes it possible to uniformly change the direction of the reflection vector at each component point of the object toward the V axis perpendicular to the flaw.

On the other hand, when it is assumed that the direction of the flaw is the direction of the V axis (the other of the first and second axes), the reflection vector R is opposite to that of FIG. Is changed (rotated) toward the U axis to obtain a reflection vector R2.
In this way, the direction of the reflection vector at each component point of the object can be uniformly changed toward the U-axis perpendicular to the flaw.

In this embodiment, shading calculation is performed using the reflection vector R2 obtained as described above, and the intensity (luminance) of specular reflection light at each component point of the object is obtained.

For example, when a phone model is used, the angle between the reflection vector R2 and the line-of-sight vector is θ
Is calculated, P _S × COS ⁿ θ is calculated, and the intensity of the specular reflected light is obtained. Incidentally, P _S is the specular coefficient (maximum coefficient of specular component), n is the coefficient of power. By changing n, the extent of the highlight can be controlled.

When the Brin model is used, an intermediate vector between the reflection vector R2 and the light source vector L is obtained, and the intensity of the specular reflected light may be obtained based on the intermediate vector and the line-of-sight vector.

By calculating the intensity of the specular reflected light as described above, in the present embodiment, the expression of the anisotropic reflection of the reflected light on the surface of the object is realized with a small processing load. This makes it possible to generate an image such as a unique light / dark pattern (brush effect) visible on the surface of the knob of the audio device or an “angel ring” (hairline effect) that looks like human hair with a small processing load.

The process of changing the direction of the reflection vector is as follows:
More specifically, it can be realized by the following method.

(I) First, as shown in FIG.
Based on the calculation of the above, each constituent point (vertex) of the object OB
Is obtained in the world coordinate system (XW, YW, ZW).

(II) Next, as shown by A1 in FIG. 5, the reflection vector R (RX, RY, RZ) is converted from the world coordinate system (first coordinate system) to the UVN coordinate system (second coordinate system). ) Is converted to a reflection vector RUVN in the UVN coordinate system.
(RU, RN, RV). This coordinate conversion can be realized, for example, by the following equation (3).

[0072]

(Equation 1) Here, one of the U axis and the V axis of the UVN coordinate system is an axis representing the direction of a flaw at each component point, and the other axis of the U axis and the V axis is an axis orthogonal to the one axis. It is. Then, (UX, UY, UZ) in the above equation (3) is a unit vector in the U-axis direction, and (VX, VY, VZ) is a unit vector in the V-axis direction. Further, the N axis is an axis set in the direction of the normal vector, and (NX, NY, NZ) in the above equation (3).
Is a unit vector in the N-axis direction.

The U axis and the V axis do not have to be orthogonal to each other, but may be any axes that intersect each other. Also, the N axis need not be the axis in the direction of the normal vector, and may be any axis that intersects the U axis and the V axis.

(III) Next, as shown at A2 in FIG.
In the UVN coordinate system, the reflection vector RUVN (RU, R
N, RV) to change the reflection vector R2UV.
N (R2U, R2N, R2V) is obtained. This can be obtained, for example, by the following equation (4).

[0075]

(Equation 2) Here, CU is a scaling factor in the U-axis component,
CV is a scaling coefficient in the V-axis direction.

(IV) Next, as shown at A3 in FIG. 5, the reflection vector R2UVN (R2U, R2N, R2V) is
The coordinates are converted from the UVN coordinate system to the world coordinate system, and the reflection vector R2 (R2X, R2Y, R2) in the world coordinate system is converted.
2Z). This can be obtained, for example, by the following equation (5).

[0077]

(Equation 3) As described above, in the present embodiment, the UVN coordinate system that defines the direction of anisotropic reflection is set, and the reflection vector RUVN is changed in this UVN coordinate system to change the reflection vector R2U.
VN is calculated. By doing so, the U-axis component RU of the reflection vector RUVN is calculated as in the above equation (4).
Is scaled by a coefficient CU, and the V-axis component RV is
The reflection vector RUVN can be obtained by changing the reflection vector RUVN in the direction of anisotropic reflection by a very simple process of only scaling with R.

For example, when the direction of the flaw is set in the U-axis direction, the scaling coefficient CU in the U-axis direction may be made smaller than 1.0, as shown in FIG. For example, in FIG. 6A, CU = 0.5 and CV = 2.0. By doing so, the reflection vector changes in the direction of the V axis, which is the direction perpendicular to the flaw, so that anisotropic reflection can be expressed.

On the other hand, when the direction of the flaw is set in the V-axis direction, the scaling coefficient CV in the V-axis direction may be made smaller than 1.0, as shown in FIG. For example, in FIG. 6B, CU = 2.0 and CV = 0.5. By doing so, the reflection vector changes in the direction of the U-axis, which is the direction perpendicular to the flaw, and anisotropic reflection can be expressed.

The method of changing the direction of the reflection vector using the scaling coefficient is based on the premise that the direction of the reflection vector does not change beyond the quadrant.

In FIGS. 6A and 6B, the direction of the reflection vector RUVN is changed by using the scaling coefficients CU and CV. A changing method may be adopted. However, this method has a disadvantage of increasing the processing load because it requires a process of rotating the reflection vector and a process of controlling the direction of the reflection vector so as not to change beyond the quadrant.

On the other hand, the method of changing the direction of the reflection vector by the scaling coefficient only requires multiplying each component of the reflection vector by the scaling coefficient.
Since there is no need to perform processing for controlling the direction of the reflection vector so as not to change beyond the quadrant, there is an advantage that the processing load is very light.

FIG. 7A is an example of a generated image in a case where the normal shading processing is performed on the object OB without performing the anisotropic reflection processing. When the anisotropic reflection processing is not performed, the intensity distribution of the reflected light is isotropic, and thus a highlight having a normal shape is generated on the surface of the object OB.

FIG. 7B is an example of a generated image when anisotropic reflection is expressed using a conventional ellipsoid model. FIG.
In (B), it is assumed that there is a concentric scratch on the upper surface of the object OB, and a highlight image expressing a brush effect is generated.

FIG. 7C shows an example of a generated image when anisotropic reflection is expressed by the method of the present embodiment. In FIG. 7C, the scaling coefficients described in FIGS. 6A and 6B are set to CU = 0.5 and CV = 2.0. Thereby, it is possible to generate a highlight image of the brush effect that appears when there is a concentric scratch on the upper surface of the object OB.

FIG. 8A is an example of a generated image when anisotropic reflection is expressed using a conventional ellipsoid model. FIG.
In (A), it is assumed that there is a flaw radially from the center of the object OB, and a highlight image expressing a hairline effect (an angel ring of hair) is generated.

FIG. 8B shows an example of a generated image when anisotropic reflection is expressed by the method of the present embodiment. In FIG. 8 (B), the scaling coefficient is CU = 2.0, CV
= 0.5. Thereby, it is possible to generate a highlight image of the hairline effect that appears when there is a scratch radially from the center of the object OB.

FIGS. 9A to 9D and FIGS.
(D) shows an object O generated according to the present embodiment when the scaling coefficients CU and CV are gradually changed.
4 shows an example of an image of B.

In FIG. 9A, CU = 0.5, CV =
It is set to 2.0. And FIG. 9 (B),
(C), (D), FIGS. 10 (A), (B), (C),
In (D), the CU increases by 0.2 and the CV decreases by 0.2. In FIG. 9A, a highlight image of the brush effect is generated, and in FIG. 10D, a highlight image of the hairline effect is generated.

As described above, according to the present embodiment, the direction of the flaw assumed on the surface of the object can be arbitrarily controlled only by changing the values of the scaling coefficients CU and CV to desired values, and the brush effect and the hairline can be controlled. Various highlight images such as effects have been successfully generated.

2.2 Use of Free-Form Surface Next, a case where an object is represented by a free-form surface will be described. If the object is represented by a free-form surface, the UVN coordinate system described with reference to FIG. 5 can be set by simple processing.

P ^x uv (u, v), which is the x component of the constituent point Puv (u, v) of the free-form surface, is obtained by the following equation (6).

[0093]

(Equation 4) The y component and z component of Puv (u, v) can also be obtained by the same equation as the above equation (6).

When rationalization is performed, the following equation (7) is used.
become that way.

[0095]

(Equation 5) In the above equations (6) and (7), Q _{00 to} Q ₃₃ are control points.

Nu _{0,4 to} Nu _3,4 , Nv _{0,4 to} Nv _3,4
Is a blending function. These blending functions are
The recurrence formula (DeBoorCox)
And the knot vectors TU, T of the following equation (10):
V.

[0097]

(Equation 6)

[0098]

(Equation 7) The knot vector is a vector that gives a parameter node as a sequence of numerical values. When the knot interval of the knot vector (the numerical difference between adjacent elements of the knot vector) is constant, it is called a uniform. When the knot interval is not constant, the non-uniform (Non-uniform) is used.
Uniform).

A non-uniform, Rationalized B-spline is represented by NURBS
(Non Uniform Rational B-Spline).

FIG. 11 shows an example of a surface patch 20 (free-form surface) generated according to the present embodiment.

As is apparent from the above equations (6) and (7), each constituent point of the curved surface patch 20 is composed of control points Q _{00 to} Q ₃₃ and a combination function Nu _{0,4 to} Nu _3,4 , Nv _{0. ,} it obtained based on 4 ~Nv _3,4. In this case, the domain of the parameter u is u
₃ ≦ u <u ₄ , and the domain of the parameter v is v ₃ ≦ v <v ₄
become.

On the other hand, when the curved surface patch 22 is generated, the set of control points to be used is from Q _{00 to} Q ₃₃ to Q ₀₁ to Q ₀₁ .
It changes to Q _34. And each constituent point of the curved surface patch 22 is:
Control points Q _{01 to} Q ₃₄ and mixing functions Nu _{1,4 to} Nu _4,4 ,
It is determined based on Nv _{0,4 to} Nv _3,4 . In this case, the range of the parameter u is u ₄ ≦ u <u ₅ , and the range of the parameter v is v ₃ ≦ v <v ₄ .

A surface patch 2 generated according to the present embodiment
Each component point of 0 is set to a vertex of the polygon, and the polygon constituted by these vertices is displayed on the screen.

FIG. 12 shows an example of an image of an object OB (wire frame display) represented by a free-form surface (NURBS). By controlling the number of divisions of the curved surface, the precision of the object OB can be changed.

When an object is represented by a free-form surface, a tangent (inclination) vector of the surface can be easily obtained.

For example, in FIG.
The x component of the tangent vector UVEC in the direction can be obtained by calculating the following equation (11). The same applies to the y component and the z component.

[0107]

(Equation 8) Further, the x component of the tangent vector VVEC in the v direction can be obtained by calculating the following equation (12). The same applies to the y component and the z component.

[0108]

(Equation 9) Note that the above equations (12) and (13) are equations in the case where rationalization is not performed, but can be similarly calculated when rationalization is performed.

By calculating the cross product of the tangent vectors UVEC and VVEC obtained by the above equations (12) and (13), the normal vector N at the constituent point P is obtained as shown in FIG. Can be.

Then, the U axis of the UVN coordinate system described in FIG. 5 is set in the direction of the tangent vector UVEC, the V axis of the UVN coordinate system is set in the direction of the tangent vector VVEC, and the UVN is set in the direction of the normal vector N. Set the N axis of the coordinate system.

In this way, a UVN coordinate system as shown in FIG. 5 can be set for each constituent point of the object. Then, by changing the direction of the reflection vector in the UVN coordinate system set for each of the constituent points as indicated by A2 in FIG. 5, anisotropic reflection can be expressed.

As described above, when the object is represented by a free-form surface, there is an advantage that the UVN coordinate system for changing the reflection vector can be set by relatively simple processing.

Further, the tangent vectors UVEC and VVEC obtained to obtain the normal vector N can be effectively used for the setting processing of the UVN coordinate system, and the processing efficiency can be improved.

It should be noted that even when the object is represented by polygons, the UVN coordinate system can be set, for example, by the following method.

For example, in FIG.
B (OB1, OB2 or OB3) in the local coordinate system (X
(L, YL, ZL), a circle centering on the YL axis and passing through each constituent point (vertex) of the object OB is assumed, and the U axis is set in the direction of the tangent vector UVEC of this circle. Then, the direction of the V-axis is obtained by calculating the cross product of the tangent vector UVEC and the normal vector given to each component point. By doing so, a UVN coordinate system can be set for each constituent point (vertex) of the object OB.

According to this method, as shown in FIG. 14B, anisotropic reflection on a metal plate or the like damaged in a certain direction (the direction of the tangent vector UVEC or the direction perpendicular to the UVEC) is prevented. Be able to express.

2.3 Specular Mapping The reflection vector R obtained from FIG.
2 is desirably realized by so-called specular mapping. In a phone model or the like that calculates the intensity of specular reflection based on the angle between the reflection vector R2 and the line-of-sight vector, the specular shape (highlight shape) becomes unnatural due to the influence of the polygon (primitive surface in a broad sense). This is because there is a case where the problem of

However, in the Ohira and Takagi / Yokoi models described above, the intensity of specular reflection light, which is a scalar quantity, is output as a calculation result. Therefore, the problem that the specular shape becomes unnatural due to the influence of the polygon shape,
It cannot be solved by the so-called specular mapping technique.

In this case, if the intensity of the specular reflected light is calculated in pixel units as in non-real-time processing CG,
The problem that the specular shape depends on the polygon shape can be solved. However, this solution
This is impractical in a game system that requires real-time processing.

On the other hand, in the present embodiment, the reflection vector R2 is obtained as in the above equation (5) instead of the scalar amount. Therefore, if the texture coordinates are obtained based on the reflection vector R2 and the specular expression texture is mapped to the object based on the texture coordinates, the specular mapping can be realized.

More specifically, for example, a specular expression texture as shown in FIG. 15A is prepared. In addition,
This specular expression texture may be generated in real time.

In the specular expression texture shown in FIG. 15A, for example, a white highlight (light source)
The image is drawn, and the brightness gradually decreases from the center to the periphery and changes to black. It is desirable to deform the shape of the highlight image drawn on the specular expression texture so that the highlight image after the final polar coordinate transformation described later has a desired appropriate shape.

With the specular expression texture shown in FIG. 15A, the virtual sphere 3 shown in FIG.
Assume 0.

Then, as shown in FIG. 16, the virtual sphere 30 is set so as to include the object OB. Next, a reflection vector at the constituent point P is obtained based on the light source vector L, and a reflection vector R2 considering anisotropic reflection is obtained from the reflection vector by the method of the present embodiment. And
By obtaining the intersection PR between the reflection vector R2 and the virtual sphere 30, the texture coordinates TX and TY (coordinate values) of the specular expression texture are obtained.
X and TY are set to the constituent points P.

Then, based on the texture coordinates TX and TY set for each constituent point in this way, FIG.
The specular expression texture shown in (A) is mapped to the object OB to realize specular mapping.

In this way, since the specular shape (highlight shape) is not affected by the polygon shape, a more natural and realistic image can be generated.

[0127] 3. Next, a detailed example of the processing of the present embodiment will be described with reference to the flowcharts of FIGS.

First, PN (number of a constituent point) is set to 0 (step S1).

Next, the tangent vectors UVEC and VVEC at the constituent points (vertexes) PN are obtained based on the above equations (11) and (12) (step S2).

Next, as described with reference to FIG. 13, the cross product of the tangent vectors UVEC and VVEC is calculated to obtain the normal vector N (step S3).

Next, a reflection vector R is obtained based on the light source information, the position of the constituent point PN, and the normal vector N at the constituent point PN (step S4). For example, in the case of a point light source, a vector connecting the light source position and the position of the constituent point PN is shown in FIG.
And a reflection vector R is determined based on the light source vector L and the normal vector N. On the other hand, in the case of a parallel light source, the reflection vector R is obtained based on the light source vector L from the parallel light source and the normal vector N.

Next, as described in A1 of FIG. 5, the world coordinate system is changed from the UVN coordinate system (UVEC, VVEC, N
Coordinate transformation of the reflection vector R into a coordinate system
RUVN is obtained (step S5).

Next, as described with reference to A2 in FIG.
In the N coordinate system, scaling calculation is performed on RUVN based on coefficients CU and CV representing the directions of anisotropic reflection to obtain a reflection vector R2UVN (step S2).
6).

Next, as described with reference to A3 in FIG.
VN is transformed into a world coordinate system, and a reflection vector R2
Is obtained (step S7).

Next, the angle θ between R2 and the line-of-sight vector
Based on, for example, performs the computation of P _S × COS ⁿ θ, obtains the intensity of the specular reflection light in the configuration point PN (step S8).

Next, it is determined whether or not PN is larger than PEND. If smaller than PEND, PN is incremented by 1 (step S10), and step S2 is performed.
Return to On the other hand, if it is larger than PEND, the process ends.

FIG. 18 is a flowchart in the case of performing specular mapping. When specular mapping is performed, in step S8 in FIG.
Will be performed.

First, when the center of the object is set to the center of the virtual sphere, the direction connecting the center of the object and the center of the highlight image on the virtual sphere (the center of the map) is
A matrix M that matches the direction of the line-of-sight vector is obtained (step S11).

That is, as shown in FIG. 19A, the virtual sphere 30 whose center coincides with the center of the object OB.
Is assumed. Then, for example, when a line-of-sight vector heading toward the viewpoint VP in the XYZ coordinate system set for the object (may be set for each constituent point) is E,
As shown in FIGS. 19B and 19C, the line-of-sight vector E ′
Is assumed to be in the X'Y'Z 'coordinate system in which the direction of. Then, the above-described matrix M is a matrix that converts the line-of-sight vector E ′ into E as in the following Expression (13).

E = M × E ′ (13) From the above equation (13), E ′ = M ⁻¹ × E (14) In the above equation (14), M ⁻¹ is an inverse transformation matrix of M.

Then, based on the inverse transformation matrix M- ¹ , the reflection vector R2 is converted as shown in the following equation (15) to obtain a reflection vector R2 '(step S12).

R2 ′ = M ⁻¹ × R2 (15) Next, as shown in FIG. 19D, the reflection vector R2 ′
Is converted to polar coordinates to obtain texture coordinates TX and TY (step S13).

That is, as shown in FIG. 19D, a vector obtained by projecting the reflection vector R2 ′ onto the X′Z ′ plane is represented by R
2 ″, and the angle between R2 ″ and the X ′ axis is θ1 (degree). The angle between the reflection vector R2 ′ and the Y ′ axis is θ
2 (degrees). In this case, the texture coordinates TX and TY can be obtained as in the following equation (16).

TX = θ1 / 360 TY = θ2 / 180 (16) For example, in the above equation (16), θ1 = 180 (degrees), θ
When 2 = 90 (degrees), as is clear from FIG. 19D, the direction of the reflection vector R2 ′ matches the direction of the line-of-sight vector E ′. The texture coordinates at this time are TX = 0.5, TY = 0.5, and the center of the highlight image of the specular expression texture (the center of the map) is referred to. That is, it can be said that the conversion of the above equation (15) is such that when the direction of the reflection vector matches the direction of the line-of-sight vector, the center of the highlight image of the specular expression texture is referred to.

Finally, the obtained texture coordinates TX,
TY is assigned to the constituent point PN (vertex) (step S1)
4). Using these texture coordinates TX and TY, FIG.
The so-called specular mapping can be realized by mapping the specular expression texture as shown in FIG.

[0146] 4. Hardware Configuration Next, an example of a hardware configuration capable of realizing the present embodiment will be described with reference to FIG.

The main processor 900 has a CD982
(Information storage medium), a program transferred via the communication interface 990, or a program stored in the ROM 950 (one of the information storage media).
Various processes such as sound processing are executed.

The coprocessor 902 assists the processing of the main processor 900, has a multiply-accumulate unit and a divider capable of high-speed parallel operation, and executes a matrix operation (vector operation) at high speed. For example, when a physical simulation for moving or moving an object requires processing such as matrix operation, a program operating on the main processor 900 instructs the coprocessor 902 to perform the processing (request ).

The geometry processor 904 performs geometry processing such as coordinate transformation, perspective transformation, light source calculation, and curved surface generation. The geometry processor 904 includes a multiply-accumulate unit and a divider capable of high-speed parallel computation, and performs a matrix computation (vector Calculation) at high speed. For example, when performing processing such as coordinate transformation, perspective transformation, and light source calculation, a program operating on the main processor 900 instructs the geometry processor 904 to perform the processing.

The data decompression processor 906 performs a decoding process for decompressing the compressed image data and sound data, and performs a process for accelerating the decoding process of the main processor 900. As a result, a moving image compressed by the MPEG method or the like can be displayed on an opening screen, an intermission screen, an ending screen, a game screen, or the like. The image data and sound data to be decoded are stored in the ROM 950,
It is stored on a CD 982 or transferred from outside via a communication interface 990.

The drawing processor 910 executes a high-speed drawing (rendering) process of an object composed of primitive surfaces such as polygons and curved surfaces. When drawing an object, the main processor 900
Uses the function of the DMA controller 970 to pass object data to the drawing processor 910,
If necessary, the texture is transferred to the texture storage unit 924. Then, the drawing processor 910 draws the object in the frame buffer 922 at high speed while performing hidden surface removal using a Z buffer or the like based on the object data and the texture. The drawing processor 910 can also perform α blending (translucent processing), depth queuing, mip mapping, fog processing, bilinear filtering, trilinear filtering, anti-aliasing, shading processing, and the like. Then, when an image for one frame is written to 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, and generates high-quality game sounds such as BGM, sound effects, and voices. The generated game sound is output from the speaker 932.

Operation data from the game controller 942, save data and personal data from the memory card 944 are transferred via the serial interface 940.

A ROM 950 stores a system program and the like. In the case of the arcade game system, the ROM 950 functions as an information storage medium,
Various programs are stored in 950. Note that a hard disk may be used instead of the ROM 950.

The RAM 960 is used as a work area for various processors.

[0156] The DMA controller 970 provides a DM between the processor and the memory (RAM, VRAM, ROM, etc.).
A transfer is controlled.

A CD drive 980 stores a CD 982 in which programs, image data, sound data, and the like are stored.
(Information storage medium) to enable access to these programs and data.

[0158] The communication interface 990 is an interface for transferring data to and from the outside via a network. In this case, a network connected to the communication interface 990 may be a communication line (analog telephone line, ISDN), a high-speed serial bus, or the like. Then, data can be transferred via the Internet by using a communication line. Further, by using the high-speed serial bus, data transfer with another game system becomes possible.

It is to be noted that each means of the present invention may be entirely executed only by hardware, or executed only by a program stored in an information storage medium or a program distributed via a communication interface. Is also good. Alternatively, it may be executed by both hardware and a program.

When each means of the present invention is executed by both hardware and a program, a program for executing each means of the present invention using hardware is stored in the information storage medium. Will be. More specifically, the program instructs the processors 902, 904, 906, 910, 930, etc., which are hardware, to perform processing, and passes data if necessary. Then, each processor 902, 904, 906, 910,
930, etc., based on the instruction and the passed data,
Each means of the present invention will be executed.

FIG. 21A shows an example in which the present embodiment is applied to an arcade game system. The player enjoys the game by operating the lever 1102, the button 1104, and the like while watching the game image projected on the display 1100. Various processors, various memories, and the like are mounted on a built-in system board (circuit board) 1106. Information (program or data) for executing each unit of the present invention is stored in a memory 1108 which is an information storage medium on the system board 1106. Hereinafter, this information is referred to as storage information.

FIG. 21B shows an example in which the present embodiment is applied to a home game system. The player enjoys the game by operating the game controllers 1202 and 1204 while watching the game image projected on the display 1200. In this case, the storage information is stored in a CD 1206 or a memory card 1208, 1209, which is an information storage medium detachable from the main system.

FIG. 21C shows a host device 1300,
The host device 1300 and the network 1302 (LA
N or a wide area network such as the Internet).
An example in which the present embodiment is applied to a system including 4-1 to 1304-n (game machine, mobile phone) will be described. In this case, the storage information is stored in an information storage medium 1306 such as a magnetic disk device, a magnetic tape device, or a memory that can be controlled by the host device 1300. Terminal 1304
If -1 to 1304-n are capable of generating a game image and a game sound in a stand-alone manner, the host device 13
From 00, game images and game programs for generating game sounds are delivered to the terminals 1304-1 to 1304-n. On the other hand, if it cannot be generated stand-alone, the host device 1300 generates a game image and game sound, transmits them to the terminals 1304-1 to 1304-n, and outputs them.

In the case of the configuration shown in FIG. 21C, each means of the present invention may be executed in a distributed manner between a host device (server) and a terminal. Further, the storage information for executing each means of the present invention may be stored separately in an information storage medium of a host device (server) and an information storage medium of a terminal.

The terminal connected to the network may be a home game system or an arcade game system. When the arcade game system is connected to a network, a save information storage device capable of exchanging information with the arcade game system and exchanging information with the home game system. (Memory card, portable game device) is desirable.

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

For example, in the invention according to the dependent claims of the present invention, a configuration in which some of the constituent elements of the dependent claims are omitted may be adopted. In addition, a main part of the invention according to one independent claim of the present invention may be made dependent on another independent claim.

As a method of changing the direction of the reflection vector, the method described with reference to FIG. 5 is particularly desirable from the viewpoint of simplification of processing. However, the present invention is not limited to this, and various modifications can be made. .

The method of setting the second coordinate system is not limited to the method described with reference to FIGS. 13, 14A and 14B.

Also, the intensity (luminance) of the specular reflection light obtained by the shading operation is set to an α value (information stored in association with each pixel and information of plus alpha other than the color information). Α synthesis based on the value (α
Blending, α addition) may be performed to express, for example, a state in which reflected light is anisotropically reflected by a scratch on the glass surface.

The present invention can be applied to various games (fighting games, shooting games, robot battle games, sports games, competition games, role playing games, music playing games, dance games, etc.).

The present invention also provides various game systems (image generation systems) such as a business game system, a home game system, a large attraction system in which many players participate, a simulator, a multimedia terminal, and a system board for generating game images. System).

[Brief description of the drawings]

FIGS. 1A and 1B are diagrams for explaining anisotropic reflection. FIG.

FIGS. 2A and 2B are diagrams for explaining a method of realizing anisotropic reflection using an ellipsoid model.

FIG. 3 is an example of a functional block diagram of the game system of the embodiment.

FIGS. 4A and 4B are diagrams for explaining a method of realizing anisotropic reflection by changing the direction of a reflection vector.

FIG. 5 is a diagram for describing a method of realizing anisotropic reflection by changing the direction of a reflection vector in a UVN coordinate system.

FIGS. 6A and 6B are diagrams for explaining a method of changing the direction of a reflection vector using a scaling coefficient.

FIG. 7A shows a case of normal shading.
FIG. 7B is an example of a generated image when an ellipsoid model is used, and FIG. 7C is an example of a generated image when the method of the present embodiment is used.

FIG. 8A shows a case where an ellipsoid model is used;
(B) is an example of a generated image when the method of the present embodiment is used.

FIGS. 9A, 9B, 9C, and 9D are examples of generated images when the scaling coefficient is gradually changed.

FIG. 10 (A), (B), (C), (D) also
It is an example of a generated image when the scaling coefficient is gradually changed.

FIG. 11 is a diagram for describing a method of expressing an object by a free-form surface.

FIG. 12 is a diagram for describing a method of expressing an object by a free-form surface.

FIG. 13 shows a tangent vector at each constituent point,
FIG. 6 is a diagram for describing a method of setting a coordinate system.

FIGS. 14A and 14B are diagrams for describing a setting method of a UVN coordinate system when an object is represented by a polygon.

FIGS. 15A and 15B are diagrams for explaining a specular expression texture and a virtual sphere; FIG.

FIG. 16 is a diagram for explaining specular mapping.

FIG. 17 is a flowchart illustrating a detailed example of a process according to the embodiment;

FIG. 18 is a flowchart illustrating a detailed example of a process according to the present embodiment.

FIGS. 19 (A), (B), (C), (D)
FIG. 4 is a diagram for explaining how to obtain texture coordinates of a specular expression texture.

FIG. 20 is a diagram illustrating an example of a hardware configuration capable of realizing the present embodiment.

FIGS. 21A, 21B, and 21C are diagrams showing examples of various types of systems to which the present embodiment is applied.

[Explanation of symbols]

 OB object LS light source VP viewpoint L light source vector N normal vector R, R2, RUVN, R2UVN reflection vector 20, 22 curved surface patch 30 virtual sphere 100 processing unit 110 reflection vector calculation unit 112 reflection vector change unit 114 shading calculation unit 130 drawing unit 132 Texture mapping unit 160 Operation unit 170 Storage unit 172 Main storage unit 174 Drawing area 176 Texture storage unit 180 Information storage medium 190 Display unit 192 Sound output unit 194 Portable information storage device 196 Communication unit

Claims (16)

[Claims] 1. A game system for generating an image, comprising: means for obtaining a reflection vector at each constituent point of an object based on light source information and normal line information; A game system comprising: means for changing a direction to obtain a second reflection vector; and means for performing a shading operation on an object based on the second reflection vector and viewpoint information. 2. The method according to claim 1, wherein the reflection vector is a second vector defining a direction of anisotropic reflection.
Coordinate transformation into a coordinate system of, the direction of the reflection vector is changed in the second coordinate system to obtain the second reflection vector, and the second reflection vector in the second coordinate system is 1. A game system, wherein coordinates are transformed into one coordinate system, and an object shading operation is performed based on the second reflection vector in the first coordinate system. 3. The method according to claim 2, wherein the second coordinate system has a first axis representing a direction of anisotropic reflection and a second axis intersecting the first axis. The direction of the reflection vector in the coordinate system 2 is changed to one of the first and second axes, and the direction of the second
A game system characterized by calculating a reflection vector of a game. 4. The case according to claim 2, wherein the second coordinate system has a first axis representing a direction of anisotropic reflection and a second axis intersecting the first axis. A component of the first axis of the reflection vector in the second coordinate system is scaled by a first coefficient, and a component of the second axis of the reflection vector in the second coordinate system is converted to a second component. A game system, wherein the second reflection vector is obtained by scaling by a coefficient of 2. 5. The second coordinate system according to claim 2, wherein the second coordinate system has a first axis representing a direction of anisotropic reflection and a second axis intersecting the first axis. In the case where the object is represented by a free-form surface, the first and second axes are set in directions of first and second tangent vectors at respective constituent points of the free-form surface. system. 6. The method according to claim 5, wherein a normal vector serving as the normal information is obtained based on the first and second tangent vectors, and a normal vector of the second coordinate system in the direction of the normal vector is obtained. A game system wherein three axes are set. 7. The specular expression texture according to claim 1, wherein texture coordinates of a specular expression texture are obtained based on the second reflection vector, and the specular expression texture is mapped to an object based on the obtained texture coordinates. A game system, characterized in that: 8. The transformation according to claim 7, wherein, when the direction of the second reflection vector coincides with the direction of the line-of-sight vector, the conversion is performed by referring to the center of a highlight image drawn on the specular expression texture.
A reflection vector, and obtaining the texture coordinates. 9. An information storage medium usable by a computer, comprising: means for obtaining a reflection vector at each constituent point of an object based on light source information and normal line information; Means for obtaining a second reflection vector by changing the direction of reflection, and means for performing shading calculation of an object based on the second reflection vector and the viewpoint information. Characteristic information storage medium. 10. The method according to claim 9, wherein the reflection vector is a second vector defining a direction of anisotropic reflection.
Coordinate transformation into a coordinate system of, the direction of the reflection vector is changed in the second coordinate system to obtain the second reflection vector, and the second reflection vector in the second coordinate system is An information storage medium, which performs coordinate conversion to one coordinate system and performs a shading operation on an object based on the second reflection vector in the first coordinate system. 11. The method according to claim 10, wherein the second coordinate system has a first axis representing a direction of anisotropic reflection and a second axis intersecting the first axis. The direction of the reflection vector in the coordinate system 2 is changed to one of the first and second axes, and the direction of the second
An information storage medium, wherein a reflection vector of the information storage medium is obtained. 12. The method according to claim 10, wherein the second coordinate system has a first axis representing a direction of anisotropic reflection and a second axis intersecting the first axis. A component of the first axis of the reflection vector in the second coordinate system is scaled by a first coefficient, and a component of the second axis of the reflection vector in the second coordinate system is changed to a second component. An information storage medium, wherein the second reflection vector is obtained by scaling by a coefficient of 2. 13. The system according to claim 10, wherein the second coordinate system has a first axis representing a direction of anisotropic reflection and a second axis intersecting the first axis. When the object is represented by a free-form surface, the first and second axes are set in directions of first and second tangent vectors at respective constituent points of the free-form surface. Storage medium. 14. The method according to claim 13, wherein a normal vector serving as the normal information is obtained based on the first and second tangent vectors, and a normal vector of the second coordinate system in the direction of the normal vector is obtained. An information storage medium, wherein three axes are set. 15. The specular expression texture according to claim 9, wherein texture coordinates of the specular expression texture are obtained based on the second reflection vector, and the specular expression texture is mapped to the object based on the obtained texture coordinates. An information storage medium characterized by the above-mentioned. 16. The transformation according to claim 15, wherein, when the direction of the second reflection vector coincides with the direction of the line-of-sight vector, the conversion is performed by referring to the center of a highlight image drawn on the specular expression texture.
An information storage medium, wherein the texture coordinates are obtained by applying the reflection vector to the reflection vector.