JPH0335376A - Triangle dividing/drawing system for convex polygon - Google Patents

Abstract

PURPOSE:To increase the painting out speed of triangles by drawing only the left side, the left and right sides, or only the right side based on the minimum value (or maximum value) at drawing of triangles obtained by dividing a convex polygon with the maximum or minimum value of the X or Y axis direction defined as a fixed point. CONSTITUTION:A triangle dividing part 1 detects the maximum or minimum value of the X or Y axis direction from a list of apex coordinates of the convex polygon and defines the maximum or minimum value as a fixed point to divide successively a polygon into triangles. A processing part 2 draws only the left side, the left and right sides, or only the right side in terms of the coordinates of the sides opposite to the fixed points of those divided triangles based on the maximum (or minimum) value. Thus it is possible to avoid the double painting out operations for the adjacent sides when a convex polygon is divided into triangles and undergoes the painting out processes. As a result, the painting out process can be applied to a convex polygon at a high speed.

Description

[Detailed Description of the Invention] (Summary) The present invention divides a convex polygon into triangles! In the triangular division drawing method for drawing, in order to solve the problem of a decrease in filling speed due to an increase in the number of drawing commands issued when drawing a polygon, and the overlapping drawing of sides when drawing a polygon, the Y-axis direction of the convex polygon is (or in the X-axis direction) is divided into triangles with the maximum value (or minimum 4!) as a fixed point, and based on the minimum (or maximum) value of the divided triangle By drawing both right sides or only the right side, the convex polygon is filled at high speed by avoiding redundant filling of adjacent sides when dividing the convex polygon into triangles and filling them.

[Industrial application field]

The present invention relates to a triangle division drawing method in which a convex polygon is divided into triangles and drawn.

[Prior art and problems to be solved by the invention] Conventionally, when filling in a polygon represented by a plurality of vertex coordinates on a focused display, the drawing device shown in FIG. , quadrilateral, circle, etc., the intersection points where the raster intersects with the sides of the polygon are determined one by one as A and B, as shown in FIG.

Next, line segment drawing commands having these intersection points A and B as parameters are sequentially issued to fill the lines. For this reason, in the case of the polygon shown in FIG. 3, it is necessary to issue a large number of drawing commands, seven times in total, to fill it in, which poses a problem in that it is not possible to draw at high speed. Furthermore, when dividing a convex polygon into triangles and filling them in, it is desired to avoid redundant filling of adjacent sides.

The configuration and operation of FIG. 4 will be briefly explained.

In FIG. 4(A), the CPU notifies the drawing device constituting the bitmap display device of a drawing command such as a line segment of the figure to be drawn via the I10 bus, and the drawing device writes the drawing command on the bitmap frame memory. It is expanded into a file and displayed on the display.

In FIG. 4(b), the drawing pre-processing device notifies the drawing device via the I10 bus of a drawing command such as a line segment that corresponds to the figure to be drawn that was notified from the CPU, and the drawing device focuses. It is expanded on the manop frame memory and displayed on the display.

Here, MS (main storage) is a memory that stores programs and data, and DISK is an external storage device that stores graphic data and the like.

The present invention divides a convex polygon into triangles using the maximum value (or minimum value) in the Y-axis direction (or X-axis direction) as a fixed point, and when drawing these divided triangles, the minimum value (or maximum value) When drawing only the left side, both the left side and the right side, or only the right side based on , and dividing a convex polygon into triangles and filling them, the overlap of adjacent sides?! [Avoiding filling and drawing the corresponding convex polygon] The purpose is to fill in quickly.

[Means to solve problems]

Means for solving the problem will be explained with reference to FIGS. 1 and 2.

1 and 2, the triangle dividing unit 1 finds the maximum and minimum values in the Y-axis direction and the X-axis direction from the list of vertex coordinates of the convex polygon, and finds the maximum value (or The minimum value) is used as a fixed point to sequentially divide into triangles.

The processing unit 2 draws only the left side, both the left side and the right side, or only the right side, based on the minimum value (or maximum value) of the coordinates of the side opposite to the fixed point of the divided triangle.

[Effect]

As shown in FIGS. 1 and 2, in the present invention, the triangle dividing unit 1 finds the maximum and minimum values in the Y-axis direction (or the X-axis direction) from a list of vertex coordinates of a convex polygon, The maximum value (or minimum value) found is used as a fixed point to sequentially divide the triangles into triangles, and the processing unit 2 calculates the coordinates of the sides of the divided triangles facing the fixed points based on the minimum value (or maximum value). Only the left side, both the left and right sides, or only the right side are drawn.

Therefore, when a convex polygon is divided into triangles and filled in, it is possible to avoid redundant filling of adjacent sides and to quickly fill in the convex polygon.

〔Example〕

Next, the configuration and operation of one embodiment of the present invention will be explained in detail using FIGS. 1 and 2.

In Figure 1 (a), ■ is ring win po
inter (ring minimum value pointer 6), rin
Set g+iax pointer (maximum value pointer 7). As shown in FIG. Set value pointer 7.

■ is y + * ax pointer s y min
painter to cent, and y day ax=point
Let it be ter. For example, as shown in FIG.
), the maximum value in the Y-axis direction, V, is the point, y
+sin pointer (minimum value pointer 5) points to V, which is the minimum value in the Y-axis direction, and further y a
+ax Pointer points to V”
Set it so that ter points.

■ is (pointer+1)<(pointer+2
). This means that it is determined whether the vertex coordinates stored in file 3 are counterclockwise or clockwise.In the case of 0 counterclockwise, @ sets 1ncle+wenter=1.

For clockwise rotation, use the incrementer in [phase].
= −1.

[Stock] is pointer + incrementer
do.

0 is 1ef 5ide on and right 5
ide off. This will fill in the left side of the divided triangle (left 5ide on), and will not fill in the right side (right 5ide on).
e off).

For example, in the case of ΔVs Va Vs in FIG. 1(d), it means that the solid line portion is filled in and the dotted line portion is not filled in.

[Phase] is % pNnjer=ylIlaX potnt
er or not. This determines whether the content of pointer is the vertex coordinate value pointed to by the maximum value pointer 4 in FIG. This means determining whether or not they have returned in sequence. If YES, the process ends (END). If No, execute the steps after @.

[Phase] is pointer=y win point
It is determined whether or not r. This means that, for example, it is determined whether V of Δvs VS v in FIG. . This figure 1 (d) △V,
V.

Regarding V in ■, it is the minimum value in the Y direction, so it is YES, and right 5ide on [phase]
(Set to fill the right side), press ■ to draw (fill) both the left and right sides of the triangle, press @ to set 1ef 5ide off (stop drawing the left side), and execute [Phase]. do. On the other hand, in the case of NO, draw either the left side or the right side of the triangle with ■. ) and execute [Phase].

[Phase] is % pojnter +1ncle+5ent
er. As a result, the steps after @ are executed for the next triangle to sequentially draw it.

Through the above processing, for example, the convex polygon shown in FIG. 1(c) can be filled in except for the dotted line portions in the order of (d) 2, 2, 3, and 3 in FIG. 1(d).

As a result, as shown in FIG. 1(C), the interior of the convex polygon, including its sides, is filled uniformly, and the sides of the boundary when divided into triangles are not filled in redundantly.

FIG. 1(b) shows the vertex coordinates of a convex polygon.

This is a file (polygon fill) 3 that stores a list of vertex coordinates of a convex polygon to be filled.

FIG. 1(C) schematically represents the convex polygon stored in the file 3 of FIG. 1(B).

FIGS. 1(D) and 1(D) show the order in which the convex polygons in FIGS. 1(B) and 1(C) are divided into triangles and drawing is performed by issuing fill-in commands in the order of (1) to (2).

At this time, specify not to fill in the dotted line area.

FIG. 2 shows an overall explanatory diagram of the present invention.

In FIG. 2(a), [phase] performs convexity discrimination.

This calculates the cross products of adjacent sides of a given polygon, and determines whether the signs of the calculated cross products are all positive or negative (convex).

0 determines whether the polygon is convex.

In the case of YES (in the case of a convex polygon), execute steps ① and subsequent steps. If No, for example, a line segment drawing command is issued by scan conversion to sequentially fill the inside of the polygon.

@ performs triangle division.

[Phase] issues a triangle fill command. This can be done according to the flowchart in Figure 1 (a) described above.
Figure (2) Triangle fill commands specified not to draw the dotted line parts of ■ and ■ are sequentially issued and filled.

@ determines whether division has ended or not. If YES,
finish. If NO, repeat ① and [phase].

FIG. 2(b) shows an example of filling in a triangle.

For example, when filling △v, V, V, our technique can be done by filling the pixels between the coordinate points generated by ODA from the largest point ■, towards other points V, ,V,. △v, V4 V, sides (left side and right side)
I'm trying to fill it in including the . On the other hand, the side (left side,
If the right side) is not filled in, only the inside of the coordinate point generated by DDA is not filled in.

〔Effect of the invention〕

As explained above, according to the present invention, the maximum value (or minimum value) in the Y-axis direction (or X-axis direction) of a convex polygon
is divided into triangles using a fixed point, and when drawing these divided triangles, only the left side (or right side), both the left side and the right side, or only the right side is drawn based on the minimum value (or maximum value). Since this method is adopted, when a convex polygon is divided into triangles and filled in, it is possible to avoid redundant filling of adjacent sides and fill in the convex polygon at high speed. Furthermore, since the convex polygon is divided into triangles and filled in, the number of issuing drawing commands can be reduced and the bus usage rate can be reduced.

[Brief explanation of drawings]

FIG. 1 is an explanatory view of the tank bottom and operation of an embodiment of the present invention, FIG. 2 is an overall explanatory view of the present invention, FIG. 3 is an explanatory view of the prior art, and FIG. 4 is a diagram showing the countries in which the system is configured. In the figure, l is a triangular division part, 2 is a processing part, 3 is a file,
4 represents a maximum value pointer, 5 represents a minimum value pointer, 6 represents a ring minimum value pointer, and 7 represents a ring maximum value pointer. Drawing example (d) Operation explanation flowchart (a) (Explanatory diagram of conventional technology

Claims (1)

[Claims] In a triangle division drawing method in which a convex polygon is divided into triangles and drawn, the maximum and minimum values in the Y-axis direction (or X-axis direction) are determined from a list of vertex coordinates of the convex polygon. Find the maximum value (or minimum value) found as a fixed point and sequentially divide it into triangles, and the coordinates of the side opposite the fixed point of these divided triangles will be the minimum value (or maximum value) found above. up to the left side (
Or, when the minimum value (or maximum value) is reached, both the left and right sides are drawn, and when the minimum value (or maximum value) is passed, only the right side (or left side) is drawn. , A triangle division drawing method for a convex polygon, characterized in that it is configured to avoid duplicate drawing of the left side and right side of the divided triangle.