JP2003288606A - Boundary discrimination device and program therefor - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a boundary discrimination system which can quickly, securely and easily judge the inside and outside areas of a line passing through a closed region. <P>SOLUTION: The present invention performs discrimination of area whether a line Ai passing through a closed region R which comprises a plurality of boundary lines Bj is inside or outside the closed region. Intersection and intersection points of the line Ai and each boundary line Bj are determined, and if the line Ai crosses an intermediate point of the boundary lines B1 and B4, the intermediate point is determined as true intersection points 1 and 2 as shown in [2] (c). If the line Ai crosses only the ends of the boundary lines B1 and B7 and the boundary lines B1 and B7 are located at the right side of the line Ai, the each of the edges is determined as the true intersection points 1 and 2 as shown in [1]. The true intersection points are then sorted in the increasing order of distance from the line Ai. Based on the sorted data string of true intersection points, the boundary discrimination to judge inside and outside is performed. <P>COPYRIGHT: (C)2004,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an area discriminating system for discriminating a portion inside a region and a portion outside a region of a line segment passing through a closed region.

[0002]

2. Description of the Related Art Filling a closed area on a drawing represented by graphic data with a predetermined color or pattern is called "painting" or "color painting" and is widely used in graphic processing. There is. For example, in GIS (geographical information system), the area where liquefaction is predicted at the time of an earthquake disaster is measured by geological boring etc.
A liquefaction prediction area may be overlaid on the base map (current situation map), and the range in which individual houses may be collapsed, partially destroyed, or partially damaged may be simulated depending on conditions such as earthquake intensity (seismic intensity). In this case, the simulated state can be accurately grasped by applying a predetermined painting (or coloring) process corresponding to the degree of damage to the house inside a predetermined closed area that represents a feature on the map. You can

In the painting (or coloring) processing, it is necessary to determine whether a line segment such as a scanning line or a drawing line that passes through a target closed region is inside or outside the region. is there. Therefore, use the rule that each time a line segment crosses a region line that constitutes a closed region, it alternates such as “outside region” → “inside region” → “outside region” → “inside region” → ... Thus, it is possible to determine whether it is inside or outside the closed area.

According to this discrimination method, when the shape of the closed region to be filled is a simple feature and the line segment crosses the middle of the region line, the inside / outside region can be discriminated without error. However, in the case of many features with uneven shapes, line segments pass over the vertices of a closed region (that is, the polygon formed by the region lines), pass through the contact points of the region lines, or over the region lines. There are many cases in which the vehicles pass over each other, and there are cases where the inside / outside area is erroneously determined or the inside / outside area cannot be determined.

[0005]

SUMMARY OF THE INVENTION In view of such circumstances, the present invention is capable of easily and reliably determining the area inside and outside the line segment passing through the closed area in a short time. An object is to provide a region discrimination system.

[0006]

According to the main feature of the present invention, a line segment (Ai) passing through a closed region (R) constituted by a plurality of region lines (Bj) is defined by the closed region (R). An area discriminating device for discriminating whether the area is inside or outside, detecting that a line segment (Ai) intersects at an intermediate point of an area line (Bj), and setting the intermediate point as an intersection point. Means (F1, F2; S2-S4) to determine ("true intersection")
And that the line segment (Ai) intersects at the end point of the area line (Bj) and the area line (Bj) is unevenly distributed on the right side or left side of the line segment (Ai), the end point is intersected. Means (F1, F2; S2-S4) for determining ("true intersection"),
Means (F3) for sorting the determined intersections ("true intersections") in order from the starting point of the line segment (Ai) to generate an intersection row ("true intersection" row), and the generated intersection row Based on (the "true intersection" column), means (F4) for alternately outputting the region determinations that the inside of the closed region (R) and the outside of the closed region (R) are sequentially output. An area discriminating apparatus (claim 1) is provided. Note that parentheses indicate symbols and the like of the corresponding examples, and the same applies below.

Further, according to this feature, a plurality of area lines (B
line segment (Ai) passing through the closed region (R) composed of j)
, The line segment (Ai) intersects the graphic information processing device (PC) that determines whether it is inside or outside the closed region (R) at the midpoint of the region line (Bj). That the line segment (Ai) is the end point of the area line (Bj), and the step (F1, F2; S2-S4) of determining that the intermediate point is the intersection ("true intersection"). A step (F1, F2;) of detecting the intersection and the area line (Bj) being unevenly distributed on the right side or the left side of the line segment (Ai) and determining the end point as an intersection point (“true intersection point”). S2 to S4) and the determined intersections are sorted in ascending order from the starting point of the line segment (Ai) to generate an intersection row (a "true intersection" row) (F
3) and the generated intersection line (“true intersection” line), the fact that the inside of the closed region (R) and the closed region (R) are sequentially
An area discriminating program (claim 2) for executing a procedure comprising the step (F4) of alternately outputting the area discriminant indicating that the area is outside.

[Operation of the Invention] According to the present invention, the line segment (Ai) passing through the closed region (R) constituted by a plurality of region lines (Bj) is inside or outside the closed region (R). When determining whether there is an area, first, the intersections and intersections of the line segment (Ai) and each area line (Bj) are determined. here,
When it is detected that the line segment (Ai) intersects at the midpoint of the area line (Bj) (FIG. 5 [1a]), the midpoint is determined to be the intersection ("true intersection") and ( F1, F2;
S2 to S4), the line segment (Ai) intersects at the end point of the region line (Bj), and the region line (Bj) is unevenly distributed on the right side or the left side of the line segment (Ai) (FIG. 5 [1b] or 5 [1
c]) is detected, the corresponding end point is determined as an intersection (“true intersection”) (F1, F2; S2 to S4). Next, the determined intersections (“true intersections”) are sorted in ascending order from the starting point of the line segment (Ai), and a sorted intersection row (“true intersection” row) is generated (F3). Then, based on the generated intersection line (“true intersection” line), region determinations of the inside of the closed region (R) and the outside of the closed region (R) are alternately output alternately. (F4; FIG. 8).

Therefore, according to the present invention, the closed region (R)
8 [2] (a)], passing through the contact point (Bj) of the area line [FIG. 8 [2] (b),
(C)], the line segment (Ai) passes over the area line (Bj) in an overlapping manner [FIG. 8 [1]], etc. It is possible to easily and reliably determine the inside / outside of the area without making a mistake.

[0010]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of the present invention will be described in detail below with reference to the drawings. The following embodiments are merely examples, and various modifications can be made without departing from the spirit of the present invention.

FIG. 1 is a block diagram schematically showing a hardware configuration example of a graphic information processing system having a region discriminating function according to an embodiment of the present invention. In this example, a personal computer (PC) is used as a control unit of the graphic information processing system, and the PC has an area discrimination function. In addition to the central processing unit (CPU) 1, the PC is
A read-only memory (ROM), a random access memory (RAM), a storage device 2 such as a hard disk (HD), an input device 3 including input operators such as a keyboard and a mouse, and a display device 4 including a display such as a CRT or LCD. Are connected to each other via a bus 5.

The CPU 1 for controlling the entire system performs various controls according to a predetermined program, and executes not only graphic processing but also text, tables, drawings, etc. by graphic processing and various other software programs installed in the system. Performs various processes such as data acquisition, creation, and editing. In particular, the CPU 1 discriminates an area in accordance with a paint processing program including an area discrimination algorithm,
A corresponding fill process can be performed.

The storage device 2 is a read-only memory (RO
M), random access memory (RAM) and external storage. The ROM includes a basic program, various application programs for executing the various processes described above,
Various fixed data / parameters are recorded. RAM is
It is used as a buffer or the like for temporarily storing various data / parameters etc. currently being worked, and for example, a "true intersection" list buffer is provided.

The external storage device is a hard disk (HD).
Also, other portable recording media such as a flexible disk (FD) and a compact disk ROM (CD-ROM) are included, and the HD stores various application programs like the ROM and is associated with the above-described various processes. Various data, for example, various graphic data for area determination can be stored. The portable recording medium can also store or retrieve various application programs and various data.

The input device 3 includes input operators such as a keyboard and a pointing device (mouse), and the display device 4 includes a display such as a CRT or LCD. The user (operator) visually recognizes various screens displayed on the display (4) and operates a predetermined key with the input operator (3) or operates an operation button on the screen.
It is possible to perform various user interface functions in various processes including the region determination process. Further, the display (4) can display a drawing or the like that has been filled in with a closed figure based on the area discrimination result.

An interface (I
/ F) 6, image scanner 7, laser printer 8, plotter (raster plotter or pen plotter)
An input / output device such as 9 is connected, and the scanner 7 can capture image data from various drawings. The printer 8 or the plotter 9 can output on paper the drawing or the like that has been filled in with the closed figure based on the area determination result.

[Outline of Painting Process] FIG. 2 is a schematic functional block diagram showing an outline of the procedure of the painting process according to an embodiment of the present invention, and FIG. 3 is a region according to the embodiment of the present invention. It is a figure for demonstrating the principle of inside / outside determination used for determination. The filling process according to the embodiment of the present invention is performed by an intersection determination block (module) F1, an intersection determination block (module) F2, an intersection sorting block (module) F3, an area determination block (module) F4, and a filled drawing block (module). ) Performed via F5.

First, in the intersection determination block F1, a closed area (closed figure) R to be painted is designated from the figure data to be drawn and output by the display device 4, the output device such as the printer 8 and the plotter 9. , The closed area (closed figure)
Area line Bj forming R (when the closed figure is an n-sided polygon:
j = 1, 2, 3, ..., N. ) Is taken out and output device 4,
It is determined whether or not each line segment Ai (i = 1, 2, 3, ...) Representing a scanning line or a drawing line used for display and printing at 8 and 9 intersects each area line Bj, and the intersection point To calculate.
Here, when the line segment Ai and the area line Bj overlap at a single point, as shown by the black circle in FIG. 3, it is determined to "intersect", and this overlapping point (shared point) is taken as the intersection point C.

In the next intersection determination block F2, the "true intersection" is determined for each obtained intersection C. here,
The “true intersection” is an intersection used to determine whether the inside of the closed region R is inside or outside. Next, in the intersection point sorting block F3, the intersection points C determined to be "true intersection points" are sorted for each line segment Ai in the order close to the start point of the line segment Ai. That is, the line segments Ai are arranged in a line with the end and start points in the order of the first line segment A1, the second line segment A2, ..., And the final line segment An, and the “true intersection” is the start point of the first line segment A1. The "true intersection" column after sorting (sorting) in ascending order of distance from (hereinafter, simply referred to as "" true intersection "column") is stored in the "true intersection" list buffer in RAM. Stored temporarily. In this sort, if there are multiple "true intersections" at the same distance, the "true intersections" at the same distance are
It should be arranged so that it can be seen that they are in the same rank,
No special consideration is required regarding the extraction order.

In the inside / outside determination block F4, as shown in FIG. 3, the coordinate points of each line segment Ai are advanced from the starting point of the line segment Ai, and sorted in the intersection sorting block F3 to the "true intersection" list buffer. Referring to the stored “true intersection” column, for example, the area “outside” is initially set, and each time the intersection with the area line Bj is encountered, the area “inside” →
The area “outside” → the area “inside” is determined. That is, each time the intersection point with the area line Bj is encountered as the coordinate point of the line segment Ai progresses, whether the coordinate point is inside the area R depending on whether the encounter frequency is odd or even. Determine if you went out. Then, in the painted drawing block F5, non-drawing or painted drawing is performed from the start point of each line segment Ai according to the determination result of the area “outside” or “inside” in the area determination block F4.

[Procedure for Area Discrimination] FIG. 4 is a flowchart showing a processing procedure for intersection / intersection determination according to an embodiment of the present invention. This processing flow shows the intersection and intersection determination processing executed in the intersection and intersection determination blocks F1 and F2 for one line segment Ai and one closed region R. It is executed for all the line segments used and all closed regions that are the targets of the filled drawing.

In the first step S1 of the intersection / intersection determination processing flow, a line segment Ai to be subjected to the inside / outside determination and one line segment Bj (j ← “1”) forming the closed region R are taken out. That is, the shape of the closed region R is usually n region lines B1 to B.
Since n is represented by an n-sided polygon (n ≧ 3) (a curved line such as a circular arc is approximated by a plurality of minute straight lines), the first one region line Bj (j = 1)
Is taken out as an object of the intersection determination (F1) with the line segment Ai.

In the next step S2, the line segment Ai is changed to the line segment B.
Compute if j is crossed. In this case, the line segment Ai to be determined inside / outside and any one boundary line B of the region R
The relationship with j is five cases [1a] to [2] shown in FIG.
b]. 5 [1a] to [1
c] is a case where the line segment Ai and one area line Bj overlap at only one point (the line segment Ai passes only one point on the area line Bj). In these cases, both Ai and Bj are It is determined that "they intersect", and one point where the two Ai and Bj overlap each other is defined as an intersection C.

That is, in FIG. 5 [1a], the midpoint of the area line Bj exists on the line segment Ai as the intersection C, and the area line Bj
Intersect without being biased to the left and right of the line segment Ai. On the other hand, in FIG. 5 [1b] and [1c], the area line B is formed on the line segment Ai.
The end point of j exists as an intersection C, and in FIG. 5 [1b], the area line Bj intersects with being biased to the right of the line segment Ai, and in FIG. 5 [1c], the area line Bj is a line. It intersects in a state of being biased to the left of minute Ai.

On the other hand, as shown in FIGS. 5 [2a] and [2b],
In the case where the line segment Ai and one area line Bj do not overlap each other at only one point, it is determined that both Ai and Bj are “not crossing =“ non-crossing ””. That is, in FIG. 5 [2a], the area line Bj exists apart from the line segment Ai, and
i and Bj obviously do not intersect. Further, in FIG. 5 [2b], since the entire area line Bj overlaps with the line segment Ai, the intersection point cannot be calculated, so that both Ai and Bj
Is considered "non-crossing".

In the next step S3, step S
Based on the result of the intersection calculation at 2, the line segment Ai is the line segment Bj.
It is determined whether or not to "cross". Here, the line segment Ai,
If the relationship of Bj corresponds to the "intersection" determination reference pattern shown in FIG. 5 [1a] to [1c] and it is determined to "intersect" (S3 → YES), the process proceeds to step S4, and further, It is determined whether the line segment Bj is not biased to the left (or right) side of the line segment Ai.

When it is determined in step S4 that the line segment Bj is not biased to the left (or right) side of the line segment Ai (S4
→ YES), the process proceeds to step S5, and the point (intersection) where the line segments Ai and Bj intersect is recognized as a “true intersection” and is determined as the intersection used for the area determination (F4).
That is, of the five cases in FIG. 5, [1a] and [1b]
Only the intersections in the cases of (or [1a] and [1c]) are determined as "true intersections".

In step S3, "do not intersect =" non-cross "
"(S3 → NO)" and when it is determined in step S4 that the line segment Bj is biased to the left (or right) side of the line segment Ai (S4 → NO), " There is no true intersection. That is, in FIG. 5 [2a], [2
b) such as “non-intersection” (S3 → NO), or even if the area line Bj intersects the line segment Ai as shown in FIG. 5 [1c] (or [1b]), the line segment Ai Left side (or right side)
In the case of being biased to (S4 → NO), it is considered that there is no “true intersection”.

After the processes of steps S5 and S6, the process proceeds to step S7, and the line segment (region line) that constitutes the region R is already formed.
It is determined whether or not Bj remains. If the line segment (area line) Bj still remains (S7 → NO),
In step S8, a new line segment Bj (j ← j + 1: increment the area line number j) is taken out, and then step S8
2, the process of steps S2 to S6 is repeated for the new line segment (region line) Bj. And the area line B
When j does not remain (S7 → YES), this intersection
The intersection determination process ends.

[Example of detection of intersection] Intersection determination (F1; S2)
In, it is necessary to detect the intersection of the line segment Ai and the area line Bj. FIG. 6 is a diagram for explaining a method of calculating an intersection of a line segment and a region line according to an embodiment of the present invention.

Now, as shown in FIG. 6, the starting point Pa1 (Xa
1, Ya1) and the end point Pa2 (Xa2, Ya2), and the area line Bj that connects one end point Pb1 (Xb1, Yb1) and the other end point Pb2 (Xb2, Yb2) to a temporary intersection Pc. (Xc, Yc). Also, the x of the line segment Ai
And y-axis components are ΔXa and ΔYa, respectively, and x of the area line Bj is
, And y-axis components are ΔXb and ΔYb, respectively, from the starting point Pa1 (Xa1, Ya1) of the line segment Ai to the temporary intersection point Pc (Xc, Y
c) and the end point Pa2 (Xa2, Ya2) are LAc and LA, respectively, and the end point Pb1 (Xb) of the area line Bj.
1, Yb1) to the temporary intersection Pc (Xc, Yc) and the other end point Pb2 (Xb2, Yb2) are LBc and LB, respectively.

First, since the coordinates of the temporary intersection Pc (Xc, Yc) are the dividing points of the line segments Ai, Bj, they can be obtained by the following equations (1), (2):

[Equation 1]

Next, since the respective expressions representing Xc and Yc in the expressions (1) and (2) are equal to each other, the following expression (3) is obtained, and the transfer is followed by the expression (4):

[Equation 2]

Equation (4) can be further expanded into the following equation (5):

[Equation 3]

Here, by subtracting the lower expression from the upper expression of the expression (5), the following expression (6) is obtained:

[Equation 4]

From equation (6), the starting point P of the line segment Ai is
Temporary intersection Pc (Xc, Yc) from a1 (Xa1, Ya1)
The distance LAc to can be obtained by the following equation (7):

[Equation 5]

Therefore, the coordinate (Xc, Yc) of the temporary intersection Pc can be determined by applying the value of LAc determined by the equation (7) to the equation (1). Since the coordinates (Xc, Yc) obtained by this are virtual points, they may be on the extension of the line segments Ai, Bj. Therefore, the obtained tentative intersection Pc (Xc, Yc) is on the line segment Ai, Bj. It is necessary to judge whether it is in. To determine this, for the line segment Ai, it is necessary to determine the ratio αA of the distances LAc, LA expressed by the following equation (8):

[Equation 6]

When the ratio αA is "0" or more and "1" 1 or less (0≤αA≤1), it can be said that the line segment Ai intersects the straight line Bj. When the ratio αA is negative, (αA
<0), the straight line Bj deviates outside the starting point Pa1 of the line segment Aj, and when the ratio αA is larger than “1” (αA>
1), it is outside the end point Pa2 of the line segment Aj. However, the denominator “ΔXa × ΔY” of the equation (7) representing the distance LAc.
When b−ΔYa × ΔXb ″ becomes 0, both straight lines Ai and B
Since j does not intersect (parallel to) even on extension, calculation of the intersection is impossible (the case of FIG. 5 [2b] is one example).

As for the area line Bj, the ratio αB (αB = αB = αB = α) of the distances LBc and LB expressed in the same manner as the equation (8).
LBc / LB) is similarly determined. For example, 0 ≦ αB ≦
1 intersects the straight line Ai on the area line Bj, and when αB <0, the straight line Ai deviates outside the one end point Pb1 of the area line Bj (FIG. 5 [2a]), and when αB> 1, the straight line Ai changes. The denominator “ΔXa × ΔYb−ΔY” of the equation of the distance LBc that deviates outside the other end point Pb2 of the area line Bj and is obtained in the same manner as the equation (7).
When a × ΔXb ″ becomes 0, both straight lines Ai and Bj do not intersect (parallel) even on the extension, and therefore the intersection cannot be calculated.

That is, when 0 ≦ αA ≦ 1 and 0 ≦ αB ≦ 1, the line segment Ai and the area line Bj “cross”. In this case, when 0 <αB <1, they intersect at the midpoint of the area line Bj and are represented by, for example, FIG. 5 [1a]. Also, αB =
When it is 0, it intersects at one end point Pb1 of the area line Bj, and is represented by, for example, FIG. 5 [1b]. When αB = 1, it intersects at the other end point Pb2 of the area line Bj, for example, FIG. [1c]
It is represented by. And in other cases (αA <0,
αA> 1, αB <0, αB> 1), line segment Ai and area line B
j exist apart from each other (for example, FIG. 5 [2a]), and further, in the case of “ΔXa × ΔYb = ΔYa × ΔXb”, they do not intersect on the extension (for example, FIG. 5 [2b]). In this case, it will be "non-crossing".

[Detection Example of Which Side of Point is on Straight Line] When it is determined in the intersection determination (F1; S2) that the line segment Ai and the area line Bj intersect, the intersection determination (F2; S2) is further performed.
In 4), it is necessary to identify that the region line Bj is unevenly distributed on the left side (or right side) of the line segment Ai. Figure 7
FIG. 6 is a diagram for explaining a method of detecting a point existing side with respect to a line segment according to an embodiment of the present invention.

Now, as shown in FIG. 7, a straight line Ai and a point Pb (Xb, Yb) are arbitrarily set on the xy coordinates, and the straight line Ai is set.
Two points on i: P1 (X1, Y1), P2 (Xa2, Ya
2) and point Pb are connected by a straight line, and points P1, P2, Pb
The intersection of the straight line parallel to the y-axis passing through and the x-axis is point S1
(X1,0), S2 (X2,0), Sb (Xb, 0), the area of the trapezoid P1-S1-S2-P2 is AR0,
Area of trapezoid P1-S1-Sb-Pb is AR1, trapezoid Pb
If the area of -Sb-S2-P2 is AR2, each area A
R0 to AR2 are represented by the following equations (1) to (3): AR0 = (Y1 + Y2) * (X2-X1) / 2 (1) AR1 = (Y1 + Yb) * (Xb-X1) / 2 ... (2) AR2 = (Yb + Y2) * (X2-Xb) / 2 ... (3)

Here, by comparing the sum "AR1 + AR2" of the area AR1 and the area AR2 with the area AR0, it can be known which side of the straight line Ai the point Pb is located on. That is, the difference AR (area of the triangles P1-P2-Pb) between the area AR0 and the area "AR1 + AR2" is calculated by the equation (1).
From (3) to (3), the difference ΔAR
The existence side can be discriminated by the value of: ΔAR = AR0- (AR1 + AR2) (4) [1] When ΔAR <0, the point Pb is on the left side of the straight line Ai, and [2] ΔAR = 0 Sometimes point Pb is straight line A
On the i, and [3] ΔAR> 0, it means that the point Pb is on the right side of the straight line Ai.

Therefore, in the intersection determination (F2; S4), when it is determined that the area line Bj is unevenly distributed on the left side (or right side) of the line segment Ai, for example, the area line Bj is 2
One of the end points Pb1 and Pb2 is the intersection P with the line segment Ai.
When it is determined to intersect with c, the start and end points Pa1 and Pa2 of the line segment Ai are set to the points P1 and P2 in FIG. 7, and the other end point of the area line Bj is treated as the point Pb in FIG. The existence side may be determined by the value of the difference AR.

[Example of Area Discrimination] FIG. 8 shows an example of area discrimination according to an embodiment of the present invention. An outline of the area discrimination according to the present invention will be described with reference to FIG. In the present invention, the line segment A passing through the closed region R formed by the plurality of region lines Bj
The area “inside” or “outside” of the area i is determined. First, the intersections and intersections of the line segment Ai and each area line Bj are determined. For example, as shown in FIG. 8 [2] (c), when the line segment Ai intersects at the midpoint of the area lines B1 and B4, the midpoint is changed to “true intersection” “1” and “2”. As shown in FIG. 8 [1], when Ai intersects the end points of the area lines B1 and B7 and these area lines B1 and B7 are unevenly distributed on the right side of the line segment Ai, the end points are set to “true”. It is decided that the intersection is "1" or "2". Then, the "true intersections" are sorted in order from the starting point of the line segment Ai, and the "inside" and "outside" area determinations are sequentially output alternately based on the sorted "true intersections" column.

Hereinafter, each example of FIG. 8 will be described in more detail. In FIG. 8, when it is determined that the line segment Ai intersects at the end points of the region line Bj, the region line Bj indicates the line segment Ai.
When it is biased to the right of i, the intersection is determined to be a "true intersection" effective for area determination. It should be noted that in FIG. 8, the circles represent the intersections, and the circles with numbers represent the "true intersections". Also, the numbers in circles are explanatory numbers for convenience, which are used to represent the appearance (encounter) order of "true intersections" for each line segment Ai, and are in the same order (same coordinate points).
When there are a plurality of "true intersections", the different numbers appear (encounter) at the same coordinate point, and the positions are shown differently.

In one embodiment of the present invention, in order to determine the area of the line segment Ai with respect to a certain closed region R, the line segment Ai is used.
The line segment number i of is sequentially incremented from "1"("+
1 ”), and for each line segment Ai,“ true intersection ”of RAM
According to the principle of FIG. 3, while referring to the “true intersection” column stored in the list buffer, the area determination is performed every time the “true intersection” with the plurality of area lines Bj forming the closed area R appears. Go forward. In the example of FIG. 8 [1], in particular, among the plurality of region lines Bj (j = 1 to 12) forming the closed region R, some of the region lines Bj (j = 2, 6, ...) Overlap. The case where the line segment Ai passes will be described by taking it as an example.

In FIG. 8, for a certain line segment Ai, R
When it is confirmed that the left end start point is not the "true intersection" by referring to the "true intersection" column in the "true intersection" list buffer in AM, the start point is determined to be the area "outside", and thereafter,
The area “outside” determination is maintained until the “true intersection” appears by moving rightward through the coordinate points on the line segment Ai while referring to the “true intersection” column.

When the coordinate point of the line segment Ai is advanced, a "true intersection" with the line segment B1 represented by an odd number "1" appears, so that the region is determined to be "inside" from this point. Switch. That is, since the line segment Ai intersects the end point of the area line B1, and the area line B1 is biased to the right side of the line segment Ai, the "true intersection point" of the number "1" is followed by the "true intersection point". It is determined to be inside the region R until is detected.

Here, the "true intersection" with the first area line B1 having the number "1" coincides with one end of the second area line B2, but the area line B2 overlaps the line segment Ai. , Area line B
The information about 2 is not used (disregarded) in the area determination, and the determination “inside” the area cannot be switched. Next, the other end of the area line B2 is the intersection of the line segment Ai and the third area line B3, and at this point the line segment Ai intersects the end point of the area line B3, but the area line B3 is the line segment Ai. Since it is biased to the left of
The intersection information with the area line B3 is not used for the area determination, and the area "inside" determination remains maintained.

Further, the line segment Ai intersects with the end point of the fifth region line B5, but since the region line B5 is biased to the left side of the line segment Ai, the region determination is not made at this point, and the region determination is still made. It remains “inside” the area. Further, the intersection with the area line B5 coincides with one end of the sixth area line B6, but since the entire area line B6 overlaps the line segment Ai, the area determination is not made and the area determination is switched again. I can't.

When the "true intersection" with the area line B7 represented by the even number "2" appears further rightward on the line segment Ai, the area is "outside" at this point. Switch judgment. That is, since the line segment Ai intersects the end point of the region line B7, and the region line B7 is biased to the right side of the line segment Ai, the “outer” of the region R from the “true intersection” of the number “2”. It is determined that Then, since the "true intersection" does not appear on the line segment Ai thereafter, the area "outside" determination is maintained.

Regarding the painting processing, from the point where the inside / outside determination of the area is switched, it is determined whether or not the painting is performed based on the determination result. For example, in the area discrimination example regarding the line segment Ai of FIG. 8 [1], the filling is started from the “true intersection” of the number “1” which intersects the end point of the first area line B1 with a bias toward the right. Since it overlaps with the line segment A on the second area line B2, it is ignored if it is not an intersection and the filling is continued, and the area lines B3 and B5 are leftward even at the intersection with the third and fifth area lines B3 and B5. If it is biased, it will be ignored and the painting will continue, and also on the sixth area line B6, the line segment A
Since it is overlapped with, it will be ignored if it is not an intersection and the painting will continue, but it will reach the "true intersection" of the number "2" that intersects the end point of the 7th area line B7 of the number "2" with a bias to the right. Then, the painting is stopped, and thereafter, the painting stopped state is maintained.

Now, when the line segment Ai described above is sequentially updated and the line segment number i is incremented by m (“+ m”), the “line segment Ai +” at the bottom of FIG.
In the case of the position state shown by "m", the line segment Ai is particularly expressed by "line segment Ai + m" to supplement the description.

In this case, the line segment Ai + m reaches the intersection with the other end of the first region line B1 after it is determined as the region "outside" at the left end start point, but the region line B1 is to the left of the line segment Ai + m. Since they are biased, the intersection with the area line B1 is ignored rather than the “true intersection”. Further, the intersection with the area line B1 coincides with one end of the twelfth area line B12, but the area line B12 is the line segment A.
Since it overlaps i, it is ignored and the area determination cannot be switched.

After that, the line segment Ai + m becomes an odd number "1".
When the "true intersection" with the eleventh area line B11 represented by is encountered, the area determination is switched to the area "inside" at this point "1", and then with the ninth area line B9 with the even number "2". When the "true intersection" is encountered, the determination is switched to the area "outside" at this point "2". That is, at the points “1” and “2”, the line segment Ai + m intersects the end points of the region lines B11, B9, and the region lines B11, B9 are biased to the right of the line segment Ai + m. Switching from "→" inside "and" inside "→" outside ".

Next, the "true intersection""2" is one end of the eighth area line B8, but since the area line B8 overlaps the line segment Ai + m, it is ignored and the area determination cannot be switched. Then, although it intersects with the other end of the seventh area line B7, it is ignored because the area line B7 is biased to the left side of the line segment Ai + 1, and the area determination is not switched until the end point (right end) of the line segment Ai + 1 is reached. , The determination of “outside” the area is maintained.

The line segment Ai is the fourth region line B of the closed region R.
4 (not shown), the "true intersections""1" and "2" with the third and fifth area lines B3 and B5 appear at the left and right ends of the area line B4. , "Outside" as in the "true intersections""1" and "2" between the line segment Ai and the first and seventh area lines B1 and B7, respectively.
It can be switched from "inside" and "inside" to "outside".

When the line segment Ai overlaps the entire tenth area line B10 (not shown), the left and right end positions of the area line B10 intersect with the other ends of the eleventh and ninth area lines B11, B9. However, since the area lines B11 and B9 are biased to the left of the line segment Ai, the above-mentioned “line segment Ai + m” and the first line
Similarly to the intersection with the other end of the seventh area line, the area determination is not switched at all, and the area is initially determined to be “outside”.

In FIG. 8 [1], as described above, the line segment Ai is the fourth area line B4, and the second and sixth area lines B2.
B6, the twelfth and eighth area lines B12, B8, and the tenth area line B10 are all overlapped with each other, as shown in FIG. , The area determination is switched every time the line segment Ai passes through this point.

In the area discrimination according to the embodiment of the present invention, the vertices of a certain closed area (closed figure), that is, the adjacent area lines Bj and Bj + 1 among the area lines Bj forming the closed area.
It is also effective when the line segment Ai passes through the end points connected to each other at. The example of FIG. 8 [2] is
The case where the line segment Ai passes over the apex of the area will be described.

In the example of FIG. 8 [2] (a), after the area “outside” is set at the left end of the line segment Ai, when the line segment Ai proceeds to the right, two adjacently joined region lines are formed. It intersects with each end point of B1 and B2 at the same coordinate point. At these intersections, since both the area lines B1 and B2 are biased to the right of the line segment Ai, the intersection point of the line segment Ai and the area line B1 and the area line B2 is
Both are “true intersections” and can be represented by the numbers “1” and “2”, for example.

In this case, referring to the "true intersection" column, the "true intersection" data "1" with the area line B1 is first taken out, and even if it is determined to switch to the "inside" area, the same result is obtained. At the coordinate point, the "true intersection" data "2" with the area line B2 is taken out, and the determination is immediately switched to the area "outside", and the inside / outside determination result at the coordinate point is the area "outside". "Keep it.

FIGS. 8B, 8C, and 8C are other examples when entering or advancing from the apex of the closed area or passing over the apex of the closed area. In this specification, a closed region (closed figure) having an apex angle of 180 ° or more as in these examples.
In particular, the vertex of is called "the contact point of the area line" (the bending point of the closed figure may be more appropriate).

In the example of FIG. 8 [2] (b), when the area “outside” is set at the left end of the line segment Ai, and when the line segment Ai proceeds to the right, two adjacent region lines B1 and B2 are formed. Intersect with each end point of the same coordinate point. Of these intersections, the area line B1
Is biased to the right of the line segment Ai, the intersection of the line segment Ai and the area line B1 is the "true intersection" represented by the odd number "1", but the area line B2 is to the left of the line segment Ai. Since they are biased, the intersection of the line segment Ai and the area line B1 is ignored and not used for area determination. Therefore, at the "true intersection" of the number "1", the area "outside" → "inside" is switched.

Then, after the line segment Ai enters the area,
It intersects at the midpoint of the area line B4. Since this point is the "true intersection" with the area line B4 represented by the even number "2", the area determination is switched from "inside" to "outside" and thereafter the area "outside" determination is maintained. .

In the example of FIG. 8 [2] (c), after the area “outside” is set at the left end of the line segment Ai, when the vehicle moves rightward on the line segment Ai, it intersects with the intermediate point of the region line B1. . Since this coordinate point is the "true intersection" represented by the odd number "1", it is determined here that the area is switched from "outside" to "inside".

Next, the line segment Ai indicates the adjacent area lines B2 and B3.
Intersect with each end point of the same coordinate point. At these intersections,
Since both the area lines B2 and B3 are biased to the left of the line segment Ai, any intersection with the line segment Ai is not used for the area determination and is ignored. The "inside" region determination is maintained. And
When it intersects with the middle point of the area line B4, this intersection is the "true intersection" of the even number "2". Therefore, the area determination is switched from the area "inside" to the "outside" here, and then the area "outside" Keep the judgment of ".

As described in these discrimination examples, by discriminating the inside and outside of the region by referring to the "true intersection" list according to the embodiment of the present invention, it is possible to construct a complicated shape with a large number of region lines. Even if the area is defined, the inside / outside judgment based on the order of “outside” → “inside” → “outside” → “inside” → “outside” does not get out of order and realizes accurate area determination. be able to.

[0070]

As described above, according to the present invention, when the line segments intersect at the midpoint of the area line, the midpoint is determined as the intersection ("true intersection") and the line segment is determined. Crosses at the end points of the area line and the area line is unevenly distributed on the right or left side of the line segment, the end points are determined as intersections (“true intersections”) and these intersections (“true intersections”) are determined. ) Are sorted in order from the starting point of the line segment Ai, and the area determination between the inside and the outside of the closed area is alternately output based on the sorted intersection row (the "true intersection" row). Therefore, even if the line segments pass over the area line or pass over the apex of the closed area or the contact point of the area line in a short time with a simple configuration, it is possible to reliably and reliably It is possible to make a distinction.

[Brief description of drawings]

FIG. 1 is a schematic hardware configuration block diagram of a graphic information processing system having a region discriminating function according to an embodiment of the present invention.

FIG. 2 is a schematic functional block diagram showing an outline of a procedure of painting processing according to an embodiment of the present invention.

FIG. 3 is a diagram for explaining the principle of inside / outside determination used for area determination according to an embodiment of the present invention.

FIG. 4 is a flowchart showing a processing procedure of intersection / intersection determination according to an embodiment of the present invention.

FIG. 5 is a diagram for explaining intersection determination according to an embodiment of the present invention.

FIG. 6 is a diagram for explaining a method of calculating an intersection of a line segment and a region line according to an embodiment of the present invention.

FIG. 7 is a diagram for explaining a method of detecting a point existing side with respect to a line segment according to an embodiment of the present invention.

FIG. 8 is a diagram showing an example of area discrimination according to an embodiment of the present invention.

[Explanation of symbols]

Ai, Ai + m (i, m = 1, 2, ...) Drawing (display /
A line segment representing a scanning line or a drawing line for printing), Bj (j = 1, 2, ...) A region line forming a closed region (closed figure) R, Pa1, Pa2; P1, P2 on the line segment Ai Point, Pb1, Pb2; Point on Pb line segment Bj, C, Pc Intersection point of line segment Ai and line segment Bj.

Claims (2)

[Claims] 1. An area discriminating apparatus which discriminates a line segment passing through a closed region composed of a plurality of region lines, which region is inside or outside the closed region, wherein the line segment is a region. Detecting that they intersect at the midpoint of the line,
Means for determining the intermediate point as an intersection, and detecting that the line segment intersects at the end point of the region line and the region line is unevenly distributed on the right or left side of the line segment, and determines the end point as the intersection point. The means and the determined intersections are sorted in order from the starting point of the line segment,
A means for generating a sequence of intersections, and means for alternately outputting region determinations indicating that the region is inside the closed region and the region that is outside the closed region based on the generated sequence of intersections. Characteristic area discrimination device. 2. A graphic information processing apparatus for discriminating a region, which is inside or outside a closed region, of a line segment passing through a closed region composed of a plurality of region lines, Detect the intersection at the midpoint of the area line,
The step of determining the intermediate point as an intersection, and detecting that the line segment intersects at the end point of the area line and the area line is unevenly distributed on the right or left side of the line segment, and determines the end point as the intersection point. Steps, sorting the determined intersections in ascending order from the starting point of the line segment, generating a sequence of intersections, and, based on the generated sequence of intersections, the fact that it is inside the closed region and outside the closed region. The area discrimination program for executing the procedure consisting of the step of alternately outputting the area determination that ".