JP2001148032A - Method and device for plotting image, recording medium and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To make fast expressible a phenomenon (refraction phenomenon) at the time when light is transmitted through an object and is refracted, in a three-dimensional image and to simply and also make fast expressible a moving transparent object. SOLUTION: This device plots a face being farther from a viewpoint in turn, advances from the viewpoint to a background image 100, also finds a range (texture range 120) to be used) that is subjected to transparent transformation with a vector obtained by considering refraction at each of vertexes (a to d) constituting a corresponding face A1, performs texture mapping about the face A1 by using the texture. The device advances from the viewpoint to the image 100 about one surface A5, also finds a range (texture range 130 to be used) that is subjected to transparent transformation with a vector obtained by considering refraction at each of vertexes (a, b, g and h) constituting the surface A5 and performs texture mapping about the surface A5 by using the texture.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image drawing method and an image drawing apparatus suitable for, for example, expressing a phenomenon (refraction phenomenon) when light passes through an object and is refracted by a three-dimensional image at a high speed. The present invention relates to a recording medium on which a program or data capable of realizing image processing is recorded, and the program itself.

[0002]

2. Description of the Related Art Recently, computer graphics (CG) processing such as hidden line processing, hidden surface elimination processing, smooth shading, and texture mapping has been rapidly progressing in conjunction with rapid development of hardware. I have.

In the CG process, generally, a plurality of three-dimensional shapes (objects) are created by CAD three-dimensional modeling, and these objects are colored and shaded, and specular reflection, diffuse reflection, refraction, and transparency. Rendering processing is performed in which optical characteristics such as are added, a surface pattern is attached, and drawing is performed in accordance with surrounding conditions (reflection of windows and scenery, reflection of light, etc.).

[0004]

By the way, for example, when the expression when light is transmitted through an object and refracted is represented by a three-dimensional image, it is conceivable to reproduce an optical physical phenomenon.
In this case, the refraction of the ray vector emitted from the viewpoint occurs when the ray enters the object and when the ray exits the object.

In order to express the above-mentioned refraction phenomenon by a three-dimensional image, it is conceivable to use a ray tracing method (ray tracing method) rather than a method using polygons.

The ray tracing method is a method of searching for the movement of a light beam in a space where an object is placed, and drawing the object from an intersection between the light beam and the object. In other words, it is a method in which the intensity of light reaching the viewpoint is traced in the opposite direction from the viewpoint while reproducing the reflection and refraction of the surface of the object in the same manner as in reality.

As a specific method, an intersection with an object is determined through a pixel on a screen by determining a viewpoint, and if there is an intersection, the point of sight is tracked to the destination of the line of sight, such as reflection or transmission of the object. Information on the intersection is stored as information on a corresponding pixel on the screen. That is, the hue,
Information such as texture, texture, shading, and the like regarding intrinsic colors, reflection, refraction, gloss and gloss, etc. relating to saturation and lightness is required.

However, in the ray tracing method, since information such as a unique color, reflection, refraction, and shading exists for each pixel, the entire data amount is enormous, and there is a disadvantage that the calculation time is long.

The present invention has been made in view of such a problem, and for example, a phenomenon (refraction phenomenon) when light passes through an object and is refracted can be expressed at a high speed in a three-dimensional image. An object of the present invention is to provide an image drawing method, an image drawing device, a recording medium, and a program capable of easily and quickly expressing a moving transparent object.

[0010]

According to the image drawing method of the present invention, when drawing an object where refraction occurs, drawing is performed from a surface of the object that is farther from the viewpoint, and the drawing of each surface is performed. In this case, the background image of each surface is used as a texture.

Further, the image drawing apparatus according to the present invention, when drawing an object in which refraction occurs, performs drawing from a surface of the object that is farther from the viewpoint, and draws each surface. It is characterized by having drawing means for using a background image of each surface as a texture.

In the recording medium according to the present invention, when drawing an object in which refraction occurs, drawing is performed from a surface of the object that is farther from the viewpoint, and when drawing each surface, A program and data including a drawing step of using a background image of the surface as a texture are recorded.

[0013] The program according to the present invention is a program readable and executable by a computer.
When drawing an object in which refraction occurs, among the surfaces constituting the object, drawing is performed from a surface farther from the viewpoint, and when drawing each surface, a drawing step of using a background image of each surface as a texture is performed. It is characterized by having.

Thus, when rendering each surface, it is only necessary to use the background image of each surface as a texture, so that high-speed processing can be performed. for that reason,
For example, a phenomenon (refraction phenomenon) when light passes through an object and is refracted can be expressed at a high speed in a three-dimensional image, and a moving transparent object can be easily and quickly expressed.

In the present invention, when drawing one surface, of the background image of the surface, the surface is directed from the viewpoint to the background image and refracted at each vertex constituting the surface. It is preferable to use, as a texture, a background image in a range in which perspective transformation (projection of a three-dimensional object onto a two-dimensional plane) is performed using a vector in consideration of the following.

In this case, the vector considering the refraction at each vertex of the surface is based on at least the direction of the normal line in the viewpoint coordinate system of the surface and the direction of the line segment from the viewpoint to each vertex. You can ask.

More specifically, a projection position on the uz plane composed of the u-axis of the background image and the z-axis of the viewpoint coordinate system at each vertex is determined, and at least a line from the viewpoint to each of the projection positions is obtained. Based on the direction of the minute and the direction of the normal on the uz plane, the coordinates of each vertex on the u-axis in the background image are obtained, and the v-axis of the background image at each vertex and the viewpoint coordinate system A projection position on a vz plane composed of the z-axis of the plurality of vertexes is determined based on at least a direction of a line segment from the viewpoint to each of the projection positions and a direction of the normal on the vz plane. The position of the surface on the background image may be obtained by obtaining coordinates on the v-axis of the background image.

According to this method, a background image to be attached to the surface can be easily obtained, and a three-dimensional image display of the refraction phenomenon can be performed at higher speed.

[0019]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, an embodiment in which an image drawing method and an image drawing apparatus according to the present invention are applied to an entertainment apparatus for performing, for example, three-dimensional CG processing (hereinafter, simply referred to as an entertainment apparatus according to the embodiment, Write)
An embodiment in which a recording medium and a program according to the present invention are applied to a recording medium and a program in which a program or data to be executed by an entertainment apparatus is recorded will be described with reference to FIGS.

As shown in FIG. 1, an entertainment device 10 according to the present embodiment includes an MPU 12 for controlling the entertainment device 10 and a main memory 14 used for operations of various programs and storage of various data.
A vector operation unit 16 for performing a floating-point vector operation required for geometry processing;
2 generates image data based on the control of
(CRT in this example) and M
PU 12 and vector operation unit 16 and image processing unit 20
A graphic interface (GIF) 22 for arbitrating a transfer path with the I / O, an input / output port 24 for transmitting and receiving data to and from an external device, and an OS for controlling a kernel or the like, which is constituted by, for example, a flash memory.
It comprises a ROM (OSDROM) 26 with a built-in D function and a real-time clock 28 with a calendar / clock function.

The MPU 12 is connected to the MPU 12 via a bus 30.
Main memory 14, Vector operation unit 16, GIF
22, OSDROM 26, real-time clock 28, input / output port 24, and the like.

The input / output port 24 includes, for example, an input device 32 for inputting data (key input data, coordinate data, etc.) to the entertainment device 10 and various programs and data (data relating to objects, texture data, etc.). ) Is recorded, for example, a CD-ROM
An optical disk device 36 for reproducing an optical disk 34 such as an optical disk is connected.

The image processing unit 20 includes a rendering engine 70, a memory interface 72, and an image memory 7.
4. It has a display control device 76 (for example, a programmable CRT controller or the like).

The rendering engine 70 is an MPU 12
In response to the drawing command supplied from the CPU, an operation of drawing predetermined image data in the image memory 74 via the memory interface 72 is executed.

A first bus 78 is connected between the memory interface 72 and the rendering engine 70,
A second bus 80 is connected between the memory interface 72 and the image memory 74. Each of the first and second buses 78 and 80 has a bit width of, for example, 128 bits.
4 can be executed at a high speed.

The rendering engine 70 is, for example, NT
The image data of 320 × 240 pixels or the image data of 640 × 480 pixels of the SC system or the PAL system, etc., is transferred in real time, that is, 10 / s to 1/30 seconds, more than 10 to 10 times. It has the ability to draw.

The image memory 74 employs, for example, a unified memory structure capable of designating a texture drawing area and a display drawing area in the same area.

The display control device 76 transmits texture data fetched from the optical disk 34 through the optical disk device 36 and texture data created on the main memory 14 to the image memory 7 via the memory interface 72.
4 in the texture drawing area or the image memory 7
4 is read via the memory interface 72 and is read by the monitor 18.
To be displayed on a screen.

Next, the characteristic functions of the entertainment apparatus 10 according to the present embodiment will be described with reference to FIGS.
This will be described with reference to FIG.

This function is used when drawing an object where refraction occurs, of the surfaces constituting the object.
Drawing is performed from a plane farther from the viewpoint, and a background image of each plane is used as a texture when drawing each plane.

For example, at the time of drawing one surface, of the background image of the surface, the vector is directed to the background image from the viewpoint with respect to the surface, and is a vector in which refraction at each vertex constituting the surface is considered. The background image in the perspective-transformed range is used as a texture.

The vector considering the refraction at each vertex of the surface can be obtained based on at least the direction of the normal in the viewpoint coordinate system of the surface and the direction of the line segment from the viewpoint to each vertex. it can.

The specific procedure of this method will be described with reference to FIGS. FIG. 2 shows an image in which a cube 102 of a substance such as glass is placed in front of a mountain landscape drawn as a background image 100. In this image, refraction processing of light transmitted through the cube 102 is performed. , Created by the method described above.

Normally, as shown in FIG. 3, the refraction phenomenon of the ray vector emitted from the viewpoint is such that the ray La
And when the ray La exits the cube 102. Here, for example, the refraction of the light ray La on the front surface viewed from the viewpoint 104 is such that the refractive index of the space is n1,
Assuming that the refractive index of the cube 102 is n2, the incident angle of the light beam La on the surface (the angle formed with the normal 106) is θ1, and the output angle of the light beam La (the angle formed with the normal 106) is θ2, Snell's law From the following relationship.

N1 sin θ1 = n2 sin θ2 This relationship is the same for the refraction of the light ray La on the surface that is farther from the viewpoint 104.

In the image drawing method according to the present embodiment, the position of each surface constituting the cube 102 on the background image is obtained by utilizing this relationship.

More specifically, as shown in FIGS. 4A and 4B, of the six faces constituting the cube 102,
First, the plane A1 farthest from the viewpoint is selected, and the vertices (a, b, c, d) constituting the plane A1 are positioned on the background image 100 (to be exact, the plane A1 is positioned on the background image 100). Position) is obtained based on at least the direction of the normal line of the plane A1 in the viewpoint coordinate system and the direction of a line segment from the viewpoint to each vertex (a, b, c, d).

The position on the background image 100 is a position on the background image 100 drawn in the image memory 74, and the position is obtained by setting the horizontal axis of the background image 100 to the u-axis.
Assuming that the vertical axis is the v-axis, this is nothing but finding the position of the uv coordinate system.

First, the projection position of each vertex (a, b, c, d) on the uz plane composed of the u axis of the background image 100 and the z axis of the viewpoint coordinate system is determined. The coordinates of each vertex (a, b, c, d) on the u-axis in the background image 100 are obtained based on the direction of the line segment toward the position and the direction of the normal on the plane A1 on the uz plane. .

For example, as shown in FIG. 5, taking one vertex a of one back surface A1 as an example, considering a line segment 110 from the viewpoint 104 to the vertex a, The angle (incident angle) θ1 between the normal line 112 and the cube 102
Is determined from the vertex a toward the background image 100 (the emission angle θ2) based on the refractive index n2 of the space and the refractive index n1 of the space. Then, a line segment 114 determined by the emission angle θ2
By performing perspective transformation of the vertex a into the background image 100 in accordance with the vector of (i), the position of the u coordinate on the background image 100 at the vertex a is determined. This is the same for the other vertices b, c and d included in the surface A1.

Next, vertices (a, a, b) on a vz plane composed of the v axis of the background image 100 and the z axis of the viewpoint coordinate system
b, c, d) are obtained, and at least the viewpoint 104
Then, the coordinates of each vertex (a, b, c, d) on the v-axis in the background image 100 are obtained based on the direction of the line segment from the to each projection position and the direction of the normal on the vz plane.

For example, although not shown here, taking one vertex a as an example, when a line segment from the viewpoint 104 to the vertex a is considered, an angle (incident angle) between the line segment and the normal line is considered. θ
1, a direction (emission angle θ2) from the vertex a toward the background image 100 is obtained based on the refractive index n2 of the cube 102 and the refractive index n1 of the space. Then, the vertex a is set to the background image 100 according to the vector of the line segment determined by the emission angle θ2.
, The position of the v coordinate at the vertex a on the background image 100 is determined. This is the same for the other vertices b, c and d included in the surface A1.

As described above, the uv coordinate (u, u, 1) on the background image 100 at one vertex a of one back surface A1
v) is obtained. Hereinafter, similarly, by obtaining the coordinates of the other vertices on the background image 100, FIG.
As shown in FIG. 4B and FIG.
04 to the background image 100, and a range obtained by performing a perspective transformation using a vector considering the refraction at each vertex (a, b, c, d) constituting the surface A1, that is, a range 120 of the texture to be used. Then, texture mapping is performed on the one surface A1 and drawing on the image memory 74 is performed.

When the drawing of the one surface A1 in the image memory 74 is completed, the next back surface A2 is selected and the same processing as described above is performed. Cube 102
Are selected in the order of the faces A as shown in FIG.
The order is 1 → surface A2 → surface A3 → surface A4 → surface A5 → surface A6.

When the three back faces A1, A2, and A3 of the cube 102 are completed, the three front faces A4, A5, and A6 of the cube 102 are processed next. The processes on the front surfaces A4, A5, and A6 are the same as described above.

As shown in FIG. 6, for example, taking one vertex a of one plane A5 as an example, when considering a line segment 122 from the viewpoint 104 to the vertex a, the plane A5 of the line segment 122 Based on the angle (incident angle) θ1 between the normal 124 and the refractive index n1 of the space and the refractive index n2 of the cube 102,
Direction from vertex a to background image 100 (emission angle θ2)
Is found. The vertex a is perspectively transformed into the background image 100 according to the vector of the line segment 126 determined by the emission angle θ2, so that the background image 10 at the vertex a is
The position of the u coordinate on 0 is determined. This is the same for the other vertices b, g, and h included in the surface A5.

Next, the background image 100 at the vertex a
Find the position of the v coordinate above. This method is the same as the above-described method, and a detailed description thereof will be omitted.

In this way, the uv coordinate (u, v) on the background image 100 at one vertex a of the surface A5 of the table is obtained. Hereinafter, similarly, by obtaining the uv coordinates on the background image 100 for the other vertices b, g, and h, as shown in FIG. 4B and FIG. Go to 100, and
A range that is perspectively transformed by a vector considering the refraction at each vertex (a, b, g, h) of the surface A5, that is, a range 130 of a texture to be used, is determined, and the texture of the one surface A5 is determined. Mapping is performed, and drawing to the image memory 74 is performed. At this time, surface A of this table
5, the background image 100 includes three back surfaces A in the mountain scenery.
Images in which 1, A2 and A3 are drawn are drawn,
As the texture used for the front surface A5, the back surface A
An image in which 1, A2, and A3 are drawn is included.

Then, at the stage where drawing of the surface A5 of the one table in the image memory 74 has been completed, the surface A5 of the next table is completed.
6 is selected and the same processing as described above is performed.

In the above example, one cube 1
Although the case where 02 is placed is shown, as shown in FIG. 7, the same applies to a case where a plurality of cubes 102A and 102B are placed in a mountain landscape. In this case, the processing is performed from the cube 102A far from the viewpoint 104.

Next, an example of software (drawing means 200) for achieving the above functions will be described with reference to FIGS.
This will be described with reference to FIG.

The drawing means 200 is, for example, a CD-RO
The storage device is provided to the entertainment apparatus 10 through a network that can be accessed randomly, such as an M or a memory card, or a network. here,
The description will proceed on the assumption that the entertainment apparatus 10 operates by being read from an optical disc 34 such as a CD-ROM.

That is, for example, the drawing unit 200 performs a predetermined process from a specific optical disc 34 reproduced in advance by the entertainment apparatus 10 through the entertainment apparatus 1.
0 is downloaded to the main memory 14 to operate on the MPU 12.

As shown in FIG. 8, the drawing means 200 includes, as shown in FIG. 8, an object selecting means 206 for selecting object data 204 relating to the objects in order of distance from the viewpoint, out of a large number of objects registered in the object data file 202. Among a plurality of surfaces constituting the object indicated by the selected object data 204, a surface selecting means 208 for selecting a surface in order from a point farthest from the viewpoint 104; A normal direction determining means 210 for determining;
A first projection position calculating unit 212 for determining a projection position of each vertex constituting the selected surface on the uz plane, and an incident angle θ
1 and an angle calculating means 214 for calculating the emission angle θ2, and a first coordinate calculating means 216 for calculating the u coordinate on the background image 100 based on the projection position on the uz plane and the emission angle θ2 for each vertex.

The drawing means 200 includes a second projection position calculating means 218 for calculating a projection position of each vertex constituting the selected surface on the vz plane, and a vz
The background image 10 based on the projection position on the plane and the emission angle θ2
A second coordinate calculating means 220 for calculating a v coordinate on 0,
A texture image determining unit 222 that determines a texture image to be used from the background image 100 based on the uv coordinates of each vertex, a texture mapping unit 224 that pastes the determined texture image on a selected surface, and determines completion of processing. End determination means 226 that performs the operation.

Next, the processing operation of the drawing means 200 will be described with reference to the flowcharts of FIGS.

First, in step S1 of FIG. 9, the drawing means 200 stores an initial value "1" in an index register m used for searching for an object, and initializes the index register m.

Next, in step S2, the object data 204 relating to the object is selected from the many objects registered in the object data file 202 in order from the viewpoint farthest through the object selecting means 206.

Next, in step S3, an initial value "1" is stored in an index register i used for searching for a surface constituting an object, and the index register i is initialized.

Next, in step S4, the selected object data 2
A surface (i-th surface) is selected from a plurality of surfaces constituting the object registered in 04 in order from the viewpoint farthest from the viewpoint.

Next, in step S5, the number of vertices constituting the i-th surface is determined. Then, step S6
In step (1), the direction of the normal on the uz plane and the direction of the normal on the vz plane in the i-th plane are obtained through the normal direction determining means 210.

Next, in step S7, an initial value "1" is stored in an index register j used for searching for a vertex, and the index register j is initialized.
In the next step S8, the first projection position calculating means 2
Through 12, the projection position (coordinates) of the j-th vertex on the uz plane is obtained.

Next, in step S9, the angle (incident angle θ1) between the line segment connecting the viewpoint and the j-th vertex and the normal line (normal line on the uz plane) is obtained through the angle calculation means 214. In the next step S10, similarly, the output angle θ2 is obtained based on the refractive index on the incident side, the refractive index on the output side, and the incident angle θ1 via the angle calculating means 214.

Next, in step S11, the j-th vertex is moved through the first coordinate calculating means 216 in the direction determined by the projection position (coordinate) of the j-th vertex on the uz plane and the emission angle θ2. Is perspective-transformed, and the position (u coordinate) of the j-th vertex on the background image 100 is obtained.

Next, in step S12 of FIG.
Through the second projection position calculation means 218, the projection position (coordinates) of the j-th vertex on the vz plane is obtained.

Next, in step S13, the angle (incident angle θ1) formed by the angle calculating means 214 with the normal (the normal on the vz plane) of the line connecting the viewpoint and the j-th vertex.
In the next step S14, the output angle θ2 is calculated based on the refractive index on the incident side, the refractive index on the output side, and the incident angle θ1 through the angle calculation means 214 in the same manner.

Next, in step S15, the j-th vertex is moved in the direction determined by the projection position (coordinate) of the j-th vertex on the vz plane and the emission angle θ2 through the second coordinate calculating means 220. Is perspective-transformed, and the position (v coordinate) of the j-th vertex on the background image 100 is obtained.

Next, in step S16, the value of the index register j is updated by +1.
In, it is determined whether or not uv coordinates have been obtained for each vertex of the i-th surface. This determination is
This is performed depending on whether the value of the index register j is larger than the number N of vertices.

If the uv coordinate for each vertex has not been obtained, the process proceeds to step S8, where u
When the v coordinate is obtained and the processing is completed, the next step S
18, and through the texture image determining means 222,
Of the background image 100, the background image 100 in a range surrounded by the uv coordinates of each vertex constituting the i-th surface is determined as a texture image.

Next, in step S 19, the determined texture image is texture-mapped to the i-th surface through the texture mapping means 224 and drawn in the image memory 74.

Next, in step S20, the value of the index register i is updated by +1 and then the next step S20 is executed.
At 21, it is determined through the end determination means 226 whether or not the processing has been completed for all surfaces constituting the object. This determination is made based on whether or not the value of the index register i is larger than the number M of the surfaces constituting the object.

If texture mapping has not been performed on all surfaces, the process proceeds to step S4, where processing is performed on the next surface. If texture mapping has been performed on all surfaces, the value of the index register m is determined in step S22. Is updated by +1 and then the next step S
At 23, it is determined through the end determination means 226 whether or not the processing has been completed for all objects. This determination is made based on whether the value of the index register m is larger than the number P of objects.

If the processing has not been completed for all the objects, the process proceeds to step S2, where the processing is performed for the next object, and when the processing has been completed for all the objects, the processing by the drawing means 200 ends. I do.

As described above, in the drawing means 200 according to the present embodiment, when drawing each surface of the object where refraction occurs, it is only necessary to use the background image 100 of each surface as a texture. It can be processed at high speed. Therefore, for example, a phenomenon (refraction phenomenon) when light passes through an object and is refracted can be expressed at a high speed in a three-dimensional image, and a moving transparent object can be easily and quickly expressed.

The image drawing method, the image drawing apparatus, the recording medium, and the program according to the present invention are not limited to the above-described embodiments, but may adopt various configurations without departing from the gist of the present invention. Of course.

[0076]

As described above, according to the image drawing method, the image drawing apparatus, the recording medium, and the program according to the present invention, for example, the phenomenon (refraction phenomenon) when light passes through an object and is refracted is three times. It is possible to express a three-dimensional image at high speed, and it is possible to easily and quickly express a moving transparent object.

[Brief description of the drawings]

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

FIG. 2 is an explanatory diagram showing an image of a state in which one cube of a substance such as glass is placed in front of a mountain scene drawn as a background image.

FIG. 3 is an explanatory diagram showing a refraction phenomenon in a cube of a ray vector emitted from a viewpoint.

FIG. 4A is an explanatory diagram showing a range of a texture image used on one back surface of a cube; FIG. 4B is a diagram showing a state where the texture image shown in FIG. 4A is pasted; FIG. 4C is an explanatory diagram showing a range of the texture image used on the front surface, and FIG. 4C is an explanatory diagram showing a state where the texture image shown in FIG. 4B is pasted.

FIG. 5 is a diagram for explaining a method of perspective-transforming a vertex forming one back surface of a cube into a background image in consideration of refraction.

FIG. 6 is a diagram for explaining a method of performing perspective transformation of a vertex constituting one surface of a cube into a background image in consideration of refraction.

FIG. 7 is an explanatory diagram showing an image in a state where two cubes of a material such as glass are placed in front of a mountain landscape drawn as a background image.

FIG. 8 is a functional block diagram illustrating a configuration of a drawing unit according to the present embodiment.

FIG. 9 is a flowchart (part 1) illustrating a processing operation of a drawing unit according to the present embodiment;

FIG. 10 is a flowchart (No. 2) showing the processing operation of the drawing means according to the present embodiment.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 10 ... Entertainment apparatus 34 ... Optical disk 74 ... Image memory 100 ... Background image 102, 102A, 102B ... Cube 104 ... View point 120, 130 ... Texture range 200 ... Drawing means 202 ... Object data file 204 ... Object data 206 ... Object selection means 208 surface selection means 210 normal direction determination means 212 first projection position calculation means 214 angle calculation means 216 first coordinate calculation means 218 second projection position calculation means 220 second coordinate calculation Means 222: Texture image determination means 224: Texture mapping means

Claims (13)

[Claims] When drawing an object in which refraction occurs, drawing is performed from a surface that is farther from a viewpoint among surfaces constituting the object, and a background image of each surface is used as a texture when drawing each surface. An image drawing method characterized by being used. 2. The image drawing method according to claim 1, wherein, when drawing one surface, among the background images of the surface, the surface is directed from the viewpoint to the background image and the surface is formed. An image drawing method characterized by using, as a texture, a background image in a range perspective-transformed with a vector considering refraction at each vertex. 3. The image drawing method according to claim 2, wherein the vector considering the refraction at each vertex of the surface is at least a direction of a normal in a viewpoint coordinate system of the surface and each vertex from the viewpoint. An image drawing method characterized in that it is determined based on the direction of a line segment heading toward. 4. The image drawing method according to claim 3, wherein a projection position of each vertex on a uz plane composed of a u-axis of the background image and a z-axis of a viewpoint coordinate system is determined, and at least each of the projection positions is determined from the viewpoint. Based on the direction of the line segment toward the projection position and the direction of the normal on the uz plane,
Finding the coordinates of each vertex on the u axis in the background image, Finding the projection position of each vertex on a vz plane composed of the v axis of the background image and the z axis of the viewpoint coordinate system, at least from the viewpoint Based on the direction of the line segment toward each of the projection positions and the direction of the normal on the vz plane,
An image drawing method, wherein a position of the surface on the background image is obtained by obtaining coordinates of each vertex on the v-axis in the background image. 5. When drawing an object in which refraction occurs, drawing is performed from a surface that is farther from the viewpoint among surfaces constituting the object, and when drawing each surface, a background image of each surface is used as a texture. An image drawing apparatus comprising drawing means to be used. 6. An image drawing apparatus according to claim 5, wherein said drawing means, when drawing one surface, of said background image of said surface, goes from said viewpoint to said background image for said surface, and An image drawing apparatus, wherein a background image in a range perspective-transformed by a vector taking into account refraction at each vertex of the surface is used as a texture. 7. The image drawing apparatus according to claim 6, wherein said drawing means includes: a vector considering a refraction at each vertex of the surface, at least a direction of a normal in a viewpoint coordinate system of the surface; An image drawing apparatus comprising: a texture coordinate calculating unit that obtains a texture coordinate based on a direction of a line segment from the viewpoint to each vertex. 8. The image drawing apparatus according to claim 7, wherein the texture coordinate calculating means is configured to project a projection position on each of the vertices on a uz plane including a u-axis of the background image and a z-axis of a viewpoint coordinate system. A first projection position calculating means for determining the direction of a line segment from the viewpoint to each of the projection positions and a direction of the normal on the uz plane.
First coordinate calculating means for obtaining coordinates of each vertex on the u-axis in the background image; and a vz plane comprising the v-axis of the background image and the z-axis of the viewpoint coordinate system at each vertex. A second projection position calculating means for determining a projection position, based on at least a direction of a line segment from the viewpoint to each projection position and a direction of the normal on the vz plane in the background image. an image drawing device comprising: a second coordinate calculation unit that obtains coordinates on a v-axis. 9. When drawing an object in which refraction occurs, drawing is performed from a surface that is farther from the viewpoint among surfaces constituting the object, and a background image of each surface is used as a texture when drawing each surface. A recording medium characterized by recording a program and data including a drawing step to be used. 10. The recording medium according to claim 9, wherein the drawing step includes, when drawing one surface, of the background image of the surface, from the viewpoint to the background image with respect to the surface, and A recording medium characterized by using a background image in a range perspective-transformed by a vector considering refraction at each vertex of a surface as a texture. 11. The recording medium according to claim 10, wherein, in the drawing step, a vector in consideration of refraction at each vertex of the surface is defined by at least a direction of a normal in a viewpoint coordinate system of the surface, and A recording medium comprising a texture coordinate calculation step for obtaining based on a direction of a line segment from a viewpoint to each vertex. 12. The recording medium according to claim 11, wherein the texture coordinate calculating step includes: projecting a projection position on each of the vertices on a uz plane including a u-axis of the background image and a z-axis of a viewpoint coordinate system. Calculating a first projection position calculating step, based on at least a direction of a line segment from the viewpoint to each of the projection positions and a direction of the normal on the uz plane,
A first coordinate calculation step for obtaining coordinates of each of the vertices on the u axis in the background image; and a vz plane formed by the v axis of the background image and the z axis of the viewpoint coordinate system at each vertex. A second projection position calculation step of calculating a projection position, based on at least a direction of a line segment from the viewpoint to each projection position and a direction of the normal on the vz plane in the background image of each vertex. a second coordinate calculation step for obtaining coordinates on the v-axis. 13. A computer-readable and executable program comprising: when drawing an object in which refraction occurs, drawing from a surface of the object that is farther from the viewpoint; A drawing step of using a background image of each surface as a texture.