JP4714919B2 - Rendering device, recording medium, and program - Google Patents

Description

TECHNICAL FIELD The present invention relates to a texture mapping method and rendering apparatus, and more particularly to a texture mapping method and rendering apparatus that can match display results of shading and texture mapping.
BACKGROUND ART With the rapid development of computer computing capabilities in recent years, extremely high-level expressions are possible even in the field of real-time CG (Computer Graphics), which requires a sufficient drawing speed to respond to human operations. I came. In real-time CG, the trade-off between reality and advanced expressions and the amount of calculation for calculating them is always a problem. Especially in the field of applied technology such as virtual reality, the requirements for both are severe, and some problems to be solved remain.
First, an overview of the real-time 3DCG image generation (rendering) process that is currently in widespread use will be summarized.
・ Calculation processing based on 3D spatial information (Transform & Lighting)
An object in 3DCG is generally represented by a set of polygonal planes (Polygons) pasted by a large number of vertices. Rendering is performed based on the position / connection information of each vertex of the stereo model, data on the material, and the like.
For this data, only the elements within the field of view are extracted (culling), and the position where each vertex is drawn on the two-dimensional image is calculated (coordinate conversion). Here, the brightness for each vertex is calculated from the positional relationship between the three-dimensional model and the light source that illuminates it (lighting process). This is the calculation processing (Transform & Lighting) based on the three-dimensional space information.
・ Calculation processing (rasterization) for each pixel on the 2D image
Subsequently, calculation processing (rasterization) is performed for each pixel on the two-dimensional image. The front-rear relationship is determined according to the distance from the viewpoint position of each rendering pixel (hidden surface processing), and the color and brightness of each vertex are interpolated to smoothly shade the polygon color pasted at that vertex (shading) ). A method of expressing details in a pseudo manner by pasting a two-dimensional image or the like on the surface of the three-dimensional object thus obtained is called texture mapping.
A typical calculation / representation technique of real-time 3D-CG that is currently widely used will be briefly described.
(1) Shading A method of shading the surface of a three-dimensional object composed of polygons based on the light source and the shape of the object is called shading. Since it is very difficult to perform physically accurate shading calculations and the calculation tatami is enormous, various calculation methods have been devised to reduce this. In general, the amount of calculation increases as shading with which high quality image quality is obtained.
As shading types, there are Flat shading, Gouraud shading, and Phong shading.
Flat shading is a method in which a normal is set for each surface of a polygon constituting the surface, and the color of the surface is determined from the inner product of this and the light source vector. Since the unit of shading is for each surface, a smooth curved surface cannot be expressed, but the amount of calculation is small and it can be displayed at high speed.
Gouraud shading is a method of determining a color at each vertex from the inner product of this and a light source vector for each vertex of a polygon constituting the surface. The vertices are colored by linearly interpolating the colors of the vertices. A relatively fast and smooth curved surface can also be simulated, but the curved surface with high curvature and highlighting become unnatural.
In the Phong shading, a normal is set for each vertex of a polygon constituting the surface, and a normal is obtained by linear interpolation from the normal vector at each vertex for each voxel of the resultant image drawn between the vertices. Based on this, the color is determined for each pixel from the inner product of the light source and the normal. High quality results are obtained, but due to the large amount of computation per pixel, it is rarely used in current real-time 3D-CG.
(2) Texture mapping Texture mapping is a technique for improving the texture by pasting an image on the surface of a three-dimensional object. The texture image to be pasted is taken with the u and v coordinate systems, and the u and v coordinate values are assigned to the respective vertices to determine how to apply (mapping method).
In the current real-time 3D-CG, an image is generally generated by using both Gouraud shading and texture mapping.
By using the real-time 3D-CG representation technique, the vertex positions of the defined objects are all accurately calculated and displayed in the three-dimensional space. For example, when an object composed only of a plane is accurately modeled, a completely correct shape viewed from an arbitrary viewpoint can be obtained.
A shadow expression by illumination, that is, shading is applied to this. Gouraud shading is currently most widely used because of the trade-off between the obtained image quality and arithmetic processing capability. As a result, a pseudo shadow is created on the plane stretched at the vertex of the correct position.
Texture mapping is applied to the object thus obtained. Texture coordinates are defined for each vertex of the object, and are stretched and pasted by linear interpolation between them. The texture applied to the plane of the object will be represented perfectly correctly from any viewpoint.
If the object is composed of only a plane, the above method can be used to obtain a problem-free result, but there are some problems when trying to represent a curved surface in the same way.
A curved surface is expressed in a pseudo manner by dividing it into a set of fine polygonal planes. At this time, a large number of vertices and planes are required, and the amount of calculation increases remarkably. Here, the number of curved surface divisions is determined by a trade-off between image quality and calculation amount. However, considering the advantage of real-time 3D-CG that an image from an arbitrary viewpoint can be obtained, the curved surface is inevitably displayed when displaying details. It is a problem that becomes rough.
With respect to shading, pseudo-curved surface representation having approximately smooth shading can be obtained by Gouraud shading. However, since the color is calculated only at the vertex position and the change in the shadow is approximated by linear interpolation, an unnatural shadow such as a Mach band is generated.
The problem becomes even more pronounced when texture mapping is applied. By linearly interpolating the texture coordinates between the vertices, the straight line portion in the texture image is pasted in a plane without bending even on the curved surface. This is because the Gouraud shading visually deceives the shadow on the curved surface by gradation, but there are many clues to perceive the shape in the texture image, and such deception is not possible visually.
Due to these reasons, the pseudo-curved surface expression breaks down particularly in the following cases. These become serious problems when considering application implementations such as virtual reality.
(1) Representation of moving objects When an object with movement is displayed, problems caused by representing a curved surface in a pseudo manner clearly appear. Unnatural changes in the outer shape of the object and the planar rotation of the texture image impair the pseudo-expression of the curved surface.
(2) Fusion When performing stereoscopic viewing, humans extract appropriate corresponding points from the images obtained from the left and right eyes, and based on this, estimate the distance between themselves and the corresponding points. Yes. When a pseudo curved surface only by shading is presented, the corresponding points on the curved surface become ambiguous due to gradation of gradation, so that there is not much discomfort. However, when texture mapping is applied to this, all the patterns in the texture image become clear corresponding points, and as a result, what is desired to be expressed as a curved surface is fused in a plane. This affects the pseudo curved surface expression by shading.
As described above, in real-time 3D-CG, an object is projected onto a two-dimensional image, subjected to approximate processes through processes such as shading by illumination and pasting of an image pattern on the object surface (texture mapping). A result image is generated.
However, there is a problem that the approximate display results of shading and texture mapping differ when drawing the curved surface portion of an object using the same method. This problem has not been discussed in the past, and was first discovered by the present inventors.
In addition to the fact that the conventional texture mapping on the curved surface impairs the pseudo-curved surface expression by shading, “When binocular stereoscopic viewing is performed, the curved surface expression clearly breaks down in the conventional shading and texture processing. It is equally important or more important that it can be effectively resolved with the processing of hardware technology. The problem that the texture impairs the shading expression has been accepted as “unavoidable” until now, but this problem appears much more prominently in a binocular stereoscopic environment that will naturally become popular in the future. Therefore, it is very meaningful to present this solution.
DISCLOSURE OF THE INVENTION The present invention has been made to solve such a new problem, that is, the problem of discrepancy between the display result of shading and texture mapping that occurs during texture mapping to a pseudo-curved surface. An object of the present invention is to provide a texture mapping method and a rendering apparatus that can perform the above-described process.
The texture mapping method according to the present invention comprises a step of preparing an object constituted by one or a plurality of polygons in three-dimensional coordinates;
Preparing a texture associated with a plurality of vertices of the polygon;
Performing perspective transformation of the object by projecting a plurality of vertices of the polygon onto screen coordinates respectively;
Rendering pixels on the screen coordinates corresponding to a plurality of vertices of the polygon based on the texture;
Obtaining texture coordinates corresponding to pixels between a plurality of vertices of the polygon on the screen coordinates by linear interpolation between the plurality of vertices;
Obtaining an angle θ formed by a viewing direction in a three-dimensional space and a surface normal of the polygon;
Obtaining a lifting amount d at each point on a plane from a plane constituting the polygon in a three-dimensional space to a predetermined curved surface;
Obtaining a texture coordinate shift amount, which is an error amount generated between the surface of the polygon and the curved surface when viewed from the line-of-sight direction, based on the angle θ and the lift amount d at each point on the plane;
Correcting the texture coordinates based on the texture coordinate shift amount;
Performing texture mapping based on the corrected texture coordinates and the texture.
A rendering device according to the present invention includes a three-dimensional model storage unit that stores an object composed of one or a plurality of polygons in three-dimensional coordinates, and a texture storage unit that stores textures associated with a plurality of vertices of the polygons A perspective transformation unit that performs perspective transformation of the object by projecting a plurality of vertices of the polygon onto screen coordinates, and pixels on the screen coordinates corresponding to the plurality of vertices of the polygon in the texture. A drawing unit for drawing based on the image, a linear interpolation unit for obtaining a texture coordinate corresponding to pixels between the plurality of vertices of the polygon on the screen coordinates by linear interpolation between the plurality of vertices, and a three-dimensional space The angle θ formed between the line-of-sight direction and the surface normal of the polygon, and the polygon in a three-dimensional space Texture that is an error amount generated between the surface of the polygon and the curved surface when viewed from the line-of-sight direction based on the lift amount d at each point on the plane from the constituting surface to a predetermined curved surface A texture coordinate shift amount calculation unit for obtaining a coordinate shift amount; and a texture coordinate correction unit that corrects the texture coordinates based on the texture coordinate shift amount. The texture data in the texture storage unit is read based on the corrected texture coordinates. A rendering device characterized in that it is rendered and rendered based on this data.
BEST MODE FOR CARRYING OUT THE INVENTION To solve the above-described problem, an embodiment of the present invention proposes a “shift in texture” technique for performing correction for this problem during texture mapping processing. In other words, instead of generating a curved surface shape in the space, the calculated curved surface shape is dynamically calculated and pasted by back-calculating the assumed curved surface shape in the final rendered image. It is a technique of obtaining an effect.
A method for dynamically generating texture images has been studied in the field of Image-based Rendering (Oliveira, Manuel M. Relief Texture Mapping. Ph. D. Dissertation, University of North Carolina, 2000). In order to reduce the amount of calculation in real time for a simple purpose, various ideas are required. This texture image generation process is realized by shifting the texture image reference position of each drawing pixel during the texture mapping process instead of actually distorting the texture image.
This has an advantage that the calculation amount of the latter half of the above-described texture mapping process is only increased compared to the conventional Polygon subdivision. In addition, since it is a process at the time of rasterization, the main calculation is selectively performed only for the pixel to be finally drawn, and the calculation is omitted for a portion outside the field of view or hidden by another object. Furthermore, since this process is always performed in units of drawing pixels, it is effective even when the polygon subdivision is enlarged to such an extent that the roughness can be seen.
An apparatus / method according to an embodiment of the present invention will be specifically described with reference to the drawings.
This apparatus / method is realized by a computer. As is well known, a computer has a central processing unit (including a CPU and a memory), an external storage device (including a hard disk, a CD-ROM drive, and a floppy disk drive), an input device (including a keyboard and a pointing device), and an output device. (Including a CRT display and a liquid crystal display) and a communication device (including a modem and a terminal adapter).
FIG. 1 is a block diagram showing a main part of an apparatus according to an embodiment of the present invention. This figure is, for example, a functional block diagram showing a main part in a computer in which a program according to this apparatus / method is installed. For convenience of explanation, only the necessary parts are shown, and this apparatus / method may include other parts not shown as needed.
In FIG. 1, reference numeral 1 denotes a three-dimensional model storage unit that stores an object composed of one or a plurality of polygons in three-dimensional coordinates, and reference numeral 2 denotes the above-mentioned by projecting a plurality of vertices of the polygons on screen coordinates. A perspective transformation unit that performs perspective transformation of an object, reference numeral 3 is a drawing unit that renders pixels on the screen coordinates corresponding to the plurality of vertices of the polygon based on texture, and reference numeral 4 is associated with the plurality of vertices of the polygon. A texture storage unit for storing the texture obtained by performing linear interpolation between the plurality of vertices for texture coordinates corresponding to pixels between the plurality of vertices of the polygon on the screen coordinates , Reference numeral 6 denotes an angle θ formed by the line-of-sight direction in the three-dimensional space and the surface normal of the polygon, and the three-dimensional space. The amount of lift d at each point on the plane from the surface constituting the polygon to a predetermined curved surface is received, and based on these, an error generated between the surface of the polygon and the curved surface when viewed from the line of sight A texture coordinate shift amount calculation unit for obtaining a texture coordinate shift amount, which is a quantity, and a texture coordinate correction unit 7 for correcting the texture coordinates based on the texture coordinate shift amount.
FIG. 2 is a flowchart of processing according to the embodiment of the present invention.
Next, the operation will be described.
In the real-time 3D-CG technology, the process of drawing each pixel as a result image after completing the coordinate conversion calculation for each vertex is called rasterization. In Gouraud shading, drawing is performed by linear interpolation between the positions, colors, and texture coordinates at which vertices are projected on the result image at this stage. At this time, the corresponding color is acquired from the texture image based on the texture coordinates calculated by interpolation, and the color of each pixel to be drawn is determined. The reason why the texture is applied to the pseudo curved surface is that the texture coordinates are defined in units of vertices, and the points between the vertices, that is, the points on the surface are all calculated by linear interpolation. Therefore, the apparatus according to the embodiment of the present invention includes a texture coordinate shift amount calculation unit 6 and a texture coordinate correction unit 7, and shifts texture coordinates according to the pseudo curved surface. This enables smooth and natural texture expression.
The texture coordinate shift amount calculation unit 6 and the texture coordinate correction unit 7 calculate the reference position of the texture coordinates at the time of rasterization. In rasterization, drawing calculation is performed for each pixel. Therefore, if a curved surface calculation can be performed in units of pixels, a very detailed curved surface display can always be performed. This corresponds to the difference between Gouraud shading and Phong shading in shading. Of course, this amount of calculation increases, but the calculation for obtaining the texture reference coordinates on the same plane is relatively simple. Hereinafter, this method is referred to as pseudo curved surface expression by texture coordinate shift. Points to keep in mind when performing this processing are: • Limit the amount of computation to be executable in real time • Do not increase the amount of data as much as possible • Implement on existing technology as much as possible.
First, the operation principle will be described. Consider a rectangular plane having texture coordinates as vertices as shown in FIG. 3 in the uv coordinate system spanned by unit vectors u and v. The normal vector of this surface is n, and the line-of-sight direction vector viewing the surface is e. It is assumed that this plane is a part of a pseudo curved surface and is lifted from the plane by d (u, v) in the normal direction at each point on the plane. FIG. 4 shows a projection of this onto the u, n plane.
_eu is a projection of the line-of-sight direction vector e on this plane. Here, if this plane is a curved surface, a point that should be present on A is a point B on the plane, so that a difference between the plane and the curved surface occurs when viewed from the e direction. To correct this, the texture coordinate for each pixel in the plane is shifted, and the texture coordinate of B is assigned to the position of C. That when calculating the texture coordinates u to draw the C, and the angle between n and e _n from u value obtained by linear interpolation may be used a value shifted by dtanθu as theta. By performing this similarly in the calculation of the texture coordinate value V, a texture map result assuming a curved surface can be obtained when each pixel is drawn by rasterization.
Here, when rendering C by rasterization, the texture coordinate value of B is required, and for this purpose, dtan θu, that is, the lift amount d at each point on the plane at B is required. In order to obtain this d, the texture coordinate value of B is still necessary. Therefore, assuming that the assumed curved surface is sufficiently smooth and the angle β between the normal line of the plane and the line-of-sight vector is sufficiently small (tan θ is small), it is approximated that d (B) ≈d (C). To do.
Here, the required angle θ between n and e may be obtained for each plane, not for each pixel. In addition, the angle formed by the line-of-sight direction vector and the normal vector needs to be obtained by illumination calculation at the time of shading, and this type of calculation can be performed at high speed on the graphic chip.
Next, a lifting amount d (u, v) from the plane to the assumed curved surface is obtained. This can be calculated approximately from the position of each vertex and the normal vector, but if this calculation is performed for each pixel during rasterization, the amount of calculation becomes very large. Here, a method for omitting this is considered.
First, it should be noted that the amount of lift to be obtained is a static value that differs at each point on the texture image but does not change with each drawing. These values may be calculated in advance and stored for each surface. Here, a texture image is prepared in which the floating amount d (u, v) is shaded, and this is referred to in the same manner as referring to the value of each pixel of the texture image at the time of rasterization.
For example, in addition to an image including normal color information, another image representing the amount of floating is prepared. A technique of pasting while mixing not only one texture but also two texture colors at the time of 3DCG drawing is general as “multi-texture technique”. For example, it is a function that can be used in an API such as DirectX. Here, the second image texture is used as the lift amount table, and instead of mixing, the process of “shifting the texture coordinates” is performed, so that even in the current hardware technology such as “multi-texture technology” and “EMBM technology”. An implementation method capable of real-time processing can be provided.
Several methods are conceivable for preparing the floating amount as a texture image.
The first is a method in which an α value (usually representing transparency) is given to the texture image together with the color of the RGB value, and the floating amount is set to the α value. In general, a texture image has a total of four channels of color information RGB and an α value to express color and transparency.
In this method, the amount of lifting suitable for each texture image can be set, and an arbitrary curved surface shape can be expressed. However, since one texture image is applied over a large number of planes, it is difficult to raise the resolution in the u and v directions of the floating amount. Also, having all textures have their respective lift amount data leads to an unnecessary increase in data amount.
The other method is a method (Multi-texture) in which a texture image having a general floating amount is prepared separately, and calculation is performed based on two texture images at the time of rasterization. As shown in FIG. 5, by setting appropriate texture coordinates for each vertex, a single floating amount texture image can be applied to various curved surfaces. In this method, if a parameter for scaling the lifting amount is prepared for each surface, an arbitrary curvature can be expressed by one lifting amount texture image.
Here, when the transparency is not required, a float amount table can be provided in the α channel, and when the transparency is required, a separate lift amount texture image may be prepared. The lift amount table can also be used as an altitude table that expresses the height in a broader sense. As a result, the present invention can be applied to a wide variety of applications, for example, not only to express a smooth curved surface but also to express an arbitrary shape such as terrain or a human face with a small number of polygons.
Based on the calculated texture coordinate shift amount, the reference position of the texture image is corrected at the stage of rasterization.
Texture mapping is performed based on the corrected texture coordinates. A known method can be used for the actual processing. For example, the Multimedia API proposed by Microsoft, Direct3D (trademark), which is a real-time 3D-CG rendering API in DirectX, can be used. The Direct3D ™ version 1998 specification supported a feature called Environment-Mapped Bump-Mapping (EMBM). This is a function originally proposed for the special effect of bump mapping in combination with environment mapping. By using this function, texture images can be set in pixel units with a grayscale texture image as the shift amount. is there. This function is implemented in hardware on some graphic cards and can be processed in real time.
An example of the processing result of the pseudo curved surface by the texture coordinate shift according to the apparatus / method according to the embodiment of the present invention is shown in FIG. FIG. 6C shows an object to be processed. In this object, the upper half is a 32 prism and the lower half is an octagon. FIG. 6B shows a case where a normal texture mapping is applied, and FIG. 6A shows a case where a pseudo curved surface process is performed by a texture coordinate shift. As can be seen from the figure, the distortion with the curvature of the texture is roughly expressed in the part near the front. Moreover, it has confirmed that this effect was implement | achieved also in the stereoscopic vision. These displays can be processed in real time on an existing graphic card having a function such as EMBM.
On the other hand, in the vicinity of the side surface where the angle formed by the normal of the surface and the line-of-sight direction is large, there is a difference in the display result with the cylinder. Also, the silhouette of the shape that cannot be corrected by the texture coordinate shift is different from that of the cylinder.
The pseudo-curved surface expression method by texture coordinate shift according to the embodiment of the present invention can express almost any uneven shape in one plane, so various details are added to the object surface by using it together with bump maple. can do.
According to the embodiment of the present invention, it is possible to solve a problem (a new problem discovered by the inventor) that the approximate display of shading and texture map pink is different in pseudo-curved surface expression in real-time 3D-CG. According to the embodiment of the present invention, processing in real time is sufficiently possible.
The present invention is not limited to the above embodiments, and various modifications can be made within the scope of the invention described in the claims, and these are also included in the scope of the present invention. Needless to say.
In the present specification, means does not necessarily mean physical means, but includes cases where the functions of each means are realized by software. Furthermore, the function of one means may be realized by two or more physical means, or the functions of two or more means may be realized by one physical means.
[Brief description of the drawings]
FIG. 1 is a block diagram of an apparatus according to an embodiment of the present invention.
FIG. 2 is a flowchart of processing according to the embodiment of the present invention.
FIG. 3 is a diagram for explaining the operation of the embodiment of the present invention.
FIG. 4 is an explanatory diagram of the operation of the embodiment of the present invention.
FIG. 5 is an explanatory diagram of the operation of the embodiment of the present invention.
FIG. 6 is an example of the processing result of the embodiment of the present invention.

Claims (10)

Instead of generating a curved surface shape in space, an in-texture shift method that dynamically calculates and pastes a distorted texture image by back-calculating the assumed curved surface shape in the image rendered during texture mapping processing A rendering device that executes a texture mapping method according to
Preparing an object composed of one or more polygons in three-dimensional coordinates;
Preparing a texture associated with a plurality of vertices of the polygon;
Performing perspective transformation of the object by projecting a plurality of vertices of the polygon onto screen coordinates respectively;
Rendering pixels on the screen coordinates corresponding to a plurality of vertices of the polygon based on the texture;
Obtaining texture coordinates corresponding to pixels between a plurality of vertices of the polygon on the screen coordinates by linear interpolation between the plurality of vertices;
Obtaining an angle θ formed by a viewing direction in a three-dimensional space and a surface normal of the polygon;
Obtaining a lifting amount d at each point on a plane from a plane constituting the polygon in a three-dimensional space to a predetermined curved surface;
Obtaining a texture coordinate shift amount, which is an error amount generated between the surface of the polygon and the curved surface when viewed from the line-of-sight direction, based on the angle θ and the lift amount d at each point on the plane;
Correcting the texture coordinates based on the texture coordinate shift amount;
Performing texture mapping based on the corrected texture coordinates and the texture,
By using the texture coordinate shift amount, the texture image generation processing is realized by shifting the texture image reference position of each drawing pixel during texture mapping processing instead of actually distorting the texture image. A rendering device for executing a texture mapping method. 2. The rendering apparatus according to claim 1 , wherein in the texture mapping method, the texture coordinate shift amount is given by an expression: d · tan θ. 2. The rendering apparatus according to claim 1 , wherein, in the texture mapping method, the texture coordinate shift amount is given by an equation: k.d.tan.theta. The texture mapping method further comprises a step of preparing a lift amount table for storing in advance a lift amount from a surface constituting the polygon in a three-dimensional space to a predetermined curved surface for each of the polygons. The rendering apparatus according to 1. In the texture mapping method, the method includes a step of preparing a lift amount table that stores in advance a lift amount from a surface constituting the polygon in a three-dimensional space to a predetermined curved surface for each of the polygons,
The lift amount table is a texture image in which the lift amount is shaded, and the texture image includes a parameter value α together with color information, and the parameter value α is set to a different value for each texture image. The rendering apparatus according to claim 1. In the texture mapping method, the method includes a step of preparing a lift amount table that stores in advance a lift amount from a surface constituting the polygon in a three-dimensional space to a predetermined curved surface for each of the polygons,
The lift amount table is a texture image in which the lift amount is shaded,
The rendering apparatus according to claim 1, wherein texture mapping is performed based on the texture and the lift amount table. 6. The rendering apparatus according to claim 5 , wherein in the texture mapping method, an arbitrary curvature is expressed by preparing a parameter for scaling the lifting amount for each surface. Instead of generating a curved surface shape in space, an in-texture shift method that dynamically calculates and pastes a distorted texture image by back-calculating the assumed curved surface shape in the image rendered during texture mapping processing A rendering device according to
A three-dimensional model storage unit that stores an object composed of one or a plurality of polygons in three-dimensional coordinates, a texture storage unit that stores textures associated with a plurality of vertices of the polygon, and a plurality of vertices of the polygon A perspective transformation unit that performs perspective transformation of the object by projecting each on screen coordinates, a drawing unit that renders pixels on the screen coordinates corresponding to a plurality of vertices of the polygon based on the texture, and A linear interpolation unit that obtains texture coordinates corresponding to pixels between a plurality of vertices of the polygon on screen coordinates by linear interpolation between the plurality of vertices; a line-of-sight direction in a three-dimensional space; and a surface method of the polygon Curved surface determined in advance from the angle θ formed with the line and the surface constituting the polygon in the three-dimensional space Texture coordinate shift amount for obtaining a texture coordinate shift amount, which is an error amount generated between the surface of the polygon and the curved surface when viewed from the line of sight based on the lift amount d at each point on the plane A calculation unit, and a texture coordinate correction unit that corrects the texture coordinates based on the texture coordinate shift amount,
By using the texture coordinate shift amount, the texture image generation processing is realized by shifting the texture image reference position of each drawing pixel during texture mapping processing instead of actually distorting the texture image. Rendering device. On the computer,
Instead of generating a curved surface shape in space, an in-texture shift method that dynamically calculates and pastes a distorted texture image by back-calculating the assumed curved surface shape in the image rendered during texture mapping processing A texture mapping method according to
Preparing an object composed of one or more polygons in three-dimensional coordinates;
Preparing a texture associated with a plurality of vertices of the polygon;
Performing perspective transformation of the object by projecting a plurality of vertices of the polygon onto screen coordinates respectively;
Rendering pixels on the screen coordinates corresponding to a plurality of vertices of the polygon based on the texture;
Obtaining texture coordinates corresponding to pixels between a plurality of vertices of the polygon on the screen coordinates by linear interpolation between the plurality of vertices;
Obtaining an angle θ formed by a viewing direction in a three-dimensional space and a surface normal of the polygon;
Obtaining a lifting amount d at each point on a plane from a plane constituting the polygon in a three-dimensional space to a predetermined curved surface;
Obtaining a texture coordinate shift amount, which is an error amount generated between the surface of the polygon and the curved surface when viewed from the line-of-sight direction, based on the angle θ and the lift amount d at each point on the plane;
Correcting the texture coordinates based on the texture coordinate shift amount;
Performing texture mapping based on the corrected texture coordinates and the texture,
By using the texture coordinate shift amount, the texture image generation processing is realized by shifting the texture image reference position of each drawing pixel during texture mapping processing instead of actually distorting the texture image. A recording medium storing a program for executing a texture mapping method. On the computer,
Instead of generating a curved surface shape in space, an in-texture shift method that dynamically calculates and pastes a distorted texture image by back-calculating the assumed curved surface shape in the image rendered during texture mapping processing A texture mapping method according to
Preparing an object composed of one or more polygons in three-dimensional coordinates;
Preparing a texture associated with a plurality of vertices of the polygon;
Performing perspective transformation of the object by projecting a plurality of vertices of the polygon onto screen coordinates respectively;
Rendering pixels on the screen coordinates corresponding to a plurality of vertices of the polygon based on the texture;
Obtaining texture coordinates corresponding to pixels between a plurality of vertices of the polygon on the screen coordinates by linear interpolation between the plurality of vertices;
Obtaining an angle θ formed by a viewing direction in a three-dimensional space and a surface normal of the polygon;
Obtaining a lifting amount d at each point on a plane from a plane constituting the polygon in a three-dimensional space to a predetermined curved surface;
Obtaining a texture coordinate shift amount, which is an error amount generated between the surface of the polygon and the curved surface when viewed from the line-of-sight direction, based on the angle θ and the lift amount d at each point on the plane;
Correcting the texture coordinates based on the texture coordinate shift amount;
Performing texture mapping based on the corrected texture coordinates and the texture,
By using the texture coordinate shift amount, the texture image generation processing is realized by shifting the texture image reference position of each drawing pixel during texture mapping processing instead of actually distorting the texture image. A program for executing the texture mapping method.

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