JPH0527154B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Application of the Invention] The present invention relates to a graphic processing device, and particularly to shading of a display object in processing three-dimensional graphics.

[Prior Art] It is well known that when displaying a three-dimensional figure on a display device such as a CRT in a figure processing device, shading is performed based on a light reflection model in order to give a natural feel to the displayed object. For example, there are the following documents:

Bui−Tuong Phoug, “Illumination for
“Computer-Generated Pictures”
Communications of ACM, 18(6), June
1975, pp. 311-317. JDFoly, A. Van Dam, “Fundamentals of
Interactive Computer Graphics”, Addison
Wesely Publishing Company. James F. Blinn, “Models of Light
Reflection for Computer Synthesized
Pictures”, SIGGRAPH'77 Proceeding. The details are given in the above-mentioned literature (especially the book by JDFoly et al.), and the principle of shedding using a reflection model is summarized below. Figure 2 shows the reflection model introduced by Blinn, and N→ is the unit normal vector of the reflective surface at the reflective point P (a vector with a length of 1 perpendicular to the tangent plane at the point P), L→ is the unit vector from the reflective point P toward the light source, and V→ is the vector from the reflective point P to the viewpoint. H→ is a unit vector in the direction of the sum of L→ and V→, so H→ just bisects the angle formed by L→ and V→.In this model, , the intensity (luminance) I of light in the viewpoint direction at the reflection point P is expressed by equation (1).

I=IaKa+Ip(Kd(N→・L→)+Ka(N→・H→)
ⁿ ) (1) where Ia: Intensity of ambient light Ka: Reflection coefficient of ambient light Ip: Intensity of light from the light source Kd: Diffuse reflection coefficient Ka: Direct reflection coefficient n: A quantity that depends on the surface roughness of the object, and is a number A number between ten and hundreds.

Note that the symbol "." represents the inner product of vectors.

A three-dimensional object surrounded by a curved surface is displayed as follows. A three-dimensional display object surrounded by a curved surface is
First, it is approximated by a polyhedron consisting of multiple polygonal faces called patch faces, and each vertex of this polyhedron has
The unit normal vector of the corresponding point on the original curved surface is given. Here, as a display object, a bowl-shaped object (for example, the shape of the tip of an airplane) on a triangular pyramid with rounded apexes and edges is considered. Now, assume that this object is placed face down on the paper surface. At this time, in FIG. 3, the polyhedron 1 that approximates the displayed object is composed of patch surfaces 11 to 13. The unit normal vectors of the vertices 1 to 4 are N→ ₁ to N→ ₄ , respectively.

[Problems to be Solved by the Invention] Here, the intensity of light at each vertex of a polyhedron that approximates a display object, that is, the brightness of each vertex 1 to 4, is calculated using equation (1), and the brightness of each vertex is calculated from the brightness of the vertex. Surfaces 11-13
Shading can be performed by interpolating and finding the luminance of each dot (pixel) necessary to display the image. This method is called Gouraud shedding. Another method related to this is to patch surfaces 11 to 1 from the unit normal vector of each vertex of a polyhedron that approximates the display object.
Interpolate and find the unit normal vector of each dot (pixel) necessary to display 3.
Shading can also be performed by calculating the brightness of using equation (1). This method is called Fongshading.

By the way, in conventional devices, one set of reflection coefficients (material coefficients) is given to one surface. Also, when calculating brightness based on equation (1), if the inner product of the normal vector and the light source direction vector is negative, there is no negative light, so simply exchange the sign and get a positive value. was converted and processed. However, in this case, the visible surfaces are displayed using the same material both on the front and back, and the light sources are displayed as if they always exist in pairs in opposite directions. In general, the normal vector is in the positive direction (the direction of the arrow)
The surface is defined as the front surface, and the surface in the opposite direction is defined as the back surface.
Consider a curved surface that forms part of a cylindrical shape, as shown in Figures 4a and 4b. Here, the outer surface of the cylinder is the surface,
The inside side is the back side. At this time, if a light source is present on the left side of the object as shown in FIG. 4a, the surface of the cylindrical hatched portion 15 is visible but is not illuminated by light. Further, the white portion 17 is a surface where the back surface is visible and is not exposed to light. When the light source is on the right side of the object as shown in FIG. 4b, the hatched portion 16 of the cylinder becomes a surface on which the back surface is visible and is illuminated by light. Further, the white portion 18 is a surface that is visible and is exposed to light. Even if you can see the surface in this way, there are times when light hits that part and times when it doesn't. Similarly, even if the back side is visible, the light may or may not hit it. However, in conventional devices, only one set of reflection coefficients (material coefficients) is given to one surface, and when the inner product of the normal vector and the light source direction vector becomes negative, the sign is mechanically converted and processing is performed. I was gone. The operation of exchanging the sign when the inner product is negative is equivalent to virtually arranging a light source having the same intensity in the completely opposite direction with respect to the actually existing light source. Moreover, setting the reflection coefficients (material coefficients) to one set means that calculations are made assuming that even if the back surface is visible, it has the same reflection characteristics as the front surface. Now, if the inner product of the normal vector and the light source direction vector is negative, it means that the angle between the surface and the light source exceeds 90 degrees, and the surface is visible as shown in Figure 4 a and b. However, there are two possible cases: 15, where no light hits that side, and 16, where the back side is visible and is hit by light. Conventional devices have the drawback of not being able to display the difference between the two types, since they do not take into account the display on the back side or whether or not light actually hits the screen. Also, if the inner product of the normal vector and the light source direction vector is positive, the angle between the surface and the light source is within 90 degrees, and the fourth
As shown in Figures a and b, there are two cases: a case 17 where the back side is visible and no light hits it, and a case 18 where the front side is visible and the light hits it. Conventional devices similarly have the drawback of not being able to display the difference between these two types. After all, with conventional equipment, there are cases where the surface is visible and the light falls on it, and cases where the surface is visible and the light does not fall on it. There are four cases in total: when the back side is visible and the light hits it, and when the back side is visible and the light doesn't hit it, but it has the drawback of not being able to display the difference between them.

SUMMARY OF THE INVENTION An object of the present invention is to provide an apparatus that performs shading, including distinguishing between the front and back sides of a three-dimensional figure, in a display of a three-dimensional figure.

[Means for solving the problem] Considering a display object with a constant reflection coefficient, on that object Equation (1) is a relationship between two inner products, and the value of the inner product is in the range of -1 to 1. Therefore, a brightness table for a series of inner products of the reflection coefficient (material coefficient) of an object can be prepared in advance, and the brightness table can be referenced from the calculation result of the inner product.

[Function] Here, at least two sets of brightness tables are prepared corresponding to the material coefficients (reflection coefficients) of the front and back sides. A brightness table is created for the positive and negative regions of the inner product. Further, for each display figure, a front material index and a back material index for selecting a set of tables to be referred to are set in advance in correspondence with the front and back sides. Furthermore, in accordance with traditional practice,
Set the coordinate axes, and then set the Z coordinate axis in a direction perpendicular to this, with the positive direction of the Z axis pointing toward you from the screen. With the Z-axis determined in this way, the front and back sides of the figure are determined based on the sign of the normal vector component in the Z direction of the figure, and different material indexes are selected for the front and back sides. In addition, in the case of tails, the inner product calculation is performed on the normal vector whose sign is reversed. This makes it possible to distinguish between displaying areas that are not exposed to light on the front and areas that are exposed to light on the back.

[Embodiment] FIG. 1 shows the overall configuration of an embodiment of the present invention.
The coordinate transformation processor 20 receives the coordinates of each vertex of the approximate polyhedron and the unit normal vector from the host computer 10, and performs processes such as rotation and translation of the coordinates as necessary. As a result, these values are ultimately converted to values in a coordinate system with the X-Y axes running parallel to the display screen of a CRT, etc., and the Z-axis perpendicular to this and pointing toward you from the screen. Ru. The contents of this process are not directly related to the present invention and are detailed in the above-mentioned book by Foly et al. The coordinate transformation processor 20 also receives from the host computer 10 the front material index, the back material index, and the surface display mode for each surface of the approximate polyhedron.

The processor 20 converts each edge of the approximate polyhedron into a polyline when the display mode is a frame (wire frame) display, and converts each face of the approximate polyhedron into a polyline when the display mode is a surface (shading) display. The data is transferred to the pixel generation processor 30 as a polygon). At this time, a broken line originally does not have front or back sides, but in order to distinguish whether the front side or the back side is visible, the front and back sides of each line segment are determined based on the normal vector of the vertex of the approximate polyhedron that is the break point. It can be so. In this way, the line segments and plane figures from the processor 20 are converted to the element generation processor 3 as polylines with normals or polygons with normals in the form of their vertex coordinates and unit normal vectors.
given to 0. At the same time, the front and back material indices are given. As described above, this material index selects a set of brightness tables having different contents for each material.

Inner product calculation processors 41 and 42 input the normal vector N→, light source direction L→, and light source/line-of-sight intermediate direction H→ from the element generation processor 30, and calculate inner products (N→・L→) and (N→・H→), receives the front or back material index from the register 43, and outputs the reference address of the brightness table. The determination of front and back is basically made based on the positive or negative of the Z component of the normal vector, but the details differ between Gouraud shading and Fong shading. It also depends on which normal vector is used. First, when performing Fongshading, by interpolating from the normal vector at each vertex of the polygon,
Dots (pixels) required to display the polygon
Find the normal vector for each. Therefore, the determination of front and back is performed by the pixel generation processor 30.
When calculating the normal vector N→ of each point of the figure, this is done based on the sign of its Z component, and in the case of tails, the sign of each component of the normal vector N→ is reversed. Also, the front or back material index is set in the register 43. However, with current CRTs, the screen size is 3 x 3 mm ²
The number of dots (pixels) required to display this figure is approximately 100 (=10×10), so
Generally, such front/back determination and register setting for each dot (pixel) requires a large number of times, and it may be necessary to perform the determination for each polygon. In this case, the average value of the normal vectors of each vertex of the polygon is taken as the normal vector of that face. Furthermore, it is also possible to simply substitute the normal vector of the first vertex that defines the polygon. In the case of Gouroshading, the normal vector for each dot (pixel) is not determined, and the front and back sides can be determined using the same method as the abbreviation of Fongshading. Also, in the case of a broken line,
For each line segment, it is possible to determine whether the line is front or back based on the average value of the normal vectors at both ends or the normal vector on the starting point side.

The brightness tables 51 to 56 calculate the brightness Iad corresponding to the sum of ambient light reflection and diffuse reflection and the brightness Is corresponding to direct reflection corresponding to each value of both inner products, into a red component (R) and a green component (G). ) and blue component (B).

Here, in equation (1), if the light source is sufficiently far from the display object, Ia and Ip can be considered to be constant on the display object. Therefore, equation (1) consists of two parts: a part consisting of the first and second terms, and a part consisting of the third term, and each part can be treated as a function of a single inner product. It is something. Therefore, it is sufficient to create two tables corresponding to each part. When the display object is made of a plurality of different materials, it is sufficient to create a plurality of sets of tables calculated using the diffuse reflection coefficient and direct reflection coefficient of each material.

In this embodiment, the contents of the brightness table are stored for a series of positive and negative values of the inner product, as shown in FIG. This is the luminance component of the part that is not illuminated by light. Furthermore, in this embodiment, sets of brightness data for 16 types of material coefficients can be stored in a table, and the material index for the front and back sides is 0.
~15 values can be selected.

These brightness data are front and back data calculated in advance using a light reflection model. Each piece of data is stored in a plane 511 of the table. There are 256 planes arranged for each material. These 256 planes are assigned 128 to each of the front and back sides, and sequentially store the brightness when the inner product is divided into 128 equal parts from 0 to 1 and from -1 to 0, respectively.

The brightness information read from the brightness tables 51 to 56 is summed for each color component by adders 61 to 63, and in the case of color shaded, the brightness of each dot (pixel) is calculated by this. has been calculated, and the result is stored in frame memory 7.
Write in numbers 1 to 73. In the case of Gouraud shedding, the brightness of the vertices of the approximate polyhedron is calculated by calculating the sum in the adders 61 to 63, and the result is read into the pixel generation processor 30 again (not shown). , the brightness of each dot on the patch plane, which is each face of the approximate polyhedron, is determined by interpolation from the brightness of the vertex and written into frame buffers 71 to 73 (not shown). Regarding the interpolation of the brightness of each dot on the patch surface and the writing process to the frame buffer,
This is detailed in the book by Floy et al., cited above.

From the frame buffer, DA converters 81 to 83
Through this, the brightness of the CRT monitor 9 is controlled, and shading is achieved.

According to this embodiment, after the inner product for each pixel is obtained by referring to the brightness table, the processing speed is faster than when calculating equation (1) one by one, and the table is not exposed to light. To be able to distinguish between a point and a point illuminated by light on the back.

[Effects of the Invention] According to the present invention, it is possible to select a set of brightness tables to refer to by determining the front and back sides of each point of a figure, so that the display that distinguishes the points hit by light and the points not hit by light, and the front and back sides can be quickly performed. There are advantages to doing so.

[Brief explanation of the drawing]

Fig. 1 is an overall configuration diagram of an embodiment of the present invention, Fig. 2 is a configuration diagram of a light reflection model, Fig. 3 is a diagram showing a display approximate polyhedron, and Fig. 4 is a diagram showing the relationship between the front and back of a surface and light. , FIG. 5 is a detailed explanatory diagram of the brightness table. 30... Image generation processor, 41, 42...
Inner product calculation processor, 51-56... Brightness table.

Claims (1)

[Claims] 1. When displaying a three-dimensional figure, the brightness of a point on the display surface of the three-dimensional figure is determined by the normal direction vector of the point, the light source direction vector, the viewpoint direction vector, and the reflection of light on the display surface. Calculated from the material coefficient indicating the coefficient,
In the figure shading device that displays the three-dimensional figure, it is determined whether the display surface is front or back, and if it is the front side, the brightness is calculated using the material coefficient of the front side, and if it is the back side, the brightness is calculated using the material coefficient of the back side. A figure shading device featuring: 2. Claim 1, characterized in that the front and back sides of the display surface are determined based on the normal direction vector.
Figure shading device as described in Section 1. 3. A patent claim characterized in that the luminance of the display surface of the three-dimensional figure is calculated by approximating the three-dimensional figure with a polyhedron and setting each point of the polygons constituting the polyhedron as a point on the display surface of the three-dimensional figure. The figure shading device according to item 1. 4 Approximating the three-dimensional figure with a polyhedron, and calculating the brightness of the display surface by making each vertex of the polygon constituting the polyhedron a point on the display surface of the three-dimensional figure, and calculating the brightness of the display surface of the three-dimensional figure. 2. The graphic shading apparatus according to claim 1, wherein the brightness of the point is calculated by interpolation from the brightness of the vertex.