JPH0799549B2 - Shading display method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention will be described in the following order.

A Industrial field of use B Outline of the invention C Conventional technology (Figs. 13 to 14) D Problems to be solved by the invention (Fig. 15) E Means for solving problems (Fig. 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 patches (Figs. 1 and 1) Fig. 2) (G3) Processing procedure (Figs. 1 to 12) (G4) Action of the embodiment H Effect of the invention A Industrial field of application The present invention relates to a shadow display method, for example, CAD (computer ai).
ded design) or CAM (computer aided manufacturin)
This is suitable for applying the shading processing to the free-form surface generated in g) and the like.

B Outline of the Invention The present invention is a shading processing method in which a triangular unit area is cut out from each patch put in a frame space to perform a shading process, and a cut patch in which the patch put in the frame space is enlarged is generated. By cutting out a triangular unit area from this and subjecting it to shading processing, it is possible to avoid the occurrence of a gear gap which has conventionally occurred between patches, and to make the shading processed free-form surface look like a curved surface having a natural shading.

C Conventional technology When designing the shape of an object having a free-form surface using a CAD method (geometric modeling), a designer generally uses a plurality of points in a three-dimensional space through which the surface should pass (this is called a node). Is specified, and a boundary curve network connecting the specified plurality of nodes is calculated by a computer using a predetermined vector function, thereby creating a curved surface represented by a so-called wire frame. Thus, it is possible to form a large number of framework spaces surrounded by boundary curves (such processing is called framework processing).

The boundary curve network formed by such framework processing itself has a rough shape that the designer intends to design, and can be represented by a predetermined vector function using the boundary curves surrounding each framework space. If the curved surface can be interpolated, it is possible to generate a free-form surface (which means one that cannot be defined by a quadratic function) designed by the designer as a whole. Here, the curved surface stretched in each frame space forms a basic element that constitutes the entire curved surface, and this is called a patch.

Conventionally, in this type of CAD system, a vector function expressing a boundary curve network is, for example, a Bezier formula or a B-spline formula that is easy to calculate.
The following tensor product is used, and it is considered to be optimal for mathematical expression of a free-form surface having no special feature in terms of shape, for example.

That is, a free-form surface that has no special features in terms of shape
When the points given to the space are projected on the xy plane, the projected points are often regularly arranged in a matrix, and when the number of the projected points is represented by m × n, The framework space can be easily extended by using a quadrilateral patch represented by a cubic Bezier equation.

On the other hand, when trying to stretch a smooth free-form surface on a curved surface having a characteristic shape (for example, a curved surface having a large distorted shape), the tangential plane continuity condition should be satisfied for the shared boundary of the framework space. It is possible to find a control point inside such an internal control point, and form a free-form surface patch by a vector function representing a free-form surface determined by the control point inside.

By the way, if the free-form surface represented by the free-form surface data generated by such a method can be shaded by performing a shading process, the curved surface is three-dimensionally displayed on the display. It is considered that it is possible to provide a high-quality image as a graphic image because it can be displayed, and a method for realizing such shading processing by linear interpolation has been proposed in the past (Japanese Patent Application No. 60-37077,
Japanese Patent Application No. 60-37078, Japanese Patent Application No. 60-37079).

This shading processing method is performed, for example, as shown in FIGS. 13 and 14, in a quadrilateral patch and a triangle patch. About Patch The u and v directions that represent the coordinates of the triangle unit area UA are divided by a predetermined number of divisions (for example, 4 × 4 divisions), and the triangle unit area UA is cut out for each division area.
The data representing the brightness of the free-form surface is calculated for the three UA vertices, and the brightness of all the pixels included in the triangular unit area UA is calculated based on the brightness plane that extends over the triangular unit area UA using the three data. Is linearly interpolated.

By doing so, it is possible to significantly execute the shading processing in a short time, as compared with the case where the brightness is calculated for every pixel included in the triangular unit area UA.

D Problem to be Solved by the Invention By the way, in the case of shadow processing by this method, if the number of patches is reduced, the processing time is shortened accordingly.

However, in the above method, the large patch and the small patch are divided by the same number of divisions. Therefore, if the number of divisions is small, the boundary between adjacent patches is displayed linearly in the large patch. There is a problem of becoming.

Conversely, if the number of divisions is large, the boundaries of large patches will be displayed as natural curve shapes, but instead, small patches will be subdivided more than necessary, and the processing time will be reduced. There is a problem that it will be long.

As one method for solving this problem, the number of divisions is changed for each patch according to the size of the patch, and a triangle unit area is cut out so that the length of one side becomes a predetermined size, and shading processing is performed. A method can be considered.

However, when shading is performed by this method, there is a possibility that a portion where shading cannot be performed (this is called a gear) may occur at the boundary position between adjacent patches.

For example, as shown in Fig. 15, two quadrilateral patches represented by cubic Bezier equations are drawn in two adjacent frame spaces. The first and second patches The two control points are set by setting the internal control points so that the condition of continuous tangential plane is satisfied via the shared boundary COM1. And connect.

At this time, a big patch Is a patch The shared boundaries COM1 and COM3 based on the length of the longer shared boundary COM3 among the shared boundaries COM1 and COM3 in the u direction that surrounds
The four dividing points (Q ₁₀₁ , Q ₂₀₁ , Q ₃₀₁ , Q ₄₀₁ ) and (Q
₁₂₁ , Q ₂₂₁ , Q ₃₂₁ , Q ₄₂₁ ) for the parameter u.

Similarly, based on the length of the long shared boundary COM4 among the shared boundaries COM2 and COM4 in the v direction, the shared boundaries COM2 and COM4
Set dividing points Q ₅₁₁ and Q _{011 above} for parameter v.

Thus patch , The triangular unit area UA is defined by 18 dividing points and nodes arranged in a matrix in the u and v directions.
Is cut out and shaded.

On the other hand, small patches Is patch Of the shared boundaries COM1 and COM6 in the u direction that surrounds the shared boundaries COM1 and COM6 based on the length of the shared boundary COM1 having the longest length.
Two dividing points (Q ₁₂₂ , Q ₂₂₂ ) and (Q ₁₀₂ , Q ₂₀₂ ) are set above for the parameter u.

Similarly, one dividing point Q ₀₁₂ and P ₃₁₂ are set for the parameter v on the shared boundaries COM5 and COM7 based on the shared boundaries COM5 and COM7 in the v direction.

Thus patch In, the triangular unit area UA is cut out by 12 division points and nodes arranged in the u direction and the v direction, and the shadow processing is performed.

However, if this is done, the first patch The triangular unit area UA of is cut out from the nodes at both ends of the shared boundary COM1 formed by the frame processing. While the space is divided into 5 segments, the second patch is used. When the triangle unit area UA is cut out, the shared boundary COM1 is divided into three.

Therefore, the node The position where one side passes along the shared boundary COM1 of the triangular unit area UA that divides the space into five, as well as the nodes There may be a case where the position of one side along the shared boundary COM1 of the triangular unit area UA that divides the space into three does not match, and the gap GUPX occurs during this time.

The portion of this gear GUPX will not be shaded, and eventually there will be a portion that is not shaded, resulting in a so-called hole.

If there is a portion that cannot be shaded in this way, the shaded free-form surface will appear unnatural.

The present invention has been made in consideration of the above points, and an object of the present invention is to propose a shading display method capable of performing shading processing in a short time without causing a gear GUPX along a shared boundary between adjacent patches. To do.

E Means for Solving the Problem In order to solve the problem, in the present invention, a large number of frame spaces surrounded by boundary curves are formed by the frame processing, and the positions are respectively expressed in the frame spaces. Patch represented by vector function with parameters In the shading display method, which is designed to shade the free-form surface generated by applying Cutout patch obtained by enlarging A large number of triangular unit areas UA are cut out from the triangular unit area UA, and the luminance information I _{1 of} the _three vertex positions P ₁ , P ₂ , P ₃ of the triangular unit area UA,
The free-form surface is shaded by interpolating the luminance information about the pixels included in the triangular unit area UA based on I ₂ and I ₃ .

F action patch Enlarged patch for cutting Is an adjacent cutting patch An overlapping portion occurs at the boundary portion between them. As a result, the cutting patch It is possible to effectively avoid the occurrence of a gear gap between the adjacent patches even if is cut out into a triangular unit area UA and the shading processing is performed.

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

FIG. 1 shows an embodiment when the present invention is applied to the free-form surface formed as described above. When cutting out the triangle unit area, Punch for cutting based on This cutout patch The triangle unit area UA is cut out from.

That is, patch Is a parameter u and v defined by the following equation 0 ≦ u ≦ 1 (1) 0 ≦ v ≦ 1 (2) and a common boundary COM1
Control point represented by a position vector that represents the position of one end of A cubic Bezier equation using (consisting of nodes that form the framework space) It is expressed as.

Where E and F are shift operators, Control point represented by the above position vector For i = 0, 1, 2, 3 (6) and j = 0, 1, 2, 3 (7).

Here, if u and v are changed in the parameters in a wider range than the ranges represented by the equations (1) and (2), the conditions of the equations (1) and (2) are based on the equation (3). Patch obtained A patch for cutting that is larger by a specified amount Can be obtained.

Here is a patch for cutting Before obtaining, the number of divisions for cutting out into the triangular unit area UA is first determined.

(G1) Determining the number of divisions Patch Control point Is a control point represented by a two-dimensional position vector obtained by perspective transformation into a plane corresponding to the display image. Corresponding to (I = 0,1,2,3, j = 0,1,2,3) 2D patch obtained by perspective transformation Corresponding to Is represented by.

Where the patch in the u direction Boundary COM1 with parameter v of v = 0 and v = 1
And the inter-control point distances R _u0 and R _u1 corresponding to COM3 are Ask in.

Here, when the result of the following equation R _u0 > R _u1 (10) is obtained, the distance between the control points in the u direction is calculated using the following equation.
Let R _u be R _u ＝ R _u0 …… (11), and if the result of the following formula R _u0 ≦ R _u1 …… (12) is obtained, put it as the following formula R _u ＝ R _u1 …… (13).

Further, the distance between adjacent pixels of the display image is represented by using a value D, and The number of divisions K _u in the u direction represented by In equation (14), the length of one side of the triangular unit area that has been perspective-transformed is the value MP.
Punches for each cutting so that the length represented by It means that the number of divisions of is determined. Furthermore, at this time,
Distance between control points R _u0 instead of the length of common boundaries COM1 and COM3
By determining the number of divisions based on R _u1 and R _u1 , for example, a portion having a small curvature can be finely divided.

Therefore, using this method, the patch for cutting S ( _{u, v} )
_{If c} is divided, the effect of reducing the gear GUPX can be obtained.

Similarly for the v direction Boundary COM4 with parameter u of u = 0 and u = 1
And the following formula corresponding to COM2 The control point distances R _v0 and R _v1 represented by

From this, when the result of the following equation R _v0 > R _v1 (17) is obtained, the control point distance R _v in the v direction is set as R _v = R _v0 (18) using the following equation, When the result of the following equation R _v0 ≤ R _v1 (19) is obtained, the following equation R _v = R _v1 (20) is put.

Furthermore, as in the case of equation (14), More cutting patch in v direction Determine the number of divisions K _v of.

(G2) Generation of cutout patch The patch for cutting out by enlarging the The method of generating is described.

For example, when cutting out the triangular unit area UA whose one side length is represented by the above-mentioned distance D · MP, this value MP is selected as MP = 5 [pixels], and the patch is selected. Is selected so as to be increased by ΔMP = 0.5 [pixel] in each direction u and v (this selection is made by an operator's setting operation).

The change range of the parameter u corresponding to the equation (1) is set to u ₁₀ and u ₂₀ corresponding to the shared boundary COM1 of v = 0, and the following equation u ₁₀ ≦ u ≦ u ₂₀ (22) The values u ₁₀ and u ₂₀ represented by

Similarly, the change range is u ₁₁ and u corresponding to the shared boundary of v = 1.
₂₁ and the following equation u ₁₁ ≤ u ≤ u ₂₁ (25) The values u ₁₁ and u ₂₁ represented by

On the other hand, if the variation range of the parameter v corresponding to the equation (2) is set to v ₁₀ and v ₂₀ corresponding to the shared boundary of u = 0,
The following formula v ₁₀ ≤ v ≤ v ₂₀ (28) The values v ₁₀ and v ₂₀ represented by

Similarly, the parameter v corresponding to the shared boundary of u = 1
The change range of v ₁₁ and v _{21 is set} , and the following equation v ₁₁ ≤ v ≤ v ₂₁ (31) Find the values v ₁₁ and v ₂₁ represented by.

By changing the parameters u and v with respect to the equation (3) within the range thus obtained, as shown in FIG. A patch for cutting out, which is larger in each direction u and v by a predetermined size (in this case, 0.5 [pixel] each). Can be obtained.

Furthermore, the patch for cutting obtained in this way In order to cut out the triangle unit area using the same method as in the past. Cutting patch corresponding to the parameters u and v of The parameters u _c and v _c that change from 0 to 1 of are set, and the dividing point Q is set using the parameters u _c and v _c .

That is, using the parameters u _k and v _k obtained by dividing the range from 0 to 1 by the division numbers K _u and K _v obtained by the equations (14) and (21), the following equation u _c = (1 -U _k ) (1-v _k ) u ₁₀ + (1-u _k ) v _k u ₁₁ + u _k (1-v _k ) u ₂₀ + u _k v _k u ₂₁ ...... (34) v _c = (1- v _k ) (1-u _k ) v ₁₀ + (1-u _k ) v _k u ₂₀ + u _k (1-v _k ) v ₁₁ + u _k v _k v ₂₁ (35) The parameters u _c and dividing point Q ( _ij ) by v _c
And set the cutout patch based on this. The triangle unit area UA is cut out from.

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

First, in step SP1, the conversion processing program is started, and in step SP2, the viewpoint 1 required for perspective conversion is set.
The position of (Fig. 3), the position of the light source required for shading processing, and the number of pixels MP when the patch is cut out into triangular unit areas.
(Representing the length of one side of the triangular unit area that has been perspective-transformed) is input by an operator's operation.

Subsequently, the CPU stores 3 in advance in step SP3.
Based on the three-dimensional free-form surface data, the three-dimensional (represented by three-dimensional coordinates of x, y, z) free-form surface image 5 represented by the free-form surface data is used for the viewpoint specified in step SP2. Virtual screen 2 (3rd
Used to convert a point on the curved surface of the three-dimensional free-form surface image 5 into a corresponding point on the virtual screen 2 when looking through on a two-dimensional plane represented by xy coordinates as shown in the figure) Generate a perspective transformation matrix.

Next, the CPU determines each patch of the free-form surface data to be converted in step SP4. Control point Data 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 an approximate size at the center position of the display screen. First, the control point data read in step SP4 is generated by the perspective transformation generated in step SP3. Using the matrix, perspective transformation is performed on the two-dimensional virtual screen 2 as shown in FIG. Two-dimensional control points on the resulting virtual screen 2 Of the maximum value X _max and the minimum value X _min in the X-axis direction, and the maximum value Y _max and the minimum value Y _{min in} the Y-axis direction, respectively, and the center of the maximum value X _max and the minimum value X _min in the X-axis direction. The position X _c is The maximum value Y _max and the minimum value in the Y-axis direction
The center position Y _c of Y _min To ask. The center position (X _c , Y _c ) thus obtained is set to the center position of the raster display screen 11 of the display, and the display image DES has a frame buffer having memory cells corresponding to the pixels forming the display screen 11 of the display. Define a display area ARE that fits within the size of.

As is apparent from FIG. 4, the display area ARE has an area of the maximum value X _max to the minimum value X _{min in} the X axis direction and an area of the maximum value Y _max to the minimum value Y _{min in} the Y axis direction. Hold.

After determining the display area ARE, the CPU executes the subsequent processing steps only for the pixels in the display area ARE. This means that the conversion calculation amount of the image to be displayed on the raster display screen can be further reduced. That is, in general, when an image that has undergone image conversion processing is to be displayed on a raster display screen, the frame buffer is calculated by calculating the presence or absence of image data to be displayed and its contents for all pixels forming the raster display screen. A method of storing the calculation result in a corresponding memory area of the memory is adopted. In this case, since the pixels of the raster display screen 11 that do not have data to be displayed are not processed, the image conversion calculation amount can be significantly reduced as a whole.

Subsequently, the CPU proceeds to step SP6 and sets the two-dimensional control points previously obtained in step SP5. Based on the above equations, the operations of the above equations (8) to (21) are executed to determine the number of divisions in the u direction and the v direction of the predetermined cutout patch, and then the operation proceeds to step SP7.

At step SP7, the CPU executes the above-mentioned equations (22) to (33) to output the cutout patch. Parameters u ₁₀ , u ₂₀ , u ₁₁ , u ₂₁ ,
After obtaining v ₁₀ , v ₂₀ , v ₁₁ and v ₂₁ , move to step SP8 and execute the operations of equations (34) and (35) to perform the clipping patch. Find the parameters u _c and v _c for partitioning.

Subsequently, the CPU proceeds to step SP9, where the parameters u ₁₀ , u ₂₀ , u ₁₁ , u ₂₁ , v ₁₀ , which were obtained in step SP7,
Based on v ₂₀ , v ₁₁ and v ₂₁ , cutting patches After generating, the parameter u obtained in step SP8
_{Using c} and v _c , the patch for cutting A division point Q (that is, each vertex data of the triangle unit area UA) for dividing is set.

In this embodiment, as shown in FIG. 5, the triangle unit area UA is cut out by one patch. Based on the above-mentioned parameters u _c and v _c
The intersection point positions of the two cutting line groups L1 and L2, which are sequentially arranged at intervals such that one side of the triangular unit area has equal intervals (not necessarily equal intervals on a curved surface), are sequentially calculated. . The number of cut lines included in the cut line groups L1 and L2 is selected to be, for example, five in the vertical and horizontal directions, and is set so that the cut line groups L1 and the cut line groups L2 cross each other in a mesh shape. Thus, the curved surface consisting of the data DATA for one patch is divided into the small areas UAX surrounded by the two adjacent cutting lines of the cutting line groups L1 and L2, and the small area UAX is divided into four intersection points PX. It is cut out so as to be surrounded by.

The small area UAX is divided into two triangular unit areas UA by a diagonal line L3 connecting two intersections facing each other, and thus the curved surface represented by the data DATA is divided into a large number of triangular unit areas UA.

Further, in step SP9, after the triangle unit area UA is cut out from the curved surface in this way, the CPU calculates normal unit vectors at three intersection points at the vertices of each triangle unit area UA, , The vertex data is processed so that the part that cannot be seen from the viewpoint is not displayed on the display. As shown in FIG. 6, when the curved surface 5A made up of the surface of the object 5 is viewed from the viewpoint 1, this processing is a visible portion (which is called a visible portion) and an invisible portion (which is called an invisible portion). This is for displaying only the portion corresponding to the visible portion on the display screen based on the occurrence of the above.

Here, the first condition for determining whether or not each portion of the curved surface 5A is the visible portion is that when the curved surface 5A of the object 5 is viewed along the line of sight EL1 from the viewpoint 1, the line of sight EL1 is the curved surface 5A. Crossing point P
Among 11, 11, P12, and P13, the surface portion of the point P12 is hidden by the surface portion because the surface portion intersecting the line of sight EL1 exists at the position P11 on the viewpoint 1 side of the line of sight EL1. Therefore, it is determined that the surface portion of the point P12 is invisible, and the vertex data conversion processing is performed so as to see through the surface portion of the position P11 that is visible on the virtual screen 2 provided between the object 5 and the viewpoint 1. To do.

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

Following this, the CPU uses one cutting patch. For each vertex of the triangular unit area UA of, as shown in FIG. 7, the distance vector from the vertex PX to the viewpoint 1 Is calculated.

That is, in order to judge visible / invisible in FIG. 6, it is necessary to judge that the surface portion of interest is not hidden by another curved surface. When another object 6 exists between the curved surface 5A of the object 5 and the viewpoint 1, and when the object 5 is seen along the line of sight EL2, the line of sight EL2 intersects the curved surface 6A of the object 6 and then the curved surface 5A of the object 5. When it intersects with the object 5, the surface portion of the curved surface 5A of the object 5 at the position P14 is the object 6 on the viewpoint 1 side.
Is hidden by the surface portion of position P15 on the curved surface 6A of
Therefore, the invisible surface portion (position
It is necessary to display the visible surface portion (the surface portion of the position P15) without displaying the surface portion of P14).

Therefore, the distance vector from the vertex PX of the triangle unit area to the viewpoint 1 The position vector of the surface And viewpoint position vector Using After calculating by The absolute value of is obtained as distance data D.

Thus, when distance data of a plurality of curved surface portions for the same pixel is obtained on the display raster display screen, the curved surface portion data closest to the viewpoint 1 can be determined as the visible portion.

Next, the generation process of the brightness data of each vertex is performed. This step is to calculate the brightness at each vertex PX as shown in FIG. Using Is the position vector for the light source 8 viewed from the vertex PX. To calculate. Then, using the calculation result, the normal unit vector of the vertex PX Based on the dot product of and Is calculated, and this is set as a variable A.

Further, using the variable A, the brightness I is calculated by the following formula I = (1-D) .A + D (41).

Here, the value of the constant D is, for example, about 0.22, while the variable A varies in the range of 0 to 1 (since θ varies in the range of ± π / 2). Thus, the brightness I changes in accordance with the change of the light incident from the light source 8 on the vertex PX, whereby the brightness data of each vertex is obtained.

Then, the CPU moves to step SP10, and from step SP6 described above.
Cutting patch obtained at SP9 As shown in FIG. 5, the three vertex data of one triangle unit area UA are extracted from each vertex data and the shading processing in the triangle unit area UA is performed by the interpolation calculation of steps SP12 to SP15.

In this way, the curved surface data DATA to be processed is divided into the triangular unit areas UA, and the data for the three vertices are obtained by converting the triangular unit areas UA when the triangular unit area UA is converted on the display raster display screen. 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 the subsequent processing based on the data of the three vertices, This means that the processing speed of can be dramatically increased.

In step SP11, the CPU determines to which triangle unit area UA the pixel (which is referred to as a processing point) P _c whose brightness is to be arithmetically determined at present among the pixels for one patch included in the display area ARE belongs to. Is determined.
This determination is made as shown in FIG.
A position vector on the XY plane that is a perspective change of two vertices Vectors based on points P ₁ , P ₂ and P ₃ represented by Is It is represented by.

Further position vector Position vector from point P ₁ represented by Up to the processing point P _c represented by Vector represented by Is expressed using The values of the variables α and β that satisfy the relational expression are determined.

At this time, if the processing point P _c is inside the triangular unit area UA, the following equation α> 0 (46) β> 0 (47) α + β <1 (48) is obtained. Such calculation is performed in advance as a vector Matrix required from It can be easily obtained by calculating the inverse matrix of.

In this way, when it is determined that the position of the processing point P _c is outside the triangle unit area UA, the CPU determines that the triangle unit area U
The determination for the new processing point P _c is repeated until a triangular unit area UA that includes the processing point P _c therein can be found without executing the subsequent interpolation calculation for A.

As a result, when the triangular unit area UA in which the processing point P _c is located is found in step SP11, the CPU proceeds to the next step SP12.
Then, the visible or invisible determination process by linear interpolation is executed. This process is performed by the CPU sequentially
The visible-invisible data stored for the vertices P ₁ , P ₂ and P ₃ of the display are read out, and as shown in FIG. 10, corresponding to the positions P ₁ , P ₂ and P ₃ on the display screen of the display. Visible-
Set invisible data VI ₁ , VI ₂ , and VI ₃ vertically. Then, a visible-invisible plane VPX is stretched at the tips of the visible-invisible data VI ₁ , VI ₂ , and VI ₃ .

This visible-invisible plane VPX is visible at the vertices P ₁ , P ₂ and P ₃ .
Depending on the values of the invisible data VI ₁ , VI ₂ and VI ₃ , when all of the visible-invisible data VI _{1 to} VI ₃ have a value of “+1”, as shown in FIG. A visible-invisible plane VPX extending parallel to the above is obtained, and all visible-invisible data VI _{1 to} VI ₃ are "-1".
In this case, as shown in FIG. 10 (B), a visible-invisible plane VPX extending in parallel below the triangular unit area UA is obtained.

On the other hand, when part of the visible-invisible data VI _{1 to} VI ₃ (for example, VI ₁ and VI ₂ ) is “+1” and the other part (that is, VI ₃ ) is “−1” As shown in FIG. 10 (C), the visible-invisible plane VPX intersects the triangular unit area UA, and the visible-invisible plane VPX on the vertices P ₁ and P ₂ sides across the intersection line LIN. Is positive, and the visible-invisible plane VPX on the side of vertex P ₃ with the boundary line LIN in between.
The sign of becomes negative.

Therefore, a straight line LC1 that passes through the processing point P _c and is perpendicular to the triangular unit area UA (hence the display raster display screen) is visible −
An intersection with the invisible plane VPX is obtained, and its value VI _pc is interpolated as visible-invisible data of the processing point P _c .

In this way, if the visible-invisible data VI ₁ , VI ₂ , VI ₃ for the _three vertices P ₁ , P ₂ , P ₃ are obtained as the data obtained from the three-dimensional curved surface to be displayed, the display The visible-invisible data at all the processing points P _c (which represent pixels on the display screen) included in the triangular unit area UA on the display screen of is represented by a straight line LC1 passing through the processing points P _c and a triangular plane. It can be easily obtained by calculating the intersection with the visible-invisible plane VPX (this becomes a linear interpolation calculation).

Incidentally, the linear interpolation calculation is a calculation for obtaining a solution between a plane and a straight line, and a solution can be simply and uniquely obtained.

Next, the CPU proceeds to step SP13 to execute a luminance determination process by linear interpolation. As shown in FIG. 11, this processing is performed based on the luminance data I ₁ , I ₂ , I ₃ of the vertices P ₁ , P ₂ , P ₃ of the triangular unit area UA on the display screen of the display. The luminance I _c at the processing point P _{c made up} of pixels included in the UA is interpolated and the arithmetic processing is executed according to the following procedure.

That vertex P _1, P ₂ corresponding on the display screen of Deisupurei the luminance data I _1, I _2, I ₃ vertices of the resulting triangular unit areas _{UA P 1, P 2, P} 3 in the previous step SP9, Stand vertically at position P ₃ . Then, a brightness plane BPX connecting the tips of the brightness data I ₁ , I ₂ , and I ₃ is stretched. Then, a straight line LC2 is drawn perpendicularly to the display screen of the display from the processing point P _c for each pixel included in the triangle unit area UA, the intersection point of the straight line LC2 and the luminance plane BPX is obtained, and the value of the luminance plane BPX at the intersection point. _Is determined as the brightness I _pc of the processing point P _c .

In this way, if all the pixels included in the triangle unit area UA are sequentially selected as the processing points P _c , the straight line LC
By executing the linear interpolation calculation for obtaining the intersection between 2 and the triangular brightness plane BPX, the brightness data for all pixels can be easily obtained from the three brightness data obtained from the three-dimensional curved surface.

Incidentally, also in this case, since the solution between the straight line LC2 and the plane BPX is obtained, the calculation is simple and the solution is uniquely determined.

Next, in step SP14, the CPU executes distance determination processing by interpolation calculation. In this process, as shown in FIG. 12, for the pixels included in the triangle unit area UA on the display screen of the display, the distance from the viewpoint is interpolated, and the CPU performs the interpolated calculation according to the following processing procedure. To execute.

That is, first, the distance data D _1, D _2, D ₃ for vertex P _1, P _2, P ₃ on the display screen of the resulting Deisupurei in the previous step SP9, the vertex P _1, P _2, P ₃ position Stand vertically. Then, a distance plane DPX is stretched so as to connect the tips of the distance data D ₁ , D ₂ , and D ₃ , and the intersection point between the distance plane DPX and a straight line LC3 that passes through the processing point P _c and is perpendicular to the data display screen is calculated. Ask by. And the value D of the distance plane DPX at this intersection
Determine _pc as distance data from the viewpoint of the processing point P _c .

Thus even in this case, by going process all pixels included in the triangular unit area UA as a sequential processing point P _c, that obtained cowpea distance data D _pc of the processing point P _c in the linear interpolation operation it can. Also in this case, since the interpolation calculation finds a solution between the straight line LC3 and the distance plane DPX, a unique solution can be obtained by a simple calculation.

After that, the CPU proceeds to step SP15 to execute a pixel data generation process by distance comparison. This process is carried out for each pixel included in the display area ARE (Fig. 4) on the display screen of the display, and the distance data D
_pc is the smallest luminance data corresponding to the curved surface I _pc and visible - gathering invisible data VI _pc, as pixel data the luminance data of the visible data is obtained and the distance data D _pc is about the smallest curved to be displayed on Deisupurei Is generated.

Actually, the CPU has a frame buffer memory having a memory cell corresponding to each pixel of the display, and a display buffer memory corresponding to each pixel of the frame buffer memory, and the distance data for each pixel at step SP14. When the D _pc is decided,
When the smallest distance data D _pc is obtained for the same pixel, the distance data is stored in the memory area corresponding to the pixel of the display buffer memory, and the brightness data I _pc determined in step SP13.
Is written in the frame buffer memory, and thus the luminance data I _pc obtained from the curved surface having the smallest distance data D _pc is written in the frame buffer memory.

A series of arithmetic processing in steps SP13 to SP15 is executed for each pixel included in one triangular unit area, and the CPU
Each time the processing of step SP15 is completed, it is determined whether or not the calculation processing for all the triangle unit areas is completed in step SP16, and if a negative result is obtained, the processing returns to step SP10 and a new triangle unit area is returned. The calculation process of the data for is repeated. On the other hand, if a positive result is obtained in step SP16, the CPU proceeds to step SP17 to determine whether or not the arithmetic processing for all the patches is completed, and when a negative result is obtained, returns to step SP4 again. Then, a cutout patch is generated for the new patch, and the data calculation process is repeated. On the other hand, step SP17
If a positive result is obtained at, the CPU proceeds to step SP18 to output the luminance data of each pixel point, and then proceeds to step SP19 to end the program.

According to the above method, the patch On the other hand, the cutting patch is After this is generated, interpolation is performed by cutting this out into triangle unit areas, and as a result, there is a portion that overlaps with adjacent cutting patches, so when cutting triangle unit areas, the gap between the patches between patches is changed as in the past. Occurrence can be effectively avoided.

Further, since the extraction patch is simply generated by extrapolation, the above-described shadow processing can be completed within a short calculation time.

Furthermore, when cutting out patches, the number of divisions was determined so that this length would be a predetermined value based on the distance between control points instead of the length of the common boundary, so A small patch is cut out at a shared boundary having a large distance between control points, for example, a small curvature, and a display image having a smooth and unnatural boundary can be obtained.

On the contrary, if the distance between the control points is not so large with respect to the length of the shared boundary, for example, in the case of a straight shared boundary, large patches will be cut out, and as a result, the number of vertices required for perspective transformation processing will decrease The time required for the shadow processing can be shortened.

Furthermore, in the above-described embodiment, the matrix represented by the vector connecting the vertices in order to determine whether the processing point P _c is inside or outside the triangular unit area. Since the determination is made by using, it is possible to further shorten the processing time as compared with the conventional case.

By the way, the enlargement amount of the above-mentioned clipping patch can be freely set by the set amount input in step SP2,
If there are still unprocessed gears on the display screen obtained after executing the above-mentioned processing program, it is possible to obtain a display image without any gears by newly setting the above-mentioned enlargement amount. it can.

In the above embodiment, the case where the free-form surface is perspective-transformed has been described. For example, if a parallel perspective transformation matrix is generated instead of the perspective transformation matrix generated in step SP3, parallel perspective transformation is performed to generate shadows. The processed image can be obtained.

H According to the present invention as described above, since the triangular unit area is cut out from the cutting patch, a free-form surface on which a natural shading process is performed without causing a gear gap between adjacent patches. Can be easily obtained.

[Brief description of drawings]

1 is a schematic diagram showing an embodiment of generation of a clipping patch according to the present invention, FIG. 2 is a flow chart showing a shading processing procedure using the clipping patch shown in FIG. 1, and FIG. 3 is a perspective view. FIG. 4 is a schematic diagram showing a conversion procedure, FIG. 4 is a schematic diagram showing a procedure for determining a display area, FIG. 5 is a schematic diagram showing a procedure for cutting out a triangle unit area, and FIG. 6 is a procedure for generating visible-invisible data. FIG. 7, FIG. 7 is a schematic diagram showing a procedure for generating distance data, FIG. 8 is a schematic diagram showing a procedure for generating luminance data, and FIG. 9 is a processing point inside or outside a triangular unit area. FIG. 10 is a schematic diagram showing a procedure for determining whether or not, FIG. 10 is a schematic diagram showing a procedure for interpolating visible / invisible data, FIG. 11 is a schematic diagram showing a procedure for interpolating luminance data, and FIG. 12 is distance data. , A schematic diagram showing an interpolation procedure of FIG. 13, FIG. 13 and FIG. 14 are schematic diagrams provided for explaining the cutting out of the conventional patch, FIG. 15 is a schematic diagram used for explaining a gear gap generated by the shading processing.

Claims (1)

[Claims] 1. A freedom generated by forming a large number of frame spaces surrounded by boundary curves by a frame process and applying a patch represented by a vector function having a parameter representing a position to each frame space. In the shade display method for shading a curved surface, a large number of triangle unit areas are cut out from a cutout patch obtained by enlarging the patch by a predetermined amount, and used as luminance information of three vertex positions of the triangle unit area. On the basis of the above, the shading display method is characterized in that the free curved surface is shaded by interpolating the luminance information of the pixels included in the triangular unit area.