JPS6252684A - Various density giving circuit for crt display device - Google Patents

Abstract

PURPOSE:To giving various densities to a polygon on a CRT by obtaining the vectors of a sight line, rays of light and normal at each vertex of the polygon so as to obtain any vectors on a plane. CONSTITUTION:A vector expressing the polygon is inputted to a vector calculating circuit 21. According to the given vector, the circuit 21 obtains the vectors of the normalized rays of light, sight line and normal at each vertex. The obtained vector is given to a various density giving circuit 22, and a vector on a ridge line and any dot vectors on the three-dimensional plane are obtained. Furthermore the vector is linearly interpolated at calculate brightness, and is given to a frame memory 23. Data stored in the frame memory 23 is given to a display controller 24, analog-converted by a D/A conversion, and is given to a CRT display 25.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of Industrial Application This invention relates to a shading circuit for a CRT display device, and in particular, in order to realistically represent an image, it specifies a light source and a viewpoint, and determines the position and position on the surface of the image. Based on this relationship, the present invention relates to a shading circuit that calculates the brightness at that position and performs shading processing.

Prior art FIGS. 6 and 7 are first views for explaining the principle of shading by a conventional CRT display device, and FIG.
The figure is a diagram for explaining how to obtain the normal vector for shading, and FIG. 9 is necessary for explaining the normal vector and line-of-sight vector for the rays of solid 1 to 3.

First, with reference to FIGS. 6 to 9, we will explain how to apply a brightness 'Ia' to an image in a C, RT display device.As shown in FIG. When displaying both images 1 and adding brightness shading to this image @1, place light source 2 at the top left of image 1.
11 and 12 of image 1 are made brighter, and 13 is made darker, and the brightness of the surface of image 1 is made different. Therefore, when looking at image 1 with line of sight 3,
Each side of image 1 looks realistic, as if it had been given a different brightness gradation.

However, if the image 1 is a cube as shown in FIG. 6, the brightness if! ! ! Although it is possible to perform lightening, if the image 4 shown in FIG. 7 is a cylinder, m-lightening is difficult. This is because the side surface 41 of the cylinder 4 is a curved surface, and it is difficult to make the left side of the side surface bright in FIG. 7 and darken the right side. Therefore, cylinder 4
The side surface 41 is divided into a plurality of parts, the curved surface is approximated by a plurality of rectangles, and the rectangular part on the left side is made brighter, and the rectangular part on the left side is made darker toward the right side. As a result, it appears as if the side surface of the cylinder 4 is shaded. Further, the upper surface 42 of the cylinder 4 is divided into triangles, and shading is applied to each of the divided triangles.

By the way, as for shading processing, constant shading, which keeps one plane at a constant brightness, and glow shading, which allows for smooth shading, are often used, but there is a method called shading, which allows for even higher quality expression. Are known.

Next, a method of shading a focus will be described with reference to FIGS. 8 and 9. First, as shown in FIG. 7 above, when the top surface 42 of the cylinder 4 is divided into polygons (triangles) 5 as shown in FIG. The normal vector N1.J3 is normalized to obtain the median vector N1. Find N2 and N3.

;In particular, the ridgeline 54 of polygon 5. ．． On 55 and 56? Incoming line vector N4. N5 each has two vertices 51
It is obtained by linearly interpolating and normalizing the edges 54 of and 52 and the edges 56 of vertices 51 and 53.

Furthermore, the normal vector N6 at any point 59 on the plane of the polygon 5 is 2 which intersects and covers the scanning plane passing through this point.
It is obtained by linearly interpolating and normalizing the normal vectors N4 and N5 at the two edges.

Next, as shown in FIG. 9, the ray vector P and line-of-sight vector E at each point are determined and normalized from the normal vector N to point 59 determined as described above. 'Z of the ray vector P and the normal vector N, the angle is 1, co
Find s i. Furthermore, the reflection of the light beam 1-le R and m
! Assuming that the angle formed with the vector E is θ, cos θ is determined.

Reflection vector R from ray vector P and normal vector N
To calculate , perform the following calculations.

In short, the ray vector P (XP , Yp , Z
p ), the normal vector N (XN, Y,, Z,) and the reflection vector R (X,, Y,, Z,) of the ray, then A −N−(P+R) /2 then △・XN = (XP +XR) / 2A-YN=
(Yp +Y,)/2 A-ZN= (Zp 10 ZR) /, 2 Therefore, Xi= =2A ”X1l-Xp...(1>
YP-2A-YN-YP...(2) Z== =2
A-ZN-Zp...(3)XR2+YR2+Z
t+ 2 -4△2 (XN' +Y++ 2+ZN 2)4A
(XN -Xp +YN -Yp +ZN
”Zp )+XP 2+Yp 2+Zp 2 By the way, the ray vector P and the normal vector N.

Since the line-of-sight vector E is a unit vector, it is expressed by the following equation.

1-4A2-4A (XN -XP +YN -YP +ZN '' Zp ) + 1 Therefore, A=XN -XP+YN -YP+zN -ZPOn the other hand,
Diffuse reflected light cos i is determined by the following equation.

os i −(P, N> =Xp −XN 10Yp −YN +ZP −Z
N...ku4) Also, the specular reflection light COS θ is obtained by the following equation.

CO3θ −(R,E) =XR−XE+Yt ・YE +ZR−ZE−(2A
-X--Xp) ・Xt:+(2A-YN YP
)・YE + (2A-ZN -Zp) ・Ze-2△(
XN -XE+YN -Y[+ZN -ZE)-(XP
・×ε +YP −YE +ZP −7ll: )・
... (5) A, CO3+, cosθ obtained as above
Based on, the brightness I is 1=Ic+Δ(Bcos i +C(cosθ)7), where lc, B, C, and n are determined by constants.

Problems to be Solved by the Invention In the above-mentioned method of shading a photo, it is necessary to normalize the normal vector N for each pixel. Further, it is necessary to obtain a normalized line-of-sight vector E and a ray vector P for each pixel. In general, vector V (
x, y, z), it is necessary to divide each element by x −←y +7. That is, normalized vector V-=(X/X-1+Z
, V/i2+z2. z/ x +y +z
).

In this way, the shading method for the fox is calculated as follows:
Since there are many numbers, the processing time becomes long and high-speed processing cannot be performed. If high-speed processing was to be achieved using a hardware configuration in a graphic display, extremely large-scale hardware would be required, and if necessary, the processing would have to be performed by a host computer.

Therefore, it is a principal object of the present invention to provide a shading circuit for a CRT display device which can perform high-quality luminance shading at high speed with as little computational processing as possible.

Means for Solving the Problems The shading circuit of the CRT display device according to the present invention has the following functions at each vertex of a polygon constituting a three-dimensional plane:
The normalized line-of-sight vector, ray vector, and normal vector are obtained by the first vector calculation means, and the line-of-sight vector, ray vector, and normal vector at two vertices constituting the edge of the polygon are linearly interpolated, respectively. A vector obtained by multiplying the angle formed by the same type of vector at each vertex by a first correction coefficient determined by the interpolation position on the ridge line is obtained by a second vector calculation means and used as a vector on the ridge line, Linearly interpolate vectors on two ridge lines that intersect the scanning plane passing through an arbitrary point on the three-dimensional plane, find the vector at that arbitrary point, and find the same type at the points on the two ridge lines that intersect the scanning plane. The third vector calculation means multiplies the angle formed by the vector by the second correction coefficient determined by the interpolation position at each arbitrary point to obtain the vector at the arbitrary point, and each vector obtained by each calculation is Based on this, shading (=I) processing is performed.

Function: To add shading to the CRT display device of the present invention, the circuit calculates the normalized line of sight vector, ray vector, and normal vector at each vertex of a polygon, and calculates each vector at the vertex and an arbitrary point on a three-dimensional plane. By linearly interpolating each vector in In addition, there is no need to normalize the vectors on the ridgeline and the vectors at arbitrary points on the three-dimensional plane, and the total number of 11ffi can be reduced. This enables high-speed processing for shading.

Examples of the invention FIG. 2 is a schematic block diagram of an embodiment of the present invention.

At J3 in FIG. 2, a vector representing a polygon is input to the vector calculation circuit 21. Although not shown, this vector calculation circuit 21 is composed of a CPU, ROM, and RAM. Then, the vector calculation circuit 21 calculates a normalized ray vector, line-of-sight vector, and normal vector at each vertex based on the given vector. Each vector obtained by the vector calculation circuit 21 is given to a circuit 22 with shading. 22 calculates a vector on the ridge line and a vector at an arbitrary point on the three-dimensional plane based on the normalized ray vector, line-of-sight vector, and normal vector at each vertex.

Further, the circuit 22 linearly interpolates the edges 1 to 1 on the ridge line and the vector [-] at an arbitrary point, calculates the brightness, and provides the calculated brightness to the frame memory 23. Frame memory 23 is CR
It has a storage area corresponding to each dot on the screen of the T-display 25, and the shading stores the data generated from the circuit 22.

The data stored in the frame memory 23 is applied to a display controller 24, converted into an analog signal by D/Δ conversion, converted into a video signal based on a color conversion table, and applied to a CRT display 25.

FIG. 1 is a flowchart for explaining the specific operation of an embodiment of this invention, and FIG. 3 is a flow diagram for explaining a light source vector, a normal vector, and a line-of-sight vector in an embodiment of this invention. FIG. 4 is a diagram for explaining a method of linearly interpolating vectors on an edge.

Next, with reference to FIGS. 1 to 4, a method for adding shading by software processing according to an embodiment of the present invention will be specifically described. First, in step SPl (abbreviated as SP in the figure), the coordinate positions of the light source P and viewpoint E are designated as shown in FIG. In step SP2, the coordinates of each vertex 51, 52, and 53 of the polygon 5 and the normal vector N4 at a5 to each vertex. N2, N- are given to the shading circuit 21. In step SP3, the shading circuit 21 applies ray vectors P, , P2, P to each of the vertices 51, 52, and 53 respectively.

and the line-of-sight vector ]-le E, , E2 , E, are determined.

These ray vectors P+, P2, P= and line of sight vector E3. E2. The method for finding E3 is the same as the conventional Fung method.

In step SP4, each vector applied to each vertex 51, 52, 53 is interpolated between the vertices for each scan line. In other words, the ridgeline 54. which connects the vertices 51.52. Ridge line 55 a3 connecting vertices 51 and 53 and vertices 55 and 5
3, a normal vector N, a ray vector P, and a line-of-sight vector E on the ridge line 56 are determined. To explain more specifically, for example, to the normal line') ttN+ (XN +
, YN + , ZN + ) and N2 (X-2, Y
N2. Z112) is linearly interpolated) ttN (X
N, YN, ZN) C. It is obtained from the following equation 6.

However, 0≦t≦1 The magnitude IN+ of this vector N is determined by the following formula 7.

l N I= (X++ 2+Y++ 2+ZN 2)
=(t2 (XN, 2 +YN, "+ZN -)
+(1j >2(XN 2' +YN 2'+ZN
2) +2t (1t) (XN+ ・XN2+Y,
, ・YN 2 + ZN I
・ Z N 2 ) ) ・・(
Since N2 is a unit vector, X N
Blind 2 + YN 1' +
Z N 1 ” = Xs 2
' + '1'N22+Zs22=1,',1Nl=(t2+(1-t)2 +2t (1-t><N+・N2)
)=(1-2t(1-t)(1-cos ρ
)1... (8) <11+-02) is the inner product of the normal vectors N and N2, so (n + "n 2 )-1N+ l ・
IN21cosρ−COSρ Therefore, if the linearly interpolated normal vector N converted into a unit vector is N-, then N=-N/IN'l-
N'[1-2t(1-t)<1-cosρ)) -N'(1+t(1-t)(1-cosρ>
)...(9) 0±2t(1-t)≦1/2 By the way, the magnitude of COSρ is the normal vector Nl, N
It is determined by the angle ρ formed by 2, and the value is determined by the number of divisions of the curved surface. For example, if a 360° curved surface is divided into 10 parts, the result will be ρ-366, but since the number of divisions is usually considered to be larger, it is considered that ρ≦36°. ρ−3,
66, it becomes COSρ-0.81. Generally 0
．． Considering 8≦COSρ≦1, Q=2t (1-t) (1-cos ρ)≦0
．． 1, and the approximation of the above-mentioned equation (9) is established.

1+t(1-t)(1-co
sρ) is a correction coefficient. In step SP5, the linearly interpolated normal vector N- is multiplied by this correction coefficient.

The ray vector P d5- on the ridgeline 54 and the line-of-sight vector E are also obtained in the same manner. Further, a normal vector on the edge line 55 connected by the vertices 51 and 53.

Similarly, the ray vector and line of sight vector are obtained by linear interpolation, and each is corrected.

Next, in step 6, the interpolated two points on the ridge are used as a starting point and an ending point, and a vector between the two points is determined by interpolation. That is, in this step SP6, the normal vector I~, the ray vector, and the line-of-sight vector of an arbitrary point on the three-dimensional plane within the polygon 5 are determined. , that is,
For example, as shown in FIG.
With the interpolated point 58 on the ridge line 55 connecting N4. Ray vector P4. Find the line-of-sight vector E. and,
In step SP7, the normal vector N4, the ray vector P4. line of sight vector E
4 is multiplied by the correction coefficient in the same manner as described above. In step SP8, cos i, co
sθ is determined, and then the brightness value is determined based on the vector corrected as described in (e) above. That is, the brightness value I
is I −IC+A (Bcos i +C(cosθ)
'')...(10) However, cos i is 003 t-Xp ・Xs +'VP ``yN + Z
p °ZN, and COSθ is determined as CO3θ=2CO3i −Z NZ p. Then, COs i obtained in this way,
The brightness value is determined by substituting cos θ into the above equation (10).

In step SP9, it is determined whether the interpolation of the points between the starting point 57 on the ridgeline 54 and the ending point 58 on the ridgeline 55 has been completed, and if the interpolation up to the ending point 58 has not been completed, 1) tJ Steps SP6 to SF3 are repeated. Furthermore, J3 is in step 5P10, and vertices 51 and 5
It is determined whether the linear interpolation of each vector at each point on the ridge lines 54 and 55 between 2 and 51 and 53 has been completed, and if it has not been completed, the steps SP4 to SF described above are performed.
Repeat step 3. In this way, the luminance value of each edge of the polygon 5 and any point on the three-dimensional plane is determined, and the series of operations is completed.

FIG. 5 is a block diagram of another embodiment of the invention. In the embodiment shown in FIG. 5, shading is performed using a hardware circuit configuration. First, referring to Figure 5,
The configuration will be explained. The buffer 60 stores data representing the coordinate positions of the light source P and viewpoint E shown in FIG. The buffer 61 also stores coordinates (XS I + '/S l ・Z S + > +
(x52 + V S 2 + Z, 2) and (
Xsa, Vs3. Zs3) is stored. Furthermore, the buffer 62 stores the normal vectors Nl, NZ, N
, the vector value (XNS11'l'N11IIZNSI
>l (XNs2.VNS21ZN52) and (X
Nsy+Yqsy+ZNS3) are stored respectively. The data representing the light source and viewpoint position stored in the buffer 60 and the data representing the vertex stored in the buffer 761 are provided to ΔL U 63.

ALU63 was given. Based on the data, data representing the ray vectors P,,P2,P,<Xp+,V
p+, Zp I), (XP2.V
F6゜ZP2) and (Xp 31VP 31ZP,
), and the line-of-sight vector E1. E2, E-
Data representing (Xi++'/E+, ZEl), (Xε
2 r V E 2 + Zε2) and (Xε3 +
V E 3 *7E,) are determined respectively. ALU・
The divider 64 calculates the slope of each edge line 54, 55.56 in order to interpolate between each vertex 51, 52.53. DDA65 is the content stored in buffer 761 and △
LU-! The coordinates between the vertices are compensated based on the slope determined by the 1 calculator 64. Similarly, DDA66 interpolates normal vectors between vertices, and DDA67 interpolates ray vectors between vertices! The DDA 68 interpolates visual monument vectors between vertices.

That is, the DDAs 66 to 68 interpolate the normal vector N, the ray vector P, and the line-of-sight vector E, respectively, to obtain a starting point vector and an ending point vector on the ridgeline of each solid.

As explained above, the ALU/multipliers 70 to 72 are
The outputs of the DDA 66 to 68 are corrected based on a correction coefficient of 1+t (1-t ) (1-cos ρ). ALU・Division 173 is polygon 5
In order to interpolate the coordinates of an arbitrary point on the three-dimensional plane, the inclination of the line segment connecting the starting point on the ridgeline 54 and the ending point on the ridgeline 55 is 'atl'. The slope determined by the ALU/divider 73 is provided to the DDA 77. D
The DA 77 adds the inclination determined by the ALU/divider 73 to the coordinates between the vertices interpolated by the DDA 65, and provides the coordinates of an arbitrary point on the three-dimensional plane in the polygon 5 to the frame memory control unit 86.

The ALU divider 74 interpolates the starting point on the edge line 54 and the ending point on the edge line 55 to find the slope of the normal vector N. The slope determined by this ALU/divider 74 is given to the DDA 78. DDA78
adds the slope determined by the ALU-divider 74 to the normal vector N between vertices interpolated by the ALU-multiplier 70, and calculates the normal vector N at any point on the plane.
It interpolates.

The ALU/divider 75 determines the slope of the ray vector P based on its starting point and ending point.

The DDA 79 adds the slope to the ray vector P between the vertices interpolated by the ALU/multiplier 71.

The ALU/divider 76 calculates the slope of the line-of-sight vector E based on the start point and the end point, and the DDA 80 adds the slope to the interpolated IQ point-to-point line-of-sight vector E.

The ALU/multiplier 82 corrects the normal vector N at any point on the plane.
3 also corrects the ray vector P, and AL
The U multiplier 84 corrects the line-of-sight vector E. ALU/multiplier 85 is △Ill/multiplier 82 to 8
The luminance is calculated based on the vectors each corrected by 4, and is provided to the frame memory control unit 86. The frame memory control unit 86 controls the ai degree of the coordinate given from the DDA 77 based on the Ri degree calculated by the A L tJ multiplier 85 and provides it to the frame memory 87 .

Next, the operation will be explained. The buffer 60 contains light r.
Data representing the respective coordinate positions of Ap and viewpoint E are stored, and the buffer 61 stores data representing the respective coordinate positions of vertices 51, 52, and 53 (Xs+, Vsl, 25+)1 (X5
2. VS2, 252) and (Xs3.Vs3+Zs,
) are stored in the buffer 62, and each vertex 51, 52 .
Data (XNI, VNl, ZNI) (XN
2゜V N z, Zh 2 ), (Xv 3
, V N s, Z N a) are stored.

ALLI63 is based on the contents of buffer 760.61,
Ray vector P= , P2 at each vertex.

Data representing P (XP + , Vp + , , Z
p+).

(XP21VP21ZP2>l (Xps*Vp3*
ZP3) and line-of-sight vectors E, , E2. Data representing E (XE+, Vg++Zg+), (XI=2, VE2
．． ZE2), (Xtz, Vts, ZI:3) are determined.

The ALtJ/divider 64 receives the calculation result of the ALU 63,
The respective contents of buffer '61.62 are given.

Based on the control from the controller 69, the AL (J-divider 64 calculates the edge line 5 that connects the vertices 51, 52, and 53, respectively.
4.55.56 slopes Δx, Δy, Δ2, and the normal plane 1-N.

N2. The slopes △XN, △VN, △zN of N3 and the ray vectors P, , P2 . Slope of P3 ΔxP, ΔyP, ΔZP
and line-of-sight vector E, ,E2. E, slope Δ×7. ΔV
Find E+Δ2ξ.

DDA65 is each vertex 51 stored in buffer 761
．． 52.53 coordinates (Xs++Vs+.

Zs+ ), (Xs2.Vsz, Zs2), (Xs3
t V S 3 r Z S 3 ), the slope ΔX, Δ
y and ΔX are added to interpolate between each vertex 51, 52, and 53.

Thereby, for example, the starting point 57 on the ridgeline 54 and the ridgeline 5
The end point 58 on 5 is determined.

Is DDA66 a buff? The normal vectors N, , N2 . For each coordinate of N, the slope △XN,
Add ΔVn and ΔZN, roughly, ALU/multiplier 70
Vector correction is performed by , and the starting point and ending point of each normal vector are determined.

Similarly, the DDA 67 adds the slopes ΔxP, ΔVp, and ΔZp to each normal vector, and further performs vector correction using the ALU/multiplier 71 to determine the starting point and ending point of the ray vector P.

DDA68 has a slope ΔxE rΔVE for each line-of-sight vector.
, ΔzI:, and the ALU-multiplier 72 performs vector correction to determine the starting point and ending point of the line-of-sight vector E.

The ALU/divider 73 determines the slopes Δx', Δy', and ΔZ' of the line segments connecting the starting point and the ending point on each edge, and provides them to the DDA 77. The DDA 77 adds the inclination to each start point and end point determined by the DOA 65 to determine the coordinates x, y, and z of the polygon 5 on the plane, and provides the coordinates x, y, and z of the polygon 5 to the frame memory control unit 86 . On the other hand, the ALU/divider 74 calculates the slope of the ray vector at a point on the plane Δ×N', ΔyN'lΔZN'
Find it and give it to 0DA78. 0DA78 is ALU・
Slopes ΔxN', ΔyN', and ΔZN' are added to the starting and ending points of the normal vector determined by the multiplier 70, and the normal vector N at the point on the plane is interpolated. DD
A79 also interpolates the ray vector P by adding the slopes Δ×P', ΔVp', and Δ2P' to the start and end points of the ray vector P, and the DDA80 calculates the 8A ray vector E.
The line-of-sight vector E is interpolated by adding the slopes ΔXε', Δyε', and ΔzE' to the starting point and ending point.

Then, the ALU/multipliers 82 to 84 respectively correct the normal vector N, the ray vector P, and the line-of-sight vector E, and the ALU/multiplier 85 calculates the brightness based on each corrected vector. The determined brightness is given to the frame memory control section 86. The frame memory control unit 86 controls the brightness of the coordinates designated by the DDA 77 based on the calculated brightness, and provides it to the frame memory 87.

The shaded image data stored in the frame memory 87 is then displayed on the CRT display.

Effects of the Invention As described above, according to the present invention, the normalized line-of-sight vector, ray vector, and normal vector at each vertex of a polygon are obtained, and each vector at the vertex is calculated from an arbitrary point on a three-dimensional plane. By linearly interpolating each vector in There is no need to convert each vector and the vector at an arbitrary point on a three-dimensional plane into positive JM. Therefore, the total number n1 can be reduced and high-speed processing becomes possible.

[Brief explanation of drawings]

FIG. 1 is a flow diagram for explaining the operation of an embodiment of the present invention. FIG. 2 is a schematic block diagram of an embodiment of the present invention. FIG. 3 is a diagram for explaining a ray vector, a normal vector, and a line-of-sight vector in one embodiment of the present invention. FIG. 4 is a diagram for explaining a method of linearly interpolating vectors on an edge. FIG. 5 is a block diagram of another embodiment of the invention. FIGS. 6 and 7 are diagrams for explaining the principle of m-shading in a conventional CRT display device. FIG. 8 is a diagram for explaining how to obtain the normal vector for S tanzuki. FIG. 9 is a diagram for explaining a ray vector, a normal vector, and a line-of-sight vector. In the figure, 21 is a circuit with shading, 22 is a DDA, and 23 is a circuit.
is frame memory, 24 is display controller,
25 is a CRT display, 60°61.62 is a buffer, 63 is an ALU, 64, 73 to 76 are ALIJ.
Divider, 65 to 68° 77 to 80 is DDA, 7
0 to 72.82 to 85 are ALU/multiplier, 86
87 represents a frame memory control unit and a frame memory. (2 others) Akuta 7th f3 G Kai 9th figure counter

Claims (1)

[Claims] In a CRT display device, a three-dimensional plane and a three-dimensional
A shading circuit that performs shading processing on the three-dimensional plane when a dimensional curved surface is approximated by a plane, the shading circuit comprising: a line-of-sight vector normalized at each vertex of a polygon constituting the three-dimensional plane, and a ray vector; a first vector calculation means for calculating a normal vector; a second vector calculation means that calculates a vector obtained by multiplying the angle formed by the vector by a first correction coefficient determined by the interpolation position on the ridgeline, and uses the vector as a vector on the ridgeline; Find the vector at the arbitrary point by linearly interpolating the vectors on the two ridge lines that intersect with the scanning plane passing through an arbitrary point of and a second correction coefficient determined by the interpolation position at each arbitrary point. A shading circuit for a CRT display device, comprising shading processing means for performing shading processing based on each vector obtained by the third vector calculation means.