JPH0348554B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to improvements in graphic display processing methods used for graphic processing in computer graphics and the like.

Since graphic processing involves handling a large amount of data, there is a need to improve processing efficiency when processing planar figures such as polygons.

[Conventional technology]

A conventional example will be explained using figures. FIG. 13 is an explanatory diagram of a conventional example. For example, when displaying a polygon with a hollow part as shown in Figure 13a, there is a processing method that divides the polygon into a set of basic shapes such as triangles and quadrilaterals and displays them.
Widely used in dimensional CAD (Computer Aided Design), etc.

When performing division, a mesh that includes the polygon to be displayed is set as shown in FIG. 13b, and the polygon is divided into grid units. If the figure in the grid becomes a triangle or square, that figure is displayed. However, if the figure in the grid is more complex than a rectangle, such as the shaded area, the figure inside the grid is displayed. Then, set a finer grid and continue dividing until the shapes in the finely divided grid become triangles or squares. Figure 13c is the result of subdividing the hatched area in Figure 13b.

[Problem that the invention seeks to solve]

As described above, in the conventional graphic processing method, a single polygon with holes is converted into a plurality of polygons without holes, so the amount of graphic data increases rapidly. Therefore, there is a problem in that the time required for data transfer from the processing device to the display device increases, and the time required for display processing increases.

[Means for solving problems]

The above problem is that the device has a memory and a display device in which three-dimensional information consisting of surface data, edge line data, etc. is stored, and the three-dimensional shape image is displayed on the screen of the display device using the three-dimensional information retrieved from the memory. In the display system, a first conversion processing means converts the three-dimensional information into two-dimensional information, a division processing means divides arc and free curve data in the two-dimensional information into a plurality of edge line data, and the division a conversion processing means for converting two-dimensional polygon information with holes including the edge line data into two-dimensional polygon information without holes; and a second conversion process for converting the two-dimensional information on polygons without holes into three-dimensional information. The problem is solved by the graphic display processing method of the present invention comprising means.

[Effect]

As described above, the present invention includes means for converting two-dimensional polygon information with holes into two-dimensional information on polygons without holes, so the amount of graphic data does not increase. Therefore, the time required for data transfer and data processing is shortened, graphics can be displayed at high speed, and graphics processing efficiency is significantly improved.

〔Example〕

Hereinafter, the present invention will be explained with reference to the drawings. FIG. 1 is a block diagram explaining one embodiment of the present invention, and FIG.
Figures 4 to 4 and 6 to 11 are diagrams illustrating an embodiment of graphic processing of the present invention, Figures 5 and 1.
FIG. 2 is an explanatory diagram of a conventional example.

In FIG. 1, file 1 stores solid model data SD. This data SD
The surface data included in the image data or the edge line data constituting the boundary lines are all three-dimensional data. Note that a mathematical model expressing a three-dimensional shape is called a solid model, and maintenance including information changes of this solid model is performed by the solid modeling section 3.

When graphic processing (such as changing the three-dimensional shape) is performed using the keyboard 5 or light pen 6 of the display control device 4, the solid data handler 2 is activated by the processing section 7.

The solid data handler 2 sends the solid model data SD taken out from the file 1 to the DA data converter 9 via the bus 8.

The DA data conversion unit 9 converts solid model data
The SD is divided into surfaces (polygons). First, three-dimensional data is converted into two-dimensional data by a two-dimensional conversion unit 10. As mentioned above, the surface data and edge data included in the solid model data SD are all three-dimensional, and this is converted into two-dimensional data. The conversion process of the two-dimensional conversion unit 10 will be explained below.

For example, a rectangular parallelepiped is a three-dimensional real space (x, y, z)
Although it can only be expressed as data within, if we limit it to the top surface of this rectangular parallelepiped, we can think about it in a second-dimensional parameter space (u, v). This conversion from three-dimensional data to two-dimensional data can be processed using a mathematical method. As an example, in the case of plane transformation, the normal vector n→ is set as n→=(n _x , _ny , _nz ), and the one with the maximum absolute value among each component is set as n _nax =Max｜｜n _x |, |n _y |, |n _z |} If n _nax = |n _x | then (u, v) = (y, z) n _nax = |n _y | then (u, v) = (z, x) n _nax = |n _z | If (u, v) = (x, y), from the 3-dimensional real space (x, y, z) to the 2-dimensional parameter space (u, v) conversion is performed.

For example, as shown in FIG. 2, the entire rectangular parallelepiped can only be expressed as data in a three-dimensional real space (x, y, z). However, if it is limited to only the upper surface, it is possible to think in a two-dimensional parameter space (u, v).

Furthermore, the polygons formed by one surface of any polyhedron on a plane in two-dimensional space, including polygons with holes, can be expressed as follows.

In Fig. 14, p→ ₁ , p→ ₂ , ..., p→ _N are three-dimensional position vectors of each vertex of a polygon existing on the same plane, p→ _i = (X _i , y _i , Z _i ), i=1~N Also, n→ is the normal vector on the infinite plane on which the polygon lies, and n→=(n _x , _ny , n _z ), and o→ is the normal vector on the infinite plane on which the polygon lies. Let o→=(o _x , o _y , o _z ) be the three-dimensional position vector of an arbitrary point on an infinite plane.

The two-dimensional transformation unit 10 in FIG. 1 converts information on a vertex sequence p→ _i (i=1 to N) constituting a polygon existing in a three-dimensional real space (x, y, z) using the following procedure. 2
Convert to dimensional parameter space (u,v).

First, find the one with the largest absolute value among n _x , n _y , and n _z .

Next, when the absolute value of n _x is the maximum, y i and z _i are adopted as u and v from p→ _i = (x _i , y _{i ,} z _i ).

In other words, the coordinate value of the vertex p→ _i in the two-dimensional parameter space (u, v) corresponding to the vertex p→ _i is p→ _i =(u _i , v _i )=(y _i , z _i ).

Similarly, if the absolute value of n _y is maximum, then p→ _i = (u _i , v _i ) = (z _i , x _i ), and if the absolute value of n _z is maximum, then p → _i = (u _i , v _i ) = (x _i , y _i ).

As shown in Figure 15, the above processing is equivalent to projecting a polygon in a three-dimensional space (x, y, z) onto one of the coordinate planes and creating a two-dimensional figure within that coordinate plane. do.

Furthermore, by the above processing, the polygon p→ _i = (x _i , y _i , z _i ), i=1 to N in the three-dimensional space is transformed into the polygon p→ _i = (u _i , v _i ), i=1 to N.

Here, the ``normal vector on the infinite plane on which the polygon lies'' used in the above two-dimensional transformation, and the ``3-dimensional position vector of an arbitrary point on the infinite plane on which the polygon lies'' o. → information is saved and used in the conversion process performed by the three-dimensional conversion unit 13.

In the present invention, when converting a polygon with holes into a polygon without holes as shown in FIG. After the transformation to a rectangle, the data is transformed back to (x, y, z) space.

The edge line data extracted from the solid model data SD is three-dimensional data consisting of: ● Coordinate values of the start and end points of each side ● Center coordinate values and radius for circular arcs ● Control point information for free curves. The coordinate values of the starting point and ending point of each side are converted to (u, v) by the two-dimensional transformation unit.
Converted to coordinate values in space.

Next, the edge line dividing unit 11 performs the third edge dividing process.
This will be explained using figures. A three-dimensional figure composed of a side A, a free curve (Bezier curve) B, and a circular arc C shown in FIG. 3a can be divided and subjected to approximation processing as shown in FIG. 3b. That is, free curve B and arc C
As shown in FIG. 3b, a sequence of points is generated on each side to divide the area, and the area is approximated by a broken line. Therefore, the graphic data (solid model data SD) shown in Figure 3a
The data extracted from (1) the coordinate values of the start and end points of each side A, (2) the control information for the free curve (Bezier curve) B, that is, the information expressed by the parameter t (0 to 1), (3) ) The arc C is expressed by the angle θ. By such edge line division processing, "a finite plane with holes surrounded by curves in three-dimensional space" can be converted into "a polygon with holes in two-dimensional space".

The bridge generation unit 12 generates two edges (doublebridge) between the inner loop and the outer loop of the “polygon with holes in two-dimensional space” generated by the edge line division unit.
The process of converting a polygon with holes into a single polygon without holes is performed by generating . The outline of bridge generation will be explained with reference to FIG.

FIG. 4a shows a polygon with holes serving as input data, and has inner loops 1 ₁ and 1 ₂ indicated by diagonal lines in the outer loop L. In the present invention, FIG.
As shown in , the apex E of the outer loop and the apex F of the inner loop are connected by two ridge _{lines R 1 and} R ₂ (double
Similarly, the vertex H of the outer loop L
and the vertex G of the inner loop 1 ₂ , and the two edges R ₃
and R ₄ to convert it into a polygon without holes.

Furthermore, as shown in FIG. 4c, when there is an inner loop ₁₃ that cannot be directly connected to the outer loop L, there is a double bridge between the apex Q of the inner loop ₁₃ and the apex P of the inner loop ₁₄ .
internal loop 1 ₄
A double bridge is formed between the vertex M of the outer loop L and the vertex K of the outer loop L, and the polygon is converted into a polygon without holes. That is, it is connected to the inner loop L and converted into a polygon without holes.

The processing of the bridge generation unit 12 in FIG. 1 is performed in the order of processing in the flowchart of FIG.
This will be explained using Figure 1.

Selection of inner loop 1 ₁ When there are multiple inner loops, first specify one inner loop i.

Selection of bridge candidates 1 vertex on inner loop i and 1 on outer loop L
Extract the vertices and use them as bridge candidate lines.

In FIG. 6, the example indicated by the broken line is an example unsuitable for a bridge.

End point check processing Checks whether the bridge is protruding towards the inside of the polygon at both end points of the bridge. In FIG. 7, all three bridge candidate lines extending to the shaded area (outside the polygon) are invalid. Bridge candidate line a in FIG. 6 is excluded by this check.

Intersection check processing An intersection check is performed on the bridge candidate line and all other ridge lines, and if there is even one ridge line that intersects, that bridge candidate line is excluded. Therefore, FIG. 6 becomes as shown in FIG. 8. Also, to speed up processing,
The intersection check is divided into the following two steps (1) Rough check The bridge candidate line or ridge line is set as a diagonal line.
A rectangle with sides parallel to the u and v coordinate axes is generated, and the presence or absence of overlap between the rectangles is checked.

In FIG. 9, the minimum and maximum values in the u- and v-axis directions of the rectangle including the bridge candidate line are defined as u _nio , u _nax , v _nio , and v _nax , respectively.

Similarly, for a rectangle that includes edges, define u′ _nio u′ _nax v′ _nio v′ _nax .

At this time, when at least one of the following conditions is satisfied, there is no intersection between the bridge candidate line and its ridgeline.

u' _nio >u _nax u' _nax <u _nio v' _nio >v _nax v' _nax <v _nio For example, the edge line C shown in FIG. 10a is determined to have "no intersection" with the bridge candidate line b.

(2) Detailed check For the ridge lines that could not be judged as ``no intersection'' in the rough check in item (1), calculate the intersection with the bridge candidate line and check whether there is an intersection.

Although the ridge line d in FIG. 10b cannot be determined by the rough check in section (1), by calculating the intersection point in the detailed check in section (2), it is possible to determine that the bridge candidate line b does not intersect.

Bridge generation process A bridge is generated along the bridge candidate line that has been determined not to intersect with any of the edges in the above check process. As a result, the polygon with holes shown in FIG. 11a is converted into the polygon without holes shown in FIG. 11b.

Note that e in FIG. 11a indicates a bridge candidate line, and f and g in FIG. 11b are newly generated points.

Determine the end of bridge generation.

Determine whether the process has ended normally.

Next, the three-dimensional transformation unit 13 in FIG.
Polygon data without holes generated in a dimensional (u, v) space is inversely transformed into a 3-dimensional (x, y, z) real space.

The polygon p→ _i = (u _i , v _i ), i=1~N, which was converted into a polygon without holes by adding a bridge, is again transformed into the polygon p→ _i = (X _i , y _i , Z _i ), to return i=1 to N,
n→ and deo→ used in the two-dimensional transformation unit 10 in FIG.
Use it again to perform the following process.

First, find the one with the largest absolute value among n _x , n _y , and n _z .

In this case, it is also possible to save the determination result in the two-dimensional transformation unit 10 shown in FIG. 1 and use it.

Next, if the absolute value of n _x is the maximum, u _i can be used as y _i and v _i can be used as z _i .

The coordinate value to be supplemented is x _i , which is obtained as follows.

As shown in Figure 16, the relationship between the vertex p→ _i = (x _i , y _i , z _i ) of a polygon in three-dimensional space and a point o → on the infinite plane on which the polygon stands The vector p→ _i −o→ is perpendicular to the normal vector n→ of the infinite plane. Here, the sum of the products of each component of two mutually perpendicular vectors is 0, so (p→−o→・n→=(x _i −o _x )n _x + (y _i −o _y )n _y + (z _i −o _z )n _z =0.

Therefore, x _i = o _x − [(y _i −o _y ) n _y + (z _i − o _z ) n _z ]/n _x = o _x − [(u _i −o _y ) n _y + (v _i −o _z ) n _z ]/n _x .

Therefore, p→ _i = (o _x − [(u _i − o _y ) n _y + (v _i − o _z ) n _z ]/n _x , u _i , v _i ) = (x _i , y _i , z _i ).

Similarly, when the absolute value of n _y is maximum, p→ _i = (v _i , o _y − [(u _i − o _z ) n _z + (v _i − o _x ) n _x ]/n _y , u _i ) = (x _i , y _i , z _i ).

Also, if the maximum value of n _z is the maximum, p→ _i = (u _i , v _i ), o _z − [(u _i −o _x ) n _x + (v _i −o _y ) n _y ] /n _z ) = (x _i , y _i , z _i ).

The polygon without holes that has been bridged in the two-dimensional parameter space (u, v) is converted into a polygon in the three-dimensional real space (x, y, z) through the above processing.

The above processing completes the processing of one surface constituting the polyhedron, so similar processing may be performed on the other surfaces as necessary.

FIG. 12 shows the series of processes described above, namely the first
It is a flowchart showing an outline of the processing of the DA data conversion unit 9 in the figure. Also, 14 in Figure 1
1 is a display data handler, 15 is a display data file, 16 is a display section, and 17 is a processing device.

〔Effect of the invention〕

As described above, the present invention can convert the graphic information of a polygon with holes into the graphic information of a single polygon without holes, so the amount of graphic data does not increase, and the processing efficiency regarding data transfer and data processing is significantly improved. It has the advantage of having the effect of

[Brief explanation of drawings]

FIG. 1 is a block diagram explaining one embodiment of the present invention, FIGS. 2 to 4 are diagrams explaining one embodiment of the present invention, and FIGS. 5 and 12 are diagrams explaining one embodiment of the present invention. Flowchart diagrams for explaining, FIGS. 6 to 11 are figures for explaining one embodiment of the present invention, FIG. 13 is an explanatory diagram for a conventional example, and FIGS. 14 to 16 are diagrams for explaining one embodiment of the present invention. Figures to be explained: In the figure, 1 is a file, 2 is a solid data handler, 3 is a solid modeling section, 4 is a display control device, 5 is a keyboard, 6 is a light pen,
7 is a processing unit, 8 is a bus, 9 is a DA data conversion unit,
10 is a two-dimensional conversion unit, 11 is an edge line division unit, 12 is a bridge generation unit, 13 is a three-dimensional conversion unit, 14 is a display data handler, 15 is a display data file,
16 is a display unit, and 17 is a processing device.

Claims (1)

[Claims] 1. In a system that has a memory in which three-dimensional information consisting of surface data, edge line data, etc. is stored and a display device, and displays a three-dimensional shape image on the screen of the display device using the three-dimensional information retrieved from the memory,
a first conversion processing means for converting the three-dimensional information into two-dimensional information; a division processing means for dividing the arc and free curve data in the second-dimensional information into a plurality of edge line data; and the divided edge line data. and a second conversion processing means that converts the two-dimensional polygon information without holes into three-dimensional information. A graphic display processing method characterized by: