JPS6383871A - Shadow display method - Google Patents

Abstract

PURPOSE:To eliminate a gap produced between patches and to ensure such a fact that a free curved surface undergone the shadow processing seems to be a curved surface having the natural shadow, by obtaining a segmenting patch by enlarging a patch and segmenting a triangular unit area to perform the shadow processing. CONSTITUTION:Many triangular unit areas UA are segmented from a segmenting patch S(u,v)c obtained by enlarging a patch S(u,v) by a prescribed rate. Then the luminance information on the pixel included in the area UA to give shadow to a free curved surface based on the luminance information on the positions of three apexes of the area UA. An overlap area is produced at the boundary part between patches S(u,v)c adjacent to each other. Therefore a fact that a gap is produced between adjacent patches can be effectively avoided even though the patch S(u,v)c is segmented to the area UA and the shadow processing is applied to this area UA.

Description

[Detailed description of the invention] The present invention will be explained in the following order.

A: Industrial field of application B: Overview of the invention C: Conventional technology (Figures 13 to 14) D: Problem to be solved by the invention (Figure 15) E: Means for solving the problem (Figure 1) ) F action (Fig. 1) G example (Figs. 1 to 12) (G1) Determination of the number of divisions (Figs. 1 and 2) (G2) Generation of cutting patch (Figs. 1 and 12) (Figure 2) (G3) Processing procedure (Figures 1 to 12) (G4) Effects of the embodiment H Effects of the invention A Field of industrial application The present invention relates to a shading display method, for example, CAD
putter aided design) or CA
M (computer teraided manufac
This method is suitable for applying shading processing to a free-form surface generated in a method such as turing.

B. Summary of the Invention The present invention provides a shading processing method in which a triangular unit area is cut out from each patch stretched in a framework space and subjected to shading processing. By cutting out triangular unit areas from this and applying shading processing, the generation of gaps that conventionally occur between patches is avoided, and the free-form surface processed with shading appears to be a curved surface with natural shading.

C Conventional technology For example, when designing the shape of an object with a free-form surface using a CAD method (geometric abod
eling), designers generally use the 3
By specifying multiple points in a dimensional space (these are called nodes) and having a computer calculate a boundary curve network connecting the specified multiple nodes using a predetermined vector function, it can be expressed in a so-called wire frame. Create a curved surface. In this way, a large number of framework spaces surrounded by boundary curves can be formed (such processing is called framework processing).

The boundary curve network formed by such framework processing itself has the rough shape that the designer intends to design, and an interpolation operation is performed to create a curved surface that can be expressed by a predetermined vector function using the boundary curves surrounding each framework space. If it is possible to do so, it is possible to generate a free-form surface (which cannot be defined by a quadratic function) that is designed by the designer as a whole. Here, the curved surfaces stretched across each framework space form basic elements constituting the entire curved surface, and these are called patches.

Conventionally, in this type of CAD system, as a vector function expressing a boundary curve network, easy-to-calculate vector functions such as Bezier equation, B-spline (13-spl
A third-order tensor product consisting of the formula (ine) is used,
For example, it is considered to be optimal for mathematically expressing free-form surfaces that have no special features in shape.

In other words, a free-form surface that has no special features in shape is
When points given in space are projected onto the xy plane, the projected points are often arranged regularly in a matrix, and when the number of projected points is expressed as m x n, the The framework space can be easily spanned using quadrilateral patches expressed by cubic Bezier equations.

On the other hand, when trying to create a smooth free-form surface on a curved surface with geometrical characteristics (for example, a curved surface with a greatly distorted shape), it is necessary to satisfy the condition of tangent plane continuity for the shared boundary of the framework space. It is possible to create a patch consisting of a free-form surface by finding internal control points and using a vector function representing the free-form surface determined by the internal control points.

By the way, if it is possible to add shading to the free-form surface represented by the free-form surface data generated by such a method by performing shading processing, it will be possible to display the curved surface three-dimensionally on the display.
It is believed that it is possible to provide high-quality graphic images, and a method has been proposed in which such shading processing is realized by linear interpolation (Japanese Patent Application No. 60-37).
No. 077, Patent Application No. 1983-37078, Patent Application No. 1983-3
No. 7079).

This shading processing method, for example, as shown in FIG. 13 and FIG.
, the patch S (U representing the coordinates of Ill Vl
For each divided area, the triangular unit area UA is cut out, and the brightness of the free-form surface is calculated for the three vertices of the triangular unit area UA. Based on the luminance plane stretched over the triangular unit area UA using the three data, linear interpolation calculation is performed to calculate the luminance of all the pixels included in the triangular unit area UA.

In this way, the shading process can be executed in a much shorter time than in the case where the brightness is calculated one by one for every pixel included in the triangular unit area UA.

D Problems to be Solved by the Invention Incidentally, when performing shading processing using this method, if the number of divided patches is reduced, the processing time will be correspondingly shortened.

However, in the above method, both large patches and small patches are divided by the same number of divisions, so if the number of divisions is set small, the boundaries between adjacent patches in large patches will be displayed as straight lines. There is a problem with becoming.

On the other hand, if you increase the number of divisions, the boundaries of large patches will be displayed with natural curved shapes, but at the same time small patches will also be divided into smaller parts than necessary, which will increase the processing time. There is a problem of becoming long.

One method to solve this problem is to change the number of divisions for each patch depending on the size of the patch, and - cut out a triangular unit area so that the side length is a predetermined size and process the shading. There are ways to do this.

However, when performing shading processing using this method, there is a risk that a portion (this is called a gap) where shading processing cannot be performed may occur at the boundary position of adjacent patches.

For example, as shown in FIG.
(un v) I % S (un v) When applying 2, the first and second patches S (un V) l and S
(u, v) t is divided into two patches S (un v) I and S (
+! Assume that +V□ is connected.

At this time, the large patch S(un vl I is the shared boundary C0M1 in the U direction surrounding the patch S(un vl l)
Based on the length of the longer shared boundary C0M3 among the shared boundaries C0M3 and C0M3, there are four dividing points (Q+.1, Q, .1, Q, .9, C4°1) and ( Q, □, , Qt□1, Q3□, C4t,) are set for the parameter U.

Similarly, based on the length of the longer shared boundary C0M4 among the shared boundaries C0M2 and C0M4 in the V direction, the dividing point C5 and QOth are set for the parameter V on the coexistence boundaries C0M2 and C0M4.

Thus, in the patch S (u+v□), the triangular unit area UA is cut out using 18 dividing points and nodes arranged in a matrix in the U direction and the V direction, and shading processing is performed.

On the other hand, a small patch S(un.2 is a patch S
(Among the shared boundaries COMI and C0M6 in the U direction surrounding un vl Z, two dividing points (Q l., C2°) are created on the shared boundaries COMI and C0M6 based on the length of the longer shared boundary COMI and (Q+.2, Qzoz) is set for the parameter U.

Similarly, one dividing point Q0 is created on the shared boundaries C0M5 and COMT based on the shared boundaries C0M5 and C0M7 in the V direction.
,2, and P3,2 are set for the parameter V.

Thus, in the patch S (un v) t, the triangular unit area UA is cut out using 12 dividing points and nodes arranged in the U direction and the V direction, and shading processing is performed.

However, if we do this, the first patch S (ur
V) Triangular unit area UA 1 is cut out using nodes P at both ends of the shared boundary COMI formed by framework processing. . 1I=P (3°1 segment is divided into 5 segments, whereas the second patch S (ur v
The triangular unit area UA of l t is cut out using the shared boundary C
OMI is divided into three parts.

Therefore, the node P,. . 1. The position along the shared boundary COMI of the triangular unit area UA that divides the area between ~P4°15 into 5 passes through, and the node P, as well. 3□ to P (331Z, which divides the triangular unit area UA into three parts, the position along the common boundary COMI of the triangular unit area UA passes through the position may not be lost, and a gap GUPX will occur between them).

This gap GUPX will not be subjected to shading processing, and as a result, there will be a portion without shading, resulting in a so-called hole.

When a portion cannot be shaded in this manner, the shaded free-form surface looks unnatural.

The present invention has been made in consideration of the above points, and attempts to propose a shading display method that does not generate gaps GUPX along the shared boundaries of adjacent patches and can perform shading processing in a short time. It is something to do.

Means for Solving Problem E In order to solve this problem, in the present invention, a large number of framework spaces surrounded by boundary curves are formed by framework processing, and parameters representing positions are assigned to each of the framework spaces. A patch S (un
In a shading display method in which a free-form surface generated by stretching vl is shaded, the patch S
Cutting out patch S (un vl obtained by enlarging un vl by a predetermined amount ΔMP) Cut out a large number of triangular unit areas UA from C (al+ vl
The three vertex positions P+ -Pz, the brightness information It of P3
, It, I:+, the free-form surface is shaded by interpolating the luminance information about the pixels included in the triangular unit area UA.

The cutout patch S (un v) which is an enlarged version of the F effect patch S (1++ v) (is the adjacent cutout patch S
(An overlapping portion occurs at the boundary between ur vl C. As a result, even if the cutout patch S (un v) is cut out into the triangular unit area UA and the shading process is performed, it is not possible to effectively eliminate the gap between adjacent patches. can be avoided.

G example An embodiment of the present invention will be described in detail below with reference to the drawings.

FIG. 1 shows an example in which the present invention is applied to a free-form surface formed as described above. When cutting out the patch S jut vl into a triangular unit area, the patch S Then, a clipping patch S (tl+vl c is generated), and a triangular unit area UA is cut out from this clipping patch S (un w> c).

In other words, the patch S Tar v) is defined by the parameters U and V defined as the following equation (1) and the shared boundary CO
3 using the control point P0° (consisting of nodes forming the framework space) represented by the position vector representing the position of one end of MI.
In the following Bezier equation, the following equation 5 (Il, Vl = (1unuE)
3(1-vlvF)'Pa.

・・・・・・(3) It is expressed as follows.

Here E and F are shift operators and patch S (un
The control point P(!+j
), the relationship is as shown in the following formula (4).

Here, if the parameters U and V are changed in a wider range than the range expressed by equations (1) and (2), then based on equation (3) under the conditions of equations (1) and (2), It is possible to obtain a cutout patch S (Ll+vl C) which is larger by a predetermined amount than the obtained patch S (un v).

Here, before obtaining the cutout patch S (un vl ()), first, the number of divisions for cutting out the triangular unit area UA is determined.

(Gl) Determination of the number of divisions The control point expressed by the two-dimensional position vector obtained by perspectively transforming the control point P (i, J) of the patch S (un v) to a plane corresponding to the display image is Corresponding to the point P(i, Jl, P +i, = +t (1 = Oll, 2.3.
j=o, i, 2.3), and similarly the patch S
The two-dimensional patch obtained by perspective transformation of (ul v) is made to correspond to patch S (un v), and S (U+ V)
, is expressed using .

Here, the patch S (u, vl) in the U direction is a common boundary C0M1 where the parameters V of T are V=O and v=l
and the distance between control points RuO and Rul corresponding to C0M3
, the following formula % formula % where the following formula Rull > Rul ...
...Once the result of (10) is obtained, the distance R between the control points in the U direction can be determined as Ru-Ru0 using the following formula.
), and when the result of the following formula % formula % (12) is obtained, the following formula R, = Rul −−・・・−(
13).

Further, the distance between adjacent pixels of the display image is expressed using a value, and the number of divisions in the U direction expressed by the following equation is obtained. Here (14)
The formula determines the number of divisions of each cutout patch S (un vl Furthermore, in this case, the shared boundary COMI
And in place of the length of C0M3, the distance between control points R8° and R
By determining the number of divisions based on □, for example, areas with small curvature can be divided finely.

Therefore, using such a method, the cutout patch S (
By dividing ul V, C, it is possible to obtain the effect of reducing the gap GUPX.

Similarly, for the V direction, the patch S (shared boundary C0M4 with parameter U of ulvl as U=O and u=1)
The inter-control point distances RvO and Rvl corresponding to C0M2 and C0M2 are determined by the following formula %.

From this, when the result of the following formula % formula % (17) is obtained, the distance Rv between control points in the V direction is calculated using the following formula Rv=Rv, -・-・(18)
When the result of the following formula % formula % (19) is obtained, the following formula Rv-Rv, ... (2
0).

Furthermore, in the same manner as in the case of equation (14), the number of divisions Kv of the patch S (ul vl c) for cutting out in the V direction is determined from the following equation.

(G2) Generation of a patch for extraction A method for generating a patch for extraction S (un v) c by enlarging the patch S (+l+v) by a predetermined size will be described below.

For example, when cutting out a triangular unit area UA whose side length is represented by the above-mentioned distance D-MP, this value MP is set to MP=5
(pixels) and the patch S lu+ vl is selected to be larger by ΔMP=0.5 (pixels) in each direction U and ■ (this selection is made by the operator's setting operation).

The change range of the parameter U corresponding to equation (1) is ul corresponding to the shared boundary COMI of v-0. and u2°,
Find the values u+o and u2° expressed by the following formula % formula % (22).

Similarly, the change ranges are set as U and ut+ corresponding to the shared boundary of v=l, and the values u11 and uz+ expressed by the following formula % formula % (25) are determined.

On the other hand, if we set the variation range of the parameter V corresponding to equation (2) as vl and v2° corresponding to the shared boundary of U=O, it is expressed by the following equation % equation % (2) Find the values v1° and v2°.

Furthermore, similarly, corresponding to the shared boundary of u=1, the parameter V
Letting the range of change in Vl+ and vz+, the following formula % formula % (3
1) Find the values Vl+ and V21 expressed by: ...... (33).

By varying the parameters U and V with respect to equation (3) within the range determined in this way, as shown in FIG. 1, the perspectively transformed patch S Tu+ V) ? It became larger in each direction U and ■ by a prescribed size than (
In this case, it is possible to obtain the extraction patch S (IIL v) (a by 0.5 [vixels]).

Furthermore, the cutout patch S obtained in this way
(u
n v) (Set parameters uC and VC that vary from O to 1, and set dividing point Q using parameters uc and vc.

In other words, using the parameters uk and vk obtained by dividing the range from 0 to 1 by the division numbers Ku and Kv obtained by equations (14) and (21), the parameters uc and vk obtained by the following equation 7 are Dividing point Q by VC
(,,,), and based on this, the patch S
(un v) A triangular unit area UA is cut out from e.

(G3) Processing procedure The image display device executes image conversion processing by the central processing unit (CPU) according to the processing procedure shown in FIG.

First, in step SPI, the conversion processing program is started, and in step SP2, the position of viewpoint 1 (Fig. 3) required for perspective conversion, the position of the light source required for shading processing,
and the number of pixels MP (representing the perspective-transformed triangular unit area - side length) when cutting out the patch into triangular unit areas are input by the operator.

Next, in step SP3, the CPU generates a three-dimensional free-form surface (represented by three-dimensional coordinates of x, y, and z) based on the three-dimensional free-form surface data stored in advance. Image 5, step SP2
When looking through a virtual screen 2 (consisting of a two-dimensional plane represented by xy coordinates as shown in FIG. 3) determined by a viewpoint 1 specified in , a three-dimensional free-form surface image 5
A perspective transformation matrix used to transform points on the curved surface of 2 to corresponding points on the virtual screen 2 is generated.

Next, in step SP4, the CPU calculates the control point P(
The data of t+Jl is read out, and the display area is determined in the next step SP5. This process is a step of determining a display area for displaying an image to be displayed at approximately the center of the display screen with appropriate dimensions. First, the control point data read in step SP4 is transformed into a perspective image generated in step SP3. Using a matrix, perspective transformation is performed on a two-dimensional virtual screen 2 as shown in FIG. The resulting two-dimensional control point P (l+417 in the X-axis direction X I
IaX and the minimum value X1n and the maximum 4fiY in the Y-axis direction
vs a x and the minimum value Y wa i n are respectively extracted, and the center position Xc of the maximum value X 1118
x, the center position Yc of the minimum value Y IIL h is determined by the following formula 7. The center position thus obtained (Xc, Yc
) is set at the center position of the rask display screen 11 of the display, and the display area A is such that the display image DBS fits within the size of a frame buffer having memory cells corresponding to pixels forming the display screen 11 of the display.
Define RE.

As is clear from FIG. 4, the display area ARE is
It has a region from maximum value X mmx to minimum value X @in in the axial direction, and from maximum value Y maw to minimum value Y in the Y-axis direction. ,
It has 4 areas.

After determining this display area ARE, the CPU executes subsequent processing steps only for pixels within the display area ARE. This means that the amount of conversion calculations for images to be displayed on the rask display screen can be further reduced. In other words, in general, when trying to display an image that has been subjected to image conversion processing on the rask display screen, it is necessary to calculate the image data to be displayed and its contents for all the pixels that make up the rask display screen. The calculation result is stored in the corresponding memory area of the frame buffer memory.
Since arithmetic processing is not performed on pixels on the raster display screen 11 for which there is no data to be displayed, the overall amount of image conversion calculation can be significantly reduced.

Next, the CPU moves to step SP6 and executes step S.
At P5, the two-dimensional control point P(i+j
After executing the above-mentioned equations (8) to (21) based on lT to determine the number of divisions of the predetermined cutout patch in the U direction and the V direction, the process moves to step SP7.

In step SP7, the CPU executes the above (22)2~(
33) Execute the calculation of formula to obtain the cutout patch S (u
n v) (parameters u1゜, u2 for generating
゜、ull、uz+、V l 0% V 20z V
After determining l l and vz+, proceed to step SP8.
Parameters uc and vc for dividing the cutout patch S (un v) c are obtained by performing calculations of equations (34) and (35).

Next, the CPU moves to step SP9, and executes step SP9.
Parameter ulo, u20% u found in 7
Ill, u! I % V I 0% V 20, Vll
, and vt+, the extraction patch S (II
+ vl c is generated, the dividing point Q (that is, each vertex data of the triangular unit area UA) for dividing the cutout patch S (un v) c is determined using the parameters uC and vc obtained in step SP8. Set.

In this embodiment, as shown in FIG. 5, the triangular unit area UA is cut out by one patch S.
(Based on the parameters uc and vc described above, the data DATA of un vl c is sequentially arranged at intervals such that the length of one side of the triangular unit area is a leading interval (not necessarily at equal intervals on a curved surface)2 Group cutting line groups L1 and L
The intersection positions of the two are sequentially calculated. Cutting line groups L1 and L
For example, the number of cutting lines included in 2 is selected to be 5 in the vertical and horizontal directions,
The cutting line group Ll and the cutting line group L2 are set to intersect with each other in a mesh pattern. In this way, the curved surface made up of data DATA for one patch is divided into a small head area UAX surrounded by two adjacent cutting lines of the cutting line groups LL and L2, and the small head area UAX is divided into four intersection points PX. It is cut out so as to surround it.

The small area UAX is divided into two triangular unit areas UA by a diagonal line L3 connecting two mutually opposing intersection points, and thus the curved surface represented by the data DATA is divided into a large number of triangular unit areas UA.

Furthermore, after cutting out triangular unit areas UA from the curved surface in this way in step SP9, the CPU calculates normal unit vectors for the three intersection points at the vertices of each triangular unit area UA, and , the vertex data is processed so that parts that are not visible from the viewpoint are not displayed on the display. As shown in FIG. 6, this process involves the visible part (this is called the visible part) when the curved surface 5A formed by the surface of the object 5 is viewed from the viewpoint 1.
This is to display only the portion corresponding to the visible portion on the display screen based on the fact that there is a visible portion and an invisible portion (this is called an invisible portion).

Here, the first condition for determining whether each part of the curved surface 5A is a visible part is that when viewing the object 50 and the curved surface 5A from viewpoint 1 along the line of sight ELL, the line of sight ELL intersects with the curved surface 5A. Among the points pH,, P12, and PI3, the surface portion of point P12 is located at the position pH of one example of the viewpoint of the line of sight EL1.
Due to the existence of a surface portion that intersects with L, it is hidden by the surface portion, and therefore, it is determined that the surface portion of point P12 is invisible, and the virtual screen provided between object 5 and viewpoint 1 is Vertex data conversion processing is performed to see through the surface portion of 1P11 that is visible on 2.

That is, for the three vertices of the triangular unit area UA, the line-of-sight unit vector E is calculated, and the inner product of the line-of-sight unit vector E and the normal unit vector N is calculated to generate visible-invisible data for each vertex. At this time, if the result of the inner product is positive, it means that the vertex is on a patch facing toward viewpoint 1, and if it is negative, it means that it is on a patch facing away from viewpoint 1. . Therefore, visibility can be determined by determining whether the result of the inner product is positive or not.

Following this, the CPU generates one cutout patch S (u
As shown in FIG. 7 for each vertex of the triangular unit area UA of + vl c, the distance vector D from the vertex px to the viewpoint l is calculated.

That is, in order to determine whether the surface is visible or invisible in FIG. 6, it is also necessary to determine whether the surface portion of interest is not hidden by another curved surface. Another object 6 exists between the curved surface 5A of the object 5 and the viewpoint 1, and the object 5 exists along the line of sight EL2.
When the line of sight EL2 intersects the curved surface 6A of the object 6 and then intersects the curved surface 5A of the object 5, the surface portion at the position P14 on the curved surface 5A of the object 5 is located at the viewpoint 1.
It is hidden by the surface portion at position P15 on the curved surface 6A of the object 6 on the side, and therefore, the visible surface is not displayed on the virtual screen 2 without displaying the invisible surface portion (the surface portion at position g P 14). It is necessary to display the part (the surface part at position P15).

Therefore, after calculating the distance vector D from the vertex px of the triangular unit area to the viewpoint 1 using the position vector S of the curved surface and the position vector E0 of the viewpoint according to the following equation 1 (38), the distance vector D is The absolute value is obtained as distance data D.

In this way, when distance data for a plurality of curved surface parts are obtained for the same pixel on the rask display screen of the display, it is possible to determine the data of the curved surface part closest to viewpoint 1 as the visible part.

Next, a process of generating brightness data for each vertex is performed.

In this step, as shown in FIG. 8, the brightness at each vertex PX is calculated, and the position vector SS of the light source 8
The position vector K relative to the light source 8 as seen from the vertex px is calculated using the following formula (39). Then, using the calculation result, the vertex PX
The cosine cos θ of the incident angle θ is calculated by the following formula based on the inner product with the O normal unit vector N, and this is set as the variable A (.

Furthermore, using this variable A, the brightness I can be calculated using the following formula (1)% (41) Calculate by

Here, the value of the constant R is, for example, about 0.22, whereas the variable A fluctuates in the range of 0 to 1 (θ is ±π/2
). In this way, the brightness I changes according to changes in the light incident on the vertex PX from the light source 8, and thereby the brightness data of each vertex is obtained.

Subsequently, the CPU moves to step 5PIO and uses the cutout patch S obtained in steps SP6 to SF3 described above.
As shown in FIG. 5, three vertex data of one triangular unit area UA are extracted from each vertex data of +ui Vl c, and shading processing within the triangular unit area UA is performed by interpolation calculations in steps 5P12 to 5P15.

In this way, dividing the data DATA of the curved surface to be processed into triangular unit areas UA and obtaining data about the three vertices means that when the triangular unit area UA is converted onto the rask display screen of the display, the converted This means that the display of the pixels included in the triangular unit area is represented by the data of the three vertices. Therefore, by performing subsequent processing based on the data of the three vertices, the data processing speed can be increased. This means that it is possible to significantly speed up the process.

In step 5PII, the CPU selects the display area ARE.
It is determined to which triangular unit area UA the pixel PC (referred to as a processing point) whose brightness is to be calculated and determined at the current moment among the pixels of one patch included in the pixel belongs. As shown in FIG. 9, this determination is made at a point Pl expressed by position vectors P, , P, and P on the
, P2 and P3 respectively.

b is expressed by the following formula % Formula % (42) Furthermore, from the point Pl represented by the position vector P to the processing point PC represented by the position vector PC, the vector R represented by the following formula % Formula % (44) is used. and the following formula R=αa+β
b... Determine the values of variables α and β that satisfy the relational expression (45).

At this time, if the processing point PC is located inside the triangular unit area UA, the following relationship is obtained. Such an operation can be simply obtained by calculating in advance the inverse matrix of the matrix [aSb] obtained from the vectors a and b.

In this way, the position of the processing point Pe is set in the triangular unit area UA.
When it is determined that the area is outside the triangular unit area UA, the CPU does not perform any subsequent interpolation calculations on the triangular unit area UA, and continues to search for a new triangular unit area UA until it can find a triangular unit area UA that includes the processing point Pc inside. The determination for each processing point PC is repeated.

As a result, when the triangular unit area UA within which the processing point PC is found is found in step 5PII, the CPU moves to the next step 5P12 and executes visible or invisible determination processing by linear interpolation. In this process, the CPU sequentially reads out visible-invisible data stored for the vertices P, , P2, and P3 of the triangular unit area UA, and determines the position P2 on the display screen of the display as shown in FIG.
, P, , P, the corresponding visible-invisible data VI+ , VIZ , VI3 are set vertically. Then, a visible-invisible plane vpx is set at the tips of the visible-invisible data VI+, Vlz, and Vlt.

This visible-invisible plane ■PX is the vertex P, , Pt, P
According to the values of visible-invisible data ■11, VI2, and VI s, when all of the visible-invisible data VIl to Vl have a value of "+1", a triangular unit area is formed as shown in FIG. 10(A). A visible-invisible plane ■PX is obtained that extends upward parallel to UA, and the visible-
When the invisible data VI+ to Vls are all "-1", a visible-invisible plane vPX extending parallel to the lower part of the triangular unit area UA is obtained, as shown in FIG. 10(B).

On the other hand, part of the visible-invisible data VI, ~■I (for example, VI and VI2) is "+1", and the other part (i.e., VI 3 ) is "-1". In this case, as shown in FIG. 10(C), the visible-invisible plane ■PX intersects the triangular unit area UA,
Visible on the vertex P and Pz side across the intersection &lIN -
The invisible plane ■PX becomes positive, and the sign of the visible-invisible plane ■PX on the vertex P3 side, sandwiching the boundary vALIN, becomes negative.

Therefore, the intersection point of the straight line LCI passing through the processing point PC and perpendicular to the triangular unit area UA (therefore, the rask display screen of the display) and the visible-invisible plane vPX is determined, and its value vIp
c is interpolated as visible-invisible data of the processing point P.

In this way, as long as the visible-invisible data VII, VIA, and VIA for the three vertices P+, Pt, and Ps are obtained as data obtained from the three-dimensional curved surface to be displayed, the triangle on the display screen of the display can be Unit area UA
The visible-invisible data at all processing points PC (this represents pixels on the display screen) included in is calculated by calculating the intersection of the straight line LCI passing through the processing point PC and the visible-invisible plane VPX, which is a triangular plane. (This is a linear interpolation calculation).

Incidentally, the linear interpolation operation is an operation for finding a solution between a plane and a straight line, and the solution can be easily and uniquely found.

Next, the CPU moves to step 5P13 and executes brightness determination processing by linear interpolation. As shown in FIG.
, It, I3, the brightness ■ at the processing point PC consisting of pixels included in the triangular unit area UA. It performs interpolation calculations, and the calculation process is performed using the following steps.

That is, the brightness data I+ of the vertices PI, Pg, and Pz of the triangular unit area UA obtained in the previous step SP9
, Iz, 13 are placed vertically at the corresponding vertices P+, Pt, and P3 on the display screen of the display. And brightness plane B connecting the tips of brightness data I+, Iz, and Is
Attach PX. Then, draw a straight line LC2 perpendicularly to the display screen of the display from the processing point PC for each pixel included in the triangular unit area UA, find the intersection of the straight line LC2 and the brightness plane BPX, and find the brightness plane B at the intersection.
The PXO value is determined as the brightness I□ of the processing point PC.

In this way, by sequentially selecting all pixels included in the triangular unit area UA as processing points Pe, a linear interpolation calculation can be performed to find the intersection of the straight 4% L C2 and the triangular brightness plane BPX. Brightness data for all pixels can be easily obtained from three pieces of brightness data obtained from a three-dimensional curved surface.

Incidentally, in this case as well, the solution between the straight line 1Lc2 and the plane BPX is determined, so the calculation is simple and the solution is uniquely determined.

Next, in step 5P14, the CPU executes distance determination processing by interpolation calculation. As shown in FIG. 12, this process interpolates the distance from the viewpoint for pixels included in the triangular unit area UA on the display screen, and the CPU performs the interpolation calculation according to the following processing steps. do.

That is, first, the vertex P I %P! on the display screen of the display obtained in the previous step SP9! , P
, the distance data D+, Dt, D3 for the vertex P
5. Stand vertically at P2 and P1 positions.

Then, a distance plane DPX is stretched so as to connect the tips of the distance data D+, Dz, and D2, and a straight line LC3 that passes through the processing point PC and is perpendicular to the data display screen is connected to the distance plane DPX.
Calculate the intersection with Then, the value D pc of the distance plane DPX at this intersection is determined as distance data from the viewpoint of the processing point PC.

Thus, in this case as well, by sequentially processing all pixels included in the triangular unit area UA as processing points PC, distance data DI,c of the processing points PC can be obtained by linear interpolation calculations. In this case as well, since the interpolation calculation involves finding a solution between the straight line LC3 and the distance plane DPX, a unique solution can be found by a simple calculation.

After that, the CPU moves to step 5P15 and executes pixel data generation processing based on distance comparison. This process includes brightness data Ipe and visible-invisible data Vl corresponding to the curved surface with the smallest distance data D and c, respectively, for all pixels included in the display area ARE (FIG. 4) on the display screen of the display. luminance data for the curved surface for which visible data is obtained and the distance data D pc is the smallest is generated as pixel data to be displayed on the display.

In practice, the CPU has a frame buffer memory having memory cells corresponding to each pixel of the display, and a display buffer memory corresponding to each pixel of the frame buffer memory, and distance data Dpc for each pixel is determined in step 5P14. The smallest distance data D for the same pixel
When pc is obtained, the distance data is stored in the memory area corresponding to the pixel of the display buffer memory, and the brightness data Ip (determined in step 5P13) is written to the frame buffer memory, In this way, the luminance data Ipe obtained from the curved surface with the smallest distance data Dpc is written into the frame buffer memory.

The series of arithmetic processing in steps 5P13 to 5P15 is executed for each pixel included in one triangular unit area, and the CPU completes the arithmetic processing for all triangular unit areas in step 5P16 every time the process in step 5P15 is completed. If a negative result is obtained, the process returns to step 5 PIO to repeat the data calculation process for a new triangular unit area. On the other hand, if a positive result is obtained in step 5P16, the CPU proceeds to step 5P17 and determines whether the calculation processing for all patches has been completed, and if a negative result is obtained, the CPU returns to step SP4 again. Then, an extraction patch is generated for a new patch, and the data calculation process is repeated. On the other hand, if a positive result is obtained in step 5P17, the CPU proceeds to step 5P18, outputs the luminance data of each pixel point, and then proceeds to step 5P18.
The program moves to step 19 and ends the program.

According to the above-mentioned method, the patch S ( un vl ) is larger than the patch S (
After generating un vl c, as a result of cutting it into triangular unit areas and performing interpolation calculations, there are overlapped parts in adjacent cutting patches, so when the triangular unit areas are cut out, there is a difference between patches as in the conventional method. The occurrence of gaps can be effectively avoided.

Furthermore, since the extraction patch can be generated by simply performing an extrapolation operation, the above-mentioned shading process can be completed within a short calculation time.

Furthermore, when cutting out a patch, the number of divisions was determined based on the distance between control points instead of the length of the shared boundary so that this length would be a predetermined value, so In a shared boundary with a large distance between control points, such as a small curvature, a small patch is cut out, and a display image having a smooth boundary without any unnaturalness can be obtained.

On the other hand, in the case of a straight shared boundary where the distance between the control points is not that large relative to the length of the shared boundary, for example, a large patch will be cut out, and as a result, the number of vertices required for perspective transformation processing will be reduced. The time required for the partial shape processing can be shortened.

Furthermore, in the above embodiment, since the vertices are used to determine whether the processing point PC is inside or outside the triangular unit area, the processing time can be further reduced compared to the conventional method. .

Incidentally, the amount of enlargement of the above-mentioned cutout patch is at step SP2.
It can be set freely depending on the setting amount entered in , so if there are still unprocessed gaps on the display screen that is displayed after running the above processing program, please reset the above enlargement amount. By doing so, a display image without gaps can be obtained.

In the above embodiment, the case where a free-form surface is subjected to perspective transformation has been described, but if a parallel perspective transformation matrix is generated instead of the perspective transformation matrix generated in step SF3, for example, the parallel perspective transformation is performed and the shading is A processed image can be obtained.

Effects of the Invention As described above, according to the present invention, a triangular unit area is cut out from a cutout patch, so that a free-form surface with natural shading processing is created without creating a gap between adjacent patches. can be easily obtained.

[Brief explanation of the drawing]

FIG. 1 is a route map showing an example of generating a patch for extraction according to the present invention, FIG. 2 is a flowchart showing a shading process procedure using the patch for extraction shown in FIG. 1, and FIG. 3 is a perspective transformation procedure. FIG. 4 is a route map showing the procedure for determining the display area, FIG. 5 is the route map showing the procedure for cutting out triangular unit areas, FIG. 6 is the route map showing the procedure for generating visible-invisible data, Figure 7 is a route map showing the procedure for generating distance data, Figure 8 is a route map showing the procedure for generating brightness data, and Figure 9 is a route map showing the procedure for determining whether a processing point is inside or outside a triangular unit area. Route map, Figure 1O is a route map showing the visible-invisible data interpolation procedure, Figure 11 is the route map showing the luminance data interpolation procedure, Figure 12 is the route map showing the distance data interpolation procedure, Figure 13 14 is a route map for explaining conventional patch cutting, and FIG. 15 is a route map for explaining gaps caused by the shading process. S (u+ V)...Patch, S (u+ v
) (... cutout patch, P li + J
), P oo・”・”control point, P(1, Jl iP
0°, 2-dimensional control point.

Claims (1)

[Claims] Generated by forming a large number of framework spaces surrounded by boundary curves through framework processing, and applying patches represented by vector functions each having a parameter representing a position in the framework spaces. In a shading display method that applies shading to a free-form surface, a large number of triangular unit regions are cut out from a cutout patch obtained by enlarging the above patch by a predetermined amount, and luminance information of three vertex positions of the triangular unit region is extracted. A shading display method characterized in that the free-form surface is shaded by interpolating luminance information about pixels included in the triangular unit area based on the above.