JP2001148028A - Device and method for displaying graphic - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a graphic display device which performs a rendering by especially using a ray tracing method about a processing display device mainly for a three- dimensional graphic such as a CAD and a CG. SOLUTION: By using the configuration of an intersection distance detecting part 11, an intersection calculating part 12, an intersection deciding part 13, a hidden surface eliminating part 14 and a distance deciding part 15, inside/outside area judgement that performs the position judgement of an intersection Q between a convex n-sided polygon on the same surface and a sight line existing on the same surface is performed, and the intersection judging part 13 consists of a 1st judging part 21 that judging whether the vector outer product between two adjacent vertexes is zero or not, a 2nd judges part 22 which judges that an intersection exists outside the convex polygon when the vector inner product between the two adjacent vertexes is larger than zero and judges that the intersection exists on the boundary line between the two vertexes when the inner product is smaller than zero, and a 3rd deciding part 23 which judges that the intersection exists inside the polygon when all signs are the same between the two vertexes from the inner product of the vector outer product between the two vertexes and the normal vector of the convex polygon and judges that the intersection exists outside the polygon when the signs are different.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a three-dimensional graphic processing and display device such as a graphic display device such as CAD and CG (computer graphics), and more particularly to a graphic display device for rendering using a ray tracing method. About.

[0002]

2. Description of the Related Art Generally, in order to display a three-dimensional figure on a two-dimensional plane such as a computer screen or the like, from the viewpoint that the figures overlap each other in the depth direction, each pixel of the image is brought to the foreground. Hidden surface elimination processing for selecting and displaying a certain figure is required. A ray tracing method is known as one of the methods for the hidden surface elimination processing, and this will be briefly described below.

As shown in the principle diagram of the ray tracing method in FIG. 3, a viewpoint R is set in a three-dimensional space.
Is set to the screen S. Pixels M are arranged at regular intervals in the vertical and horizontal directions on the screen S, and a line of sight (ray) L passing through each of the pixels M from the viewpoint R is sequentially generated. It is determined whether each line of sight L intersects with the target three-dimensional figure, and the viewpoint R
This is a method of searching for an intersection Q with a figure on the side.

FIG. 5 is a block diagram showing an example of a hidden surface elimination processing apparatus using the ray tracing method. This hidden surface elimination processing device includes a line-of-sight (ray) generation unit 51, an intersection determination / intersection detection unit 52, and a luminance calculation unit 53. The line-of-sight generation unit 51 generates viewpoint coordinates and line-of-sight vectors serving as line-of-sight data from the given visual field data.

Here, as shown in FIG. 3, the line-of-sight vector is obtained when line-of-sight L passing through the screen S is generated at regular intervals in both the horizontal and vertical directions within a predetermined size of the screen S. The direction of the line of sight L is represented by a vector. In general, the interval between the lines of sight L is often the interval between the pixels B on the screen S, but may be smaller than that.

The next intersection determination / intersection detection unit 52 determines, based on the supplied line-of-sight data and graphic data, that each line-of-sight L for the target three-dimensional figure (on the other side of the screen S).
A figure which intersects at a point (Q) closest to the viewpoint R is specified, and the coordinates of the intersection and the normal vector are detected.

[0007] Further, the luminance calculator 53 calculates the characteristics of the intersecting figures such as the color and reflectance of the object obtained from the intersection coordinates / normal vectors detected by the intersection judging / intersection detector 52 and the supplied figure data. , The light source data, etc., based on a predetermined method, the pixel B of the screen S of this line of sight L
Obtain the above luminance value.

FIG. 6 shows an example of the configuration of the intersection judging / intersection detecting unit 52 of the conventional hidden surface elimination processing apparatus. In FIG. 6, the viewpoint coordinates and the line-of-sight vector are used as the line-of-sight data.
As well as the position of each target figure separately
Graphic data indicating a shape is supplied. This graphic data may be data related to a specific shape, such as a sphere, a cylinder, or a rectangular parallelepiped, but in many cases it is composed of multiple convex polygons.
The graphic data of each convex polygon is indicated by its vertex coordinates. Therefore, the case of a convex polygon will be described below.

The intersection determining / intersection detecting section 52 includes an intersection distance detecting section 61, an intersection coordinate calculating section 62, an intersection determining section 63,
And a hidden surface erasing unit 64. Intersection distance detector 6
In step 1, a convex polygon is sequentially extracted, and a process of detecting a distance from an intersection Q between an infinite plane including the convex polygon and the line of sight to the viewpoint R is performed.

A next intersection coordinate calculation unit 62 calculates the coordinates of the intersection Q by substituting the distance from the intersection Q to the viewpoint R into an equation of a straight line (actually, a half line) indicated by the viewpoint R and the line-of-sight vector. Is performed. Further, the intersection determination unit 63 determines whether the intersection Q is inside or outside the target convex polygon,
That is, it is determined whether or not the line of sight L intersects the convex polygon at the intersection Q.

The next hidden surface removing unit 64 includes the intersection distance detecting unit 61, the intersection coordinate calculating unit 62, and the intersection determining unit 6.
If the convex polygon intersects the line of sight L as a result of the process 3, the distance from the intersection Q obtained by the convex polygon processed so far to the viewpoint R is compared with the distance obtained here. Then, when it is determined that the distance is shorter, the convex polygon is set as the current intersection figure.

By performing the processing of the intersection distance detecting section 61 through the hidden surface removing section 64 on all the convex polygons, the intersection figure for each line of sight L is determined, and the resulting intersection coordinate / normal vector The position information of the intersecting intersecting figure / convex polygon (which figure intersects which convex polygon) and the like are sent to the luminance calculation unit 53.

FIG. 7 shows an example of the principle of judgment in the conventional intersection judgment section 63. As shown in FIG. The intersection Q between the line of sight L and the infinite plane including the convex polygon whose coordinates have been calculated by the intersection coordinate calculation unit 62
, A half line is drawn to each vertex Pn of the convex polygon, and it is determined whether each half line intersects a side of the convex polygon that is not adjacent to the target vertex. If all the half lines do not intersect the corresponding side, it is determined that the intersection point Q exists inside the convex polygon (FIG. 7A).

If it is determined that even one half line intersects with the side of the convex polygon, it is determined that the intersection Q exists outside the convex polygon (FIG. 7B). That is, when all the half lines do not intersect with the corresponding side, the line of sight intersects with this convex polygon at the intersection Q. When even one half line intersects with the side of the convex polygon, the line of sight becomes convex. It is determined that they do not intersect the polygon.

[0015]

However, in the example of FIG. 7, the intersection between each half line and the side of the corresponding convex polygon is obtained.
The process of determining whether or not this intersection is on a convex polygon based on the positional relationship between this intersection and the intersection Q is performed for all half-lines.
There has been a problem that the processing has to be performed by a combination of sides, and the processing becomes very complicated.

In the conventional example, when the intersection Q with the line of sight is located at the boundary between two convex polygons as shown in FIG. 8, the processing for determining that the boundary is outside the convex polygon is as follows:
Depending on the positional relationship of the borders, there was a problem that it was determined that some of the borders did not intersect with the convex polygon even though they originally intersected, and the background color appeared at this border. .

In the process of determining that the boundary is inside the convex polygon, the boundary portion overlaps the two polygons E and F, and the hidden surface elimination process is performed. Since the distance from Q to the polygons E and F is almost the same, the calculation of the intersection-viewpoint distance of the hidden surface removal processing at this boundary due to the calculation error may partially vary between the polygons E and F. As a result, there has been a problem that two polygons are intricately formed at the boundary portion, which makes it difficult to see.

[0018]

Therefore, in order to solve the above-mentioned problem, the present invention according to claim 1 employs a method in which a vertex P is located on the same plane.
An intersection Q between a convex n-sided polygon having 1, 1, P2,..., Pn (an integer of n> 2) and a line of sight existing on the same plane exists inside the convex n-sided polygon or the convex n-sided polygon The intersection distance detection unit 11, the intersection coordinate calculation unit 12, the intersection determination unit 13, the hidden surface elimination Part 14
And a distance determination condition setting unit 15 in the graphic display device, wherein the intersection determination unit 13 is formed by connecting each vertex vector formed by connecting each vertex of the convex polygon to the intersection from the intersection coordinate calculation unit. Are sequentially supplied, and a first intersection determination unit 21 that determines whether the outer product of vectors between two adjacent vertices is zero, output information indicating that the outer product of the first intersection determination unit is zero, A vertex vector is supplied, and if the inner product in a vector where the outer product between the two adjacent vertices is zero is greater than zero, the intersection is outside the convex polygon; if the inner product is less than zero, A second intersection determination unit that determines that the intersection is on a boundary between two vertices of the convex polygon, and an output that the outer product of the first intersection determination unit is not all zero in the convex polygon Information and said exchange When the normal vector of the convex polygon is supplied from the coordinate calculation unit, and the inner product between the outer product of the vector between the two vertices and the normal vector of the convex polygon is larger than zero, sign = 1 is set. , If it is smaller than zero, it is determined that sign = −1, and if the signs are all the same between all the two adjacent vertices, the intersection is inside the convex polygon and different from the sign. In the case where there is a graphic display device, a third intersection determining unit 23 that determines that the intersection is outside the convex polygon is provided. Item 1. In the graphic display device according to Item 1, the hidden surface elimination unit determines the distance from the intersection of the convex polygon to the viewpoint by the distance determination condition setting unit only when it is determined that the intersection is on a boundary line. An instruction to add a constant value to the distance is supplied, and the hidden surface 4. The graphic display device according to claim 3, wherein the unit compares the magnitude with the distance of the convex polygon processed so far, and selects an intersection of the convex polygon having a shorter distance. The invention uses the vertices P1, P2,.
The intersection Q with the line of sight existing on the same plane as the convex n-gon having Pn (an integer of n> 2) exists inside the convex n-gon, at the boundary of the convex n-gon, or The area inside / outside determination for determining whether or not the area exists outside the convex n-gon includes an intersection distance detection step, an intersection coordinate calculation step, an intersection determination step, a hidden surface removal step, and a distance determination condition setting step. In the graphic display method performed by the configuration, in the intersection determining step, each vertex vector formed by connecting each vertex of the convex polygon and the intersection from the intersection coordinate calculating step is sequentially supplied, and a vector between two adjacent vertices is provided. A first intersection determination step of determining whether the outer product of the first intersection determination is zero, output information indicating that the outer product of the first intersection determination step is zero and the vertex vector are supplied, and If the inner product in the vector whose outer product between the two vertices is zero is greater than zero, the intersection is at the outer step of the convex polygon, and if the inner product is less than zero, the intersection is the convex polygon. A second intersection determination step of determining that the intersection is on the boundary line between the two vertices, output information indicating that the outer product of the first intersection determination step is not all zero in the convex polygon, and an intersection coordinate calculation step. A normal vector of a convex polygon is supplied, and if the inner product between the outer product of the vector between the two vertices and the normal vector of the convex polygon is larger than zero, sign = 1 and smaller than zero. In this case, it is determined that sign = −1, and when the signs are all the same between all the adjacent two vertices, the intersection is inside the convex polygon, and when there is a different sign, the intersection is The intersection is outside the convex polygon And a third intersection determining step of determining that the hidden surface is located in the hidden surface of the graphic display method according to the third aspect. In the erasing step, only when it is determined that the intersection is on the boundary line, an instruction to add a fixed value to the distance from the intersection of the convex polygon to the viewpoint is supplied from the distance determination condition setting step, and the hidden In the face erase step,
It is another object of the present invention to provide a graphic display method characterized in that the magnitude is compared with the distances of the convex polygons processed up to that point, and an intersection of the convex polygons having a shorter distance is selected.

(Operation) As shown in FIG.
First, the vertices P1, P2,..., Pn of the convex polygon are defined on the same plane in a fixed direction (clockwise or counterclockwise), and the infinite plane including the convex polygon and the line of sight L at the intersection Q. At the time of intersection, vectors connecting the intersection Q and the vertices Pn are sequentially obtained, and vectors between adjacent two vertices (P1Q, P2Q, P2
The outer product and inner product of Q and P3Q,..., PnQ and P1Q) are obtained. The cross product of the vectors between the two vertices indicates a vector perpendicular to the two vectors whose direction is determined by the positional relationship between these two vectors.

That is, in FIG. 2, P1Q × P2Q and P2Q ×
The direction of P1Q is opposite, P1Q × P2Q and P3Q × P4Q
Are the same in FIG. 2 (a) but opposite in FIG. 2 (b). By examining the sign of the inner product between the outer product vector between each two vertices and the previously obtained normal vector of the convex polygon between adjacent vertices, the direction of the outer product vector and the normal vector (the inner product is Positive direction indicates the same direction, negative direction indicates the opposite direction).

Since the normal vectors are common and the direction of the outer product vector differs depending on the positional relationship between the two vertices, as described above, the combination of the outer product vector between the two vertices and the normal vector is obtained in all combinations. By examining the identity of the sign of the inner product, the positional relationship between the intersection Q and the corresponding convex polygon (square) can be known.

That is, if the sign of the inner product between the outer product vector and the normal vector between the two vertices is the same, it is determined that the intersection Q is inside the convex polygon (FIG. 2 (a)). The above 2
If there is a difference in the sign of the inner product between the outer product vector and the normal vector between the vertices, it is determined that the intersection Q is outside the convex polygon (FIG. 2B).

On the other hand, the outer product of the vector between two vertices is almost 0
In the case of (a value close to 0 in consideration of the influence of the error), it is not possible to make the inner / outer judgment based on the sign of the inner product with the normal vector. In this case, the intersection Q
Is determined by the inner product of the vector between the two vertices.

That is, when the inner product of the vector between the two vertices is greater than 0 (the angle formed by the vector between the two vertices = 0), the intersection Q exists outside these two vertices (FIG. 2 (d)). The intersection Q is determined to be outside the convex polygon.

When the inner product of the vector between the two vertices is smaller than 0 (the angle formed by the vector between the two vertices = π), the intersection Q exists inside the two vertices (FIG. 2 (c)). Q
Is determined to be on the boundary of the convex polygon.

When it is determined that the intersection Q is on the boundary of the convex polygon, it is determined that the convex polygon intersects with the line of sight, and the hidden surface elimination unit determines
The distance from the intersection obtained by the convex polygon processed up to that point to the viewpoint is compared with the distance in the convex polygon.

At this time, only when it is determined that they are on the boundary, if the difference in distance is within a certain range, the previously determined convex polygon is prioritized and the intersection figure is not updated. Thus, the determination intersection graphic becomes the same on the boundary line, and the two polygons become complicated and unsightly.

[0028]

FIG. 1 is a block diagram showing an embodiment of an intersection judging / intersection detecting unit of a graphic display device according to the present invention. The embodiment of the intersection judging / intersection detecting unit of the present invention shown in FIG. 1 includes an intersection distance detecting unit 11, an intersection coordinate calculating unit 12, an intersection judging unit 13, a hidden surface removing unit 14, and a distance judging condition setting unit 15. Be composed.

First, the line-of-sight data (viewpoint coordinates, line-of-sight vectors) and data of each convex polygon (vertex coordinates / normal vectors) are input to the intersection distance detecting unit 11. The intersection distance detecting unit 11 performs a process of sequentially extracting the convex polygons and detecting a distance from the intersection Q between the infinity plane including the convex polygon and the line of sight L to the viewpoint R.

The convex polygon does not intersect the line of sight if the line of sight vector is parallel to the infinite plane, or if the intersection of the line of infinity and the line of sight is not a valid value such as protruding from a predetermined graphic area. Therefore, the subsequent determination processing regarding this convex polygon of the line of sight is not performed.

Next, the intersection coordinate calculation unit 12 calculates the coordinates of the intersection Q by substituting the distance from the intersection Q to the viewpoint R into the equation of the line (actually, a half line) indicated by the viewpoint R and the line-of-sight vector. Then, it is sent to the intersection determining unit 13 together with the line-of-sight data and the data of the convex polygon.

The parts different from the conventional example of the present invention are an intersection judging unit 13 to a distance judging condition setting unit 15. Intersection determination unit 1
Reference numeral 3 includes a vertex outer product determining unit 21, a vertex inner product determining unit 22, and a normal inner product determining unit 23.

The intersection judging unit 13 calculates the coordinates between the vertex and the intersection (Pk in FIG. 2) from the coordinates of the intersection Q of the convex polygon and the line of sight calculated by the intersection coordinate calculating unit 12 and the vertex coordinates of the convex polygon sent together. −Q, k = 1... N) (vertex V in FIG. 2) is obtained, and the vector between two adjacent vertices (P1Q and FIG. P2
Q, P2Q and P3Q,..., PnQ and P1Q).

A vertex cross product determination unit (first intersection determination unit) 21
In the case where the outer product of the vectors between two vertices is substantially zero, the inner product determination unit (second intersection determining unit) 22 then determines the vector whose outer product between the two vertices is substantially zero by the inner product. And if the dot product is greater than 0,
The intersection Q is determined to be outside the convex polygon. Dot product is 0
If smaller, the intersection Q is determined to be on the boundary between the two vertices of the convex polygon.

On the other hand, when the outer product of the vectors between the two vertices is not substantially zero for the convex polygon, the normal inner product determining unit (third intersection determining unit) 23 next calculates the vector of the two vertices. An inner product is taken between the outer product and the normal vector of the convex polygon. If the inner product is larger than 0, sign = 1 is set. If the inner product is smaller than 0, sign = 1 is determined.

The above processing is performed for all adjacent two vertices. (A) When the cross product of the vectors between the two vertices is not all zero, (a) the sign is the same between the two vertices (1 or −
1) If the intersection Q is inside the convex polygon, (b) if there is a difference in sign between the two vertices ... The intersection Q is outside the convex polygon, (B) (C) When the vector inner product between the two vertices is 0, the intersection Q is on the boundary of the convex polygon, and (d) When vector inner product between two vertices is greater than 0: Intersection Q is determined to be outside of the convex polygon.

If it is determined that the intersection point Q is outside the convex polygon at least once, it is determined that the line of sight does not intersect with the convex polygon at that time, and the line of sight is not related to the convex polygon. The subsequent determination processing is not performed.

When it is determined that the intersection Q is on the boundary of the convex polygon, the determination that the convex polygon intersects with the line of sight is made in the same manner as when the intersection Q is inside the convex polygon. Is sent to the hidden surface erasing unit 14 together with the data.

The hidden surface elimination unit 14 calculates the distance from the intersection to the viewpoint in the polygon in the same manner as in the conventional example, and calculates the distance obtained here and the convex polygon processed up to that point. By comparing the distance from the intersection to the viewpoint, the one closest to the viewpoint, that is, the one with the shortest distance is selected.

However, the difference from the conventional example is that the distance is compared by a simple magnitude judgment for a normal intersection figure, but only when it is determined that the intersection Q is on the boundary line.
The distance determination condition setting unit 15 issues an instruction to add a constant value to the distance from the intersection of the convex polygon to the viewpoint, and compares the magnitude with the distance of the convex polygon processed up to that time.

Thus, when the difference between the distances is within a certain range, the convex polygon which has not been added with the above-mentioned predetermined value is given priority and the intersection figure is not updated. Thus, it is possible to solve the problem that the determined intersection graphic is the same on the boundary line thus far, and the two polygons become complicated and unsightly.

In the above description, the target convex polygon is assumed to be a convex n-gon (an integer of n> 2) defined on the same plane, but the convex polygon is not on the same plane. Will divide the plane into triangles that can be determined, and perform the same processing for each triangle.

In the rendering by the ray tracing method, not only is the intersection between the line of sight generated from the viewpoint as described above and the figure closest to the viewpoint determined, and the luminance value at the intersection is determined. As described above, due to the nature of the figure in which the line of sight intersects, rays corresponding to the reflected light / refractive light of the line of sight are skipped from the intersection, and the reflected light /
For each ray corresponding to the refracted light, a new intersection point of the figure is obtained, a luminance value at the new intersection point is obtained, and rays corresponding to the reflected light / refracted light are skipped from the intersection point. There is a method in which the tree processing is repeated, and the luminance value at each intersection of the rays forming the binary tree is added at a predetermined ratio to obtain the luminance value at each pixel on the screen.

Further, when determining the luminance value at each intersection, it is determined whether or not there is a figure that blocks the light vector from the given light source, so that the displayed figure is shaded to provide a more realistic display. There is also a method of rendering. The present invention can be applied to the determination of intersection of a figure with a ray corresponding to such reflected light or refracted light, and the determination of intersection of a figure that blocks a light vector from a light source at the time of shadowing.

In the above description, only the hidden surface elimination processing in the ray tracing method has been described. However, the processing method in the intersection determination unit 13 of the present invention is not limited to this, and a convex n-gon (n> 2) ) Can be applied to all systems that require the inside / outside determination means.

[0046]

According to the present invention, the vertices of a convex polygon are defined in a fixed direction (clockwise or counterclockwise) in determining the intersection between the line of sight and the convex polygon in the hidden surface elimination by the ray tracing method. When the line of sight intersects with the plane at which the convex polygon exists, vectors connecting the intersection and the vertices are sequentially obtained, and the inner and outer products of the vectors between two adjacent vertices and the normal of the outer product and the convex polygon are obtained. Judge whether the intersection exists inside the convex polygon, the boundary, or the outside by the inner product with the vector, and if the intersection exists inside or on the boundary of the convex polygon, the convex polygon Is determined to intersect with the line of sight, and processing by the hidden surface removing unit is performed.
By changing the distance judgment in the hidden surface elimination processing when it is judged that the object exists at the boundary, it is possible to simplify the intersection judgment and to solve the problem near the boundary of the polygon at the time of graphic display.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an embodiment of an intersection determination / intersection detection unit of a graphic display device according to the present invention.

FIG. 2 is a diagram illustrating a principle of determination by an intersection determining unit of the graphic display device of the present invention.

FIG. 3 is a diagram illustrating the principle of a ray tracing method.

FIG. 4 is a diagram illustrating the principle of a ray tracing method that also takes into account reflection / refraction and shadow determination with a light source.

FIG. 5 is a diagram showing a block configuration of a ray tracing system.

FIG. 6 is a diagram illustrating an example of a block configuration of a conventional intersection determination / intersection detection unit.

FIG. 7 is a diagram illustrating an example of a determination principle in a conventional intersection determination unit.

FIG. 8 is a diagram illustrating an example of a case where there is an intersection with a line of sight at a boundary between two convex polygons.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 11 Intersection distance detection part 12 Intersection coordinate calculation part 13 Intersection judgment part 14 Hidden surface elimination part 15 Distance judgment condition setting part 21 Vertex outer product judgment part (first intersection judgment part) 22 Vertex inner product judgment part (Second intersection judgment part) 23) Normal inner product determination unit (third intersection determination unit) L line of sight M pixels P1, P2,..., Pn Vertices of convex polygons (n> 2 integers)

Claims (4)

[Claims] 1. Vertices P1, P2,..., P on the same plane
an intersection Q with a line of sight existing on the same plane as a convex n-sided polygon having n (n> 2) is present inside the convex n-sided polygon, at a boundary of the convex n-sided polygon, or The convex n
The inside / outside determination for determining whether the region exists outside the polygon is performed by a configuration including an intersection distance detection unit, an intersection coordinate calculation unit, an intersection determination unit, a hidden surface removal unit, and a distance determination condition setting unit. In the graphic display device, the intersection determination unit is sequentially supplied with each vertex vector formed by connecting each vertex of the convex polygon with the intersection from the intersection coordinate calculation unit, and an outer product of vectors between two adjacent vertices is obtained. A first intersection determination unit for determining whether the cross product is zero, output information indicating that the outer product of the first intersection determination unit is zero and the vertex vector are supplied, and a cross product between the two adjacent vertices is provided. If the dot product in a vector that is zero is greater than zero, the intersection is outside the convex polygon; if the dot product is less than zero, the intersection is two of the convex polygon.
A second intersection determination unit that determines that the intersection is on the boundary between vertices, output information indicating that the outer product of the first intersection determination unit is not all zero in the convex polygon, and a convexity obtained by the intersection coordinate calculation unit. A normal vector of a polygon is supplied, sign = 1 if the inner product between the outer product of the vector between the two vertices and the normal vector of the convex polygon is greater than zero, and sign = 1 if less than zero. Is determined to be sign = -1, and all adjacent 2
When the signs are all the same between the vertices, the intersection is inside the convex polygon, and when there is a different sign, the intersection is determined to be outside the convex polygon. A graphic display device comprising an intersection determining unit. 2. The graphic display device according to claim 1, wherein the hidden surface elimination unit is configured to determine the convex polygon by the distance determination condition setting unit only when it is determined that the intersection is on a boundary line. An instruction to add a constant value to the distance from the intersection to the viewpoint is supplied, and the hidden surface elimination unit compares the magnitude with the distance in the convex polygon processed so far, and the convex polygon having a shorter distance is used. A graphic display device for selecting an intersection of polygons. 3. Vertices P1, P2,..., P on the same plane
an intersection Q with a line of sight existing on the same plane as a convex n-sided polygon having n (n> 2) is present inside the convex n-sided polygon, at a boundary of the convex n-sided polygon, or The convex n
The inside / outside determination for determining whether the region exists outside the polygon is performed by a configuration including an intersection distance detection step, an intersection coordinate calculation step, an intersection determination step, a hidden surface elimination step, and a distance determination condition setting step. In the graphic display method, in the intersection determination step, each vertex vector formed by connecting each vertex of the convex polygon and the intersection from the intersection coordinate calculation step is sequentially supplied, and an outer product of vectors between two adjacent vertices is calculated. A first intersection determination step of determining whether the value is zero, output information indicating that the outer product of the first intersection determination step is zero and the vertex vector are supplied, and the outer product between the adjacent two vertices is calculated. If the dot product in a vector that is zero is greater than zero, the intersection is at the outer step of the convex polygon; if the dot product is less than zero, the intersection is A second intersection determination step of determining that the intersection is on the boundary between two vertices of the convex polygon, and output information that the cross product of the first intersection determination step is not all zero in the convex polygon The normal vector of the convex polygon from the intersection coordinate calculation step is supplied,
If the inner product between the outer product of the vectors between the two vertices and the normal vector of the convex polygon is greater than zero, sign = 1,
If it is smaller than zero, it is determined that sign = −1, and if all of the signs are the same between all the two adjacent vertices, the intersection is inside the convex polygon, And a third intersection determination step of determining that the intersection is outside the convex polygon in some cases. 4. The graphic display method according to claim 3, wherein the hidden surface removing step is performed by the distance determination condition setting step only when the intersection is determined to be on a boundary line. An instruction to add a constant value to the distance from the intersection to the viewpoint is supplied. In the hidden surface elimination step, the magnitude is compared with the distance in the convex polygon processed so far, and the convex polygon having a shorter distance is used. A graphic display method characterized by selecting intersections of polygons.