JP2000030081A - Drawing method of three-dimensional drawing apparatus - Google Patents

Abstract

(57) [Summary] To draw a concave / convex polygon, a single polygon (triangle) is drawn at high speed without further subdivision. A CPU has a texture memory (T).
M) Set a texture image and a texture height in 300, divide an object represented by a plurality of polygons into triangles,
Issue a triangle drawing command. The RP 200 divides the drawing line in the triangle based on the line segment projected in the normal direction for each triangle, and sequentially displaces the pixels on the drawing line according to the corresponding texture height information. Is drawn by interpolating the image data of the texture of the adjacent pixel between the pixel positions after the displacement. The group of interpolated pixels due to this displacement represents irregularities including the periphery of the triangle. This drawing process is repeated for all the lines of the triangle and for all the triangles constituting the object.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a three-dimensional drawing apparatus based on a polygon model, and more particularly to a method for drawing irregular polygons using texture mapping.

[0002]

2. Description of the Related Art A three-dimensional object handled by three-dimensional graphics is represented as a polyhedron divided into three-dimensional polygons (the smallest unit is a triangle), and projected and displayed on a two-dimensional (flat) screen. . To draw a polygon, an intersection point between the contour line and the scanning line is obtained, and a line processor performs an arithmetic process for filling the intersection area. Dots on a single polygon have a monotonous shape of the same color. For this reason, when an object having a complicated surface such as unevenness is to be displayed, the number of polygon divisions is greatly increased and the processing takes time, so that a large-scale arithmetic processing device is required.

On the other hand, a technique of texture mapping is known in the field of computer graphics. That is, image information of a three-dimensional object is separately prepared into image information and texture information of a polyhedron, and drawing is performed by pasting the texture information on the polyhedron.

[0004] Conventional texture mapping is described in, for example, "The Latest Three-Dimensional Computer Graphics (ASGLASSN)".
ER, edited by Kosaku Shirada, ASCII Publishing Bureau, pp. 137-147) "
Familiar with. Here, a handwritten or digitized image is used as a texture, and data arranged in a grid is prepared.
A basic mapping method has been described in which each vertex of a polygon is associated with texture coordinates, and when the computer determines the color of each coordinate at which to draw the polygon, the color is determined with reference to the texture. I have.

In addition, when shading is to be applied to a specific place on a smooth spherical surface, a texture called a bump mapping, which performs shading by slightly shifting the normal vector of the surface calculated at each point in a specific direction. There is an explanation. The adjustment of the normal vector at each point is determined by the value of the texture at that point. In other words, the pixel is drawn with whiter pixels so that the more the normal vector of a point on the surface faces the direction of the light source, the brighter the point becomes.

[0006]

In the drawing of an uneven polygon by the above-described texture method, it is basically necessary to divide a single polygon to be drawn into a plurality of fine polygons based on height information of a texture to be mapped. Therefore, the number of processes such as coordinate conversion increases, and high-speed drawing cannot be performed. Also, if the prepared texture is an image with a rough texture like a rock surface or a brick-like groove, the picture will be drawn on a smooth surface if the polygon after drawing is viewed from near or diagonally. I can only see it and it lacks realism.

Further, in the above-described bump mapping method, since the shadow is merely changed without changing the shape of the surface, it is advantageous in terms of the number of processes. However, when applied to large models, pasting the texture does not change the silhouette. For example, even when a texture having irregularities is pasted on a spherical surface, the contour is always circular, and the real feeling is poor.

SUMMARY OF THE INVENTION It is an object of the present invention to overcome the above-mentioned problems of the prior art and to render a realistic uneven polygon by a texture method capable of drawing at high speed without dividing a single polygon into a plurality of fine polygons. It is an object of the present invention to provide a method and an apparatus.

[0009]

In order to achieve the above object, the present invention uses a polygon model obtained by dividing a three-dimensional object into a plurality of triangles, and renders the triangles in a frame memory in order by drawing pixels in a frame memory. When performing a method of drawing a textured polygon that maps a texture expressing irregularities on the surface of the triangle, a projection vector to a two-dimensional display coordinate system is obtained from a normal vector for each triangle, and the vector The triangle is divided into a plurality of lines by a plurality of parallel line segments (hereinafter referred to as drawing lines), and image data of the texture corresponding to the starting points of the pixels on the drawing line are taken in order. Is calculated in accordance with the above, and the pixel obtained by interpolating the displacement between the similarly obtained adjacent pixel is drawn in the frame memory, and this is drawn all over the triangle. In repeated for all the triangles showing still the object, characterized by representing said irregularities by the interpolation pixel. Here, the interpolation of the pixels between the displaced positions is performed based on the luminance of the color data of each texture of the pixel before the displacement and the adjacent pixel.

According to the present invention, unevenness can be mapped on the surface of a triangle without subdividing it as in the prior art, so that the processing can be speeded up. In addition, the interpolated pixels representing the irregularities are displaced according to the height information, and are drawn, for example, at the positions of the displacements entering and exiting the periphery of the triangle, so that realistic irregularities can be given.

The starting point of the pixel position on the drawing line is an intersection with one side of the triangle where the scanning line of the display coordinate system first intersects, and the drawing line is incremented by +1 for each scanning line. It is characterized by incrementing. Thus, the increment of the drawing line having an inclination with respect to the scanning line follows the positive number increment of the scanning line, so that the drawing error does not occur due to the accumulated error of the real number operation.

Further, the depth value of the pixel before the displacement is compared with the depth value of the pixel in the frame memory corresponding to the displacement, and when the former is closer, the interpolated pixel is drawn in the frame memory. And As a result, hidden surface elimination processing can be performed between pixels that have already been developed due to displacement.

Further, the three-dimensional drawing apparatus for realizing the above-described method of the present invention includes setting means for changing the magnification factor when obtaining the height information of the texture and calculating the displacement. It is possible to realize a realistic expression by changing the height information while observing the displayed uneven polygon.

[0014]

Embodiments of the present invention will be described below in detail with reference to the drawings. FIG. 1 shows an embodiment of a three-dimensional drawing apparatus for realizing the present invention. The drawing apparatus calculates coordinates, calculates the vertex information and the normal line information of the triangle in the display coordinate system, the CPU 100 that performs pixel development in units of triangles, and the texture image data for each grid-like pixel. A texture memory (TM) 300 for storing, and a frame memory (F) for storing drawing pixels of a target object on which a texture is pasted (synthesized).
M) 400, CRT5 displaying the drawing pixels of FM400
00, a hardware configuration such as an input device not shown.

The CPU 100 controls the entire drawing apparatus, including input / output processing, and divides a polygon (polyhedron) representing an object into a single polygon (triangle in this embodiment) based on the coordinates of its vertices. Division 11
0, drawing line in triangular units (hereafter, nk line)
And a rendering command issuing unit 120 that converts the coordinates of the three vertices and the coordinates of the texture corresponding to each vertex into a display coordinate system and issues them.
The texture image setting unit 130 that captures the coordinates and color information of each pixel of the texture by handwriting or digitizer and stores it in the TM 300, the texture height information setting unit 140 that basically sets the height information of each pixel of the texture image, and the texture height It has a magnification setting unit 150 that varies the magnification of the information.

The RP 200 is a line dividing unit 210 for developing a triangle representing a single polygon into a line segment having an inclination (hereinafter, a line segment having an inclination is referred to as a line), and a displacement amount calculating unit for expanding a line into pixels. 220 and a line drawing unit 230 with interpolation.

Next, the operation of the three-dimensional drawing apparatus according to this embodiment will be described. FIG. 2 shows a schematic flow of the drawing procedure.
First, a texture image and height information corresponding to each pixel of the texture image are set from the CPU 100 to the TM 300 (s101, s102). The height information is created such that the higher the whiteness, the higher the value based on black in the texture image.

Next, the shape of the object is divided into a plurality of triangles based on the vertex coordinates (s103). Then, a three-dimensional normal N is obtained for each triangle, and is converted into coordinate values of the display coordinate system together with vertex coordinates (s104). The normal line N is uniform for one triangle.

Each value after conversion is a normal N vector (component: n
x, ny), coordinate values of three vertices (x1, y1), (x2, ny)
y2), (x3, y3), depth values w1, w of three vertices
2, w3, and the coordinate values (u1, v1), (u2, v2), (u3, v) of the texture corresponding to each vertex of the triangle.
3).

The normal N vector (component: nx, ny) is a projection vector on the display coordinate system that projects the normal of each triangle on the three-dimensional object. The depth w is the relative distance from the projection plane to the vertex when the distance from the viewpoint to the projection plane is normalized. The CPU 100 calculates these pieces of information and passes them to the RP 200.

FIG. 3 shows a major axis (l) in the display coordinate system,
The relationship between the short axis (s) and the x and y values of the triangle is shown. In this embodiment, in order to facilitate the calculation processing of the nk line, which will be described later, the major axis of the display coordinate system is 1 and the minor axis is s, and the nx and ny values of the normal N vector are compared according to the magnitude comparison. , X-axis and y
The axis is being replaced. Note that the coordinate values of the display coordinate system (x, y) immediately after the three-dimensional conversion are represented by x and y values, and the coordinate values of the display coordinate system (l, s) after replacement are represented by l values and s.
It shall be represented by a value.

As shown in (a), the major axis is the x-axis (nx ≧ ny)
In the case of, the x-axis is defined as the l-axis and the y-axis is defined as the s-axis. When the major axis is the y-axis (nx <ny) as in (b), the y-axis is defined as l-axis.
The axis and the x axis are defined as the s axis. Therefore, the normal N (nx, n
y) and the coordinate values of the three vertices of the triangle are expressed in the display coordinate system (l,
s) is replaced by Equation 1. (1) to (4) show the case where the major axis is the x-axis, and (5) to (8) show the case where the major axis is the y-axis.

[0023]

(Nx, ny) ⇒ (nl, ns) (1) (x1, y1) ⇒ (11, s1) (2) (x2, y2) ⇒ (12, s2) (3) ( (x3, y3) ⇒ (13, s3) (4) (nx, ny) ⇒ (ns, nl) (5) (x1, y1) ⇒ (s1, l1) (6) (x2, y2) ⇒ (S2, l2) (7) (x3, y3) ⇒ (s3, 13) (8) Assuming that the ratio of the change amount ns of the s-axis to the change amount n1 of the l-axis is the slope nk, the slope nk becomes From. This slope n
The k line is called an nk line. The nk line is a line segment parallel to a projection vector from the normal line N of the triangle on the three-dimensional object to the display coordinate system (l, s). The nk line is divided as follows and becomes a triangular drawing line.

[0024]

Nk = ns / nl (0 ≦ nk ≦ 1) (9) Then, the triangle is divided into lines having a slope of nk (s10
5) By drawing one line at a time, a triangle can be drawn. Since the value of ns / nl in Expression 2 is always equal to or less than 1 by the replacement of Expression 1, the division process is facilitated.

FIGS. 4 and 5 show the flow of the triangular line division processing. First, the major axis of the vector component (nx, ny) of the normal N in the display coordinate system is determined (s20).
1). As a result of the determination (s202), if the major axis is the x-axis, x
With the axis as the l-axis and the y-axis as the s-axis, the correspondence between the normal vector and the three vertices of the triangle is set by the equations (1) to (4) (s203). When the long axis is the y axis, the y axis is set as the l axis and the x axis is set as the s axis, and the corresponding setting is performed by the equations (5) to (8) (s204).

Next, the gradient nk of the vector (nl, ns)
Is calculated from Expression (9) (s205). Also, for each vertex of the triangle, a straight line equation of the slope nk, that is, a constant term nc
Is obtained by Expression 3 (s206).

[0027]

Nc = s−nk · l (s: s1 to s3, l: 11 to 13) (10) Next, the constant terms nc (ac, bc, cc) of each vertex are compared, and the minimum The vertex A is the vertex A, the maximum vertex is the vertex C, and the others are the vertex B (s207). Then, each side between vertices A, B, and C is defined by Equation 4 (s20
8).

[0028]

Vertex AB: s = abk · l + abc (11) Vertex BC: s = bck · l + bcc (12) Vertex CA: s = cak · l + cac (13) Next, nc = ac and (s209) , Nc <cc, the following processing (s210 to s210)
s215) is repeated. First, the drawing start point (sl, ss) of the l value and the s value is calculated by Expression 5 (s210).

[0029]

Sl = (nc−cac) / (cak−nk) (14) ss = nk · sl + nc (15) Next, Equation 6 when nc <bc, and Equation 7 when nc ≧ bc , The drawing end point (el, es) is calculated (s212, s213).

[0030]

[Mathematical formula-see original document] el = (nc−abc) / (abk−nk) (16) es = nk · el + nc (17)

[0031]

[Mathematical formula-see original document] el = (nc−bcc) / (bck−nk) (18) es = nk · el + nc (19) Next, pixels on the line are sequentially determined in units of nk lines for which the start point and the end point have been calculated. Then, the displacement amount is calculated based on the height information of the texture (s106), and the adjacent pixel before the displacement is moved to the displaced pixel position, and a line is drawn by interpolating between them (s107).

FIG. 6 is an explanatory view of drawing a triangle by the divided nk lines. (A) draws an nk line using the nk line as the starting point on the AC side of the triangle.
This is an example of drawing while incrementing by +1 on the side. The inclination of the nk line changes depending on the viewpoint and the direction of the triangle, and may not be parallel to the display coordinate system (l, s), that is, the hard scanning line. At this time, the increment of +1 along the AC side becomes a decimal value in dl and ds of the display coordinate system, and it is necessary to add a real number corresponding to the scanning line. Therefore, due to the precision of the real number calculation, errors accumulate at every increment, and the end point of the AC side cannot be reached, or a gap that is not drawn between the nk lines due to a shift of the start point occurs.

In (b), the starting point is set to l value = 0 in the display coordinate system, and the s component is incremented by +1.
Therefore, the increment can be speeded up only by the integer operation, and there is no omission in drawing due to the accumulated error as shown in FIG. Note that the actual drawing start point and drawing end point are clipped with a triangular frame. However, in order to render a pixel outside the triangular frame due to a pixel displacement due to the texture height, pixel development is performed including displacement outside the triangular frame.

FIG. 7 illustrates a method of determining the range of the nk line group including the triangular frame. This corresponds to the step s described above.
This is due to the processing of steps 206 to s208. The coordinates (l) of the three vertices A, B, and C of the triangle in the display coordinate system (l, s)
(1, s1), (l2, s2), (l3, s3) by
, And the constant term nc of the equation of the straight line of the nk line passing through each vertex is calculated. As a result, the vertex A having the minimum nc has nc = ac, the vertex C having the maximum nxc has nc = cc, the other vertices B have nc = bc, and a
The range from c to cc is the range of the nk line group including the triangle on the s axis (on the axis whose l value is 0). Therefore, ac ≦
In the range of nc <cc, while adding nc by +1, n
Processing of the k-line group is performed.

Equation 4 defines each side between the vertices of the triangle, the drawing start point of the nk line is between the vertices CA, and ac ≦
If nc <bc, the drawing end point is between vertices AB, bc ≦ nc
If <cc, the drawing end point is between the vertices BC. Then, n
From the pixels forming the k-line, the starting point and the ending point of the pixels included in the triangular frame are obtained by the following equations (5) to (7). As a result, the pixel processing range at the l-axis coordinate is sl ≦ l <el, so that processing is performed on a pixel-by-pixel basis while changing l by +1. Note that the value of the s-axis coordinate is obtained by substituting the value 1 into Equation 3.

FIG. 8 shows a flow of a process of calculating a displacement amount based on texture height information and a process of drawing a line with interpolation of texture pixels, and FIG. 9 is an explanatory diagram thereof. The data of each vertex of the triangle and the data of the corresponding texture are defined as follows.

The coordinates (la, sa) of the vertex A and the depth value w
a, coordinates of texture (ua, va), height ha, coordinates of vertex B (lb, sb), depth value wb, coordinates of texture (ub, vb), height hb, coordinates of vertex C (lc, s)
c), depth value wc, texture coordinates (uc, v
c) and height hc. Also, the height magnification coefficient set by the copy ratio setting means 150 is d.

First, the depth values wa, wb, wc of the three vertices
Then, the depth value w corresponding to the display coordinate system (l, s) is calculated (s301). Next, nl of the l component of the nk line
From the height magnification coefficient d, the height h of the texture pixel read from the TM 300 corresponding to the three vertices, and the calculated depth value w, the l value (pl) of the displaced coordinate pt of the pixel at the coordinate l, The s value (ps) is calculated by Equation 8 (s3
02).

[0039]

## EQU8 ## pl = nl.d.h / w + 1 (20) ps = nk.pl + nc (21) FIG. 9 is an explanatory diagram showing a drawing process of pixels P1 and P2 adjacent on the nk line. The pixel P1 at the coordinate 1 is displaced to P1 'of the displacement amount pt1 (l value is pl1), the pixel P2 at the coordinate l + 1 is displaced to P' of the displacement amount Pt2 (pl2), and the interpolation pixel is between p1 'and P2'. Cm is drawn.

The RP200 displays p on the nk line being processed.
1 = pl1, ps = ps1 (s303), FM40
From 0, the depth value wf of the pixel data stored at the coordinates (pl, ps) is read (s304). The coordinates (pl, ps) of the FM 400 may have already been drawn from another pixel position by the displacement interpolation of this embodiment. Further, another image to be combined, such as a background image, may be stored.

Therefore, hidden surface elimination is required. The w value of P1 received from the drawing command is compared with the stored wf of P1 ′ to P2 ′ read from the FM 400. If w ≦ wf, that is, if the interpolation pixel due to the current displacement is nearer (s305), the FM 400 To the coordinates (pl, ps) of P
Interpolation drawing of 1 'to P2' is performed. Here, the pixels from pt1 to pt2 are uniform as w values of the pixel P1. The method of using a uniform w value is easy to process,
When a plurality of triangles are adjacent to each other, accurate hidden surface processing cannot be performed. In order to perform more accurate hidden surface processing, it is necessary to perform an interpolation calculation of the w value in consideration of the z component of the normal line N.

Here, the brightness value of each pixel in the interpolation drawing between P1 'and P2' is calculated by interpolation (interpolation) from the brightness of the color data of the texture image corresponding to the pixel P1 to the brightness of the color data of the pixel P2. (S306).

Next, pl (initially pl1) is incremented by 1 (s
307), the processing from step s304 is repeated until pl ≧ pl2 (s308). Thus, line drawing with interpolation using the nk line as the drawing line is performed.

By performing the above processing for all the pixels constituting the nk line in the triangular frame, the processing of one nk line is completed. Further, nc is incremented by one in the range of ac ≦ nc <cc, and drawing of all nk lines in the range is completed, whereby drawing of one triangle having concavities and convexities is completed.

FIG. 10 is an explanatory diagram showing a drawing process of nk lines near the outline of a triangle. On the nk line, the adjacent pixels P1 and P2 before the displacement are displaced to Pt1 and Pt2, and are drawn as interpolation drawing pixels Cm outside the BC side of the triangle. In the present embodiment, clipping is used to select a drawing start point and a drawing end point, but is not applied to the result of the subsequent line drawing with interpolation, so that drawing outside the triangular frame is possible.

FIG. 11 shows a display example of a triangle drawn according to the present embodiment. The color of each pixel is changed every nk line. As shown in the drawing, the interpolation drawing pixel group gives a sense of unevenness to the surface of a triangular surface which is originally flush. In particular, in the peripheral portion of each triangle, the displacement based on the texture height results in drawing with ingress and egress from the ideal line of the triangle, thereby making the sense of irregularities stand out. The image quality of the unevenness is CRT50
The desired image quality can be obtained by changing the height h magnification coefficient by the magnification setting unit 150 while displaying the image at 0.

As described above, according to the present embodiment, when rendering a triangle according to a plurality of nk lines parallel to a projection vector of a display coordinate system on which a three-dimensional normal vector of a triangle is projected, the nk lines are drawn. Are sequentially displaced according to the height information of the corresponding texture, and the pixels generated by the displacement are interpolated and drawn with the texture luminance. As a result, since the height and the luminance of the texture are reflected as the interpolation pixels, it is possible to draw a realistic unevenness including a peripheral portion thereof on a triangular (single polygon) which is originally flush. In addition, since subdivision of polygons is not required and basically only line division and calculation of displacement can be performed, the processing can be realized with a simple and general-purpose (normal processing capability) drawing apparatus.

[0048]

According to the present invention, a drawing line for dividing the triangular system on the display system is determined based on the line projected in the normal direction of the triangle, and pixels on the drawing line are sequentially adjusted in texture height. Line drawing is performed by interpolating between displaced pixels based on the original, so polygons with irregularities including peripheral parts can be drawn at high speed without increasing the number of processes such as coordinate conversion by subdividing polygons, and inexpensive There is an effect that can be realized with a simple device.

[Brief description of the drawings]

FIG. 1 is a configuration diagram of a three-dimensional drawing apparatus according to an embodiment of the present invention.

FIG. 2 is a schematic flowchart showing a procedure of drawing a concave and convex polygon according to an embodiment of the present invention.

FIG. 3 is an explanatory diagram showing replacement of the major and minor axes (l, s) of a coordinate display system and the major and minor axes (x, y) of a triangle;

FIG. 4 is a flowchart showing the procedure of triangular line division processing.

FIG. 5 is a flowchart showing a continuation of FIG. 4;

FIG. 6 is an explanatory diagram showing nk line division at the time of drawing a triangle.

FIG. 7 is an explanatory diagram showing a range of an nk line group including a triangular frame.

FIG. 8 is a flowchart of a line drawing process including displacement amount calculation and interpolation.

FIG. 9 is an explanatory diagram showing drawing processing of pixels adjacent on the nk line.

FIG. 10 is an explanatory diagram showing a drawing process of a pixel in a peripheral portion of a triangle.

FIG. 11 is an explanatory diagram showing an example of drawing a concave and convex triangle by the drawing processing according to the embodiment.

[Explanation of symbols]

100 CPU, 110 Triangulation unit, 120 Drawing command issuing unit, 130 Texture image setting unit, 140
Texture height information setting section, 150: magnification setting section, 20
0: RP, 210: line dividing unit, 220: displacement amount calculating unit, 230: line drawing unit with interpolation, 300: TM, 40
0 ... FM, 500 ... CRT.

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Takatoshi Ueno 5-2-1 Omika-cho, Hitachi City, Ibaraki Prefecture Inside Hitachi Process Computer Engineering Co., Ltd. (72) Inventor Masamitsu Akatsu 5-chome, Omika-cho, Hitachi City, Ibaraki Prefecture No. 1 Hitachi Process Computer Engineering Co., Ltd. (72) Inventor Kazunori Oniki 5-2-1 Omikacho, Hitachi City, Ibaraki Prefecture Inside Omika Plant, Hitachi, Ltd. (72) Koji Ozawa Omika, Hitachi City, Ibaraki Prefecture 5-2-1, Machi-cho F-term (reference) at Hitachi, Ltd. Omika Plant 5B050 BA07 BA18 EA09 EA28 EA30 5B080 AA14 AA19 GA14 GA22 GA23

Claims (6)

[Claims] 1. A polygon model in which a three-dimensional object is divided into a plurality of triangles. When the triangles are sequentially developed into pixels in a frame memory and the object is drawn, irregularities are expressed on the surface of the triangles. In the method of drawing an uneven polygon for mapping a texture to be projected, a projection vector to a two-dimensional display coordinate system is obtained from a normal vector for each triangle, and a plurality of line segments (hereinafter, drawing lines) parallel to the vector are obtained. The triangle is divided into lines, the image data of the corresponding texture is sequentially taken from the starting point of the pixel on the drawing line, the displacement corresponding to the height information of the texture is obtained for the pixel, and the same drawing obtained in the same manner is obtained. A pixel interpolated between the displacement of the adjacent pixel on the line is drawn in the frame memory, and this is drawn on all drawing lines in the triangle, and further on the object. Repeated for to all triangles, the method of drawing unevenness polygons, characterized by representing said irregularities by the interpolation pixel. 2. The method according to claim 1, wherein the pixel interpolation between the displacements is performed based on the luminance of the color data of each texture of a certain pixel before the displacement and its adjacent pixels. 3. The method according to claim 1, wherein a starting point of a pixel position on the drawing line is an intersection with one side of the triangle where a scanning line of the display coordinate system first intersects, and the drawing line is + For each scan line
A method for drawing a concave and convex polygon, which is incremented by one. 4. The method according to claim 1, wherein a depth value of a pixel before the displacement is compared with a depth value of a pixel of the frame memory corresponding to the displacement. A method for drawing a concave and convex polygon, wherein the drawing is performed on the frame memory. 5. A drawing command calculating means for dividing a three-dimensional object into a plurality of triangles which are the minimum units of a polygon, converting the three-dimensional object into a two-dimensional display coordinate system in triangular units, and issuing a drawing command; In the three-dimensional rendering apparatus, comprising: a rendering processor and a frame memory that sequentially expands the triangles into pixels according to pixels; and a display device that displays the pixels developed in the frame memory. A texture memory for storing image data including height information, wherein the drawing command calculating means corresponds to a projection vector from a normal vector for each triangle to a display coordinate system and a two-dimensional transformed vertex of the triangle; The drawing processor obtains the coordinates of the texture to be rendered, and calculates the triangle by using a plurality of line segments (hereinafter, drawing lines) parallel to the projection vector. The shape is divided into lines, the image data of the corresponding texture is taken in order from the starting point of the pixel on the drawing line, and a displacement according to the height information is obtained for the pixel. A three-dimensional rendering apparatus, which renders pixels interpolated in the frame memory. 6. The three-dimensional drawing apparatus according to claim 5, further comprising magnification setting means for varying height information of the texture.