JP3988945B2 - GRAPHIC DATA PROCESSING METHOD, GRAPHIC DATA PROCESSING PROGRAM, AND RECORDING MEDIUM CONTAINING THE PROGRAM - Google Patents

Description

  The present invention relates to a graphic data processing method for displaying a planar area as a polygon, and more particularly to a graphic data processing method for correcting graphic data used in a geographic information system.

In the shape file format widely adopted as a data format used in the geographic information system, for example, a plane area having an enclave or a hole such as a municipal area is represented by a plurality of polygons according to the following rules.
(1) The polygon must not self-intersect.
(2) The polygons should not intersect. You may touch at the apex, but you must not share the edge.
(3) The right side with respect to the direction of the vertex row of the polygon shall be the inside of the plane area that the polygon intends to express.
(4) The polygon is closed. In other words, the start point and end point of the polygonal vertex row have the same coordinate value.

However, data used in geographic information systems is often created by manually reading from a map using a digitizer, etc., and it is difficult to follow the above rules completely in detail. Data that does not comply may be mixed. And even if there is a small amount of data that does not comply with the rules, the geographic information system may not be able to handle it properly, and it does not comply with the rules from a large amount of data. There is a problem that a great deal of labor is required to detect and correct the portion.
Japanese Patent Laid-Open No. 61-180378 Japanese Patent Laid-Open No. 10-154237 Japanese Patent Laid-Open No. 10-21367

  The present invention relates to a graphic data processing method that automatically corrects data representing a planar area created for the purpose of performing processing such as display and processing by a geographic information system when there is a portion that does not comply with the above rules. Is intended to provide.

In the present invention, a polygon is represented by an array of vertex data consisting of x-coordinate values and y-coordinate values (hereinafter referred to as “vertex row”), and data in such a form that a plurality of polygons constitute one plane area is given. If so, the following processing is performed on the data of one plane area.
(1) Self-intersecting polygon division processing Among polygons constituting the plane area, a polygon having a self-intersection or a self-contact (hereinafter referred to as “cut point”) is divided into a plurality of polygons at the cut point. FIG. 18A shows a state before performing the self-intersecting polygon division processing, and FIG. 18B shows a state after performing the self-intersecting polygon division processing.
(2) Deduplication processing of multiple polygons Among the polygons constituting the plane area, when multiple polygons intersect and overlap at a part of the area (including the case where a part of the side is shared, the same applies hereinafter) ), The plurality of polygons are converted into a plurality of non-overlapping polygons. Specifically, the following three processes are included. (A) Unify the directions of all vertex rows. (B) Search for an intersection or contact between two polygons (hereinafter referred to as “intersection etc.”). (C) Two overlapping polygons are converted into a plurality of polygons. A necessary one is selected from the plurality of polygons thus obtained. FIG. 19A shows the state before the multi-polygon deduplication processing is performed, and FIG. 19B shows the state after the multi-polygon deduplication processing is performed.
(3) Nested polygon vertex row direction adjustment processing When multiple polygons are nested among the polygons constituting the plane area, the direction of the vertex row of the outermost polygon is turned clockwise. The direction of the vertex row of the inner polygon is set to be opposite to the direction of the vertex row of the immediately outer polygon. FIG. 20A shows a state before the vertex row direction adjustment processing is performed, and FIG. 20B shows a state after the vertex row direction adjustment processing is performed.
(4) Post-processing A vertex having the same coordinate value as the start point of the vertex row is added to the end points of the vertex rows of all polygons constituting the plane area.

  The above-described series of processing is performed on the data of all planar areas, and the processed data is stored in an external storage medium.

According to the present invention, irregular portions included in the data representing the planar area are automatically and easily corrected, so that processing such as display and processing can be normally performed by the geographic information system.
According to the present invention, when creating data using a digitizer or the like, rules can be created without much concern, and efficiency can be improved by omitting confirmation work.

  FIG. 1 is a block diagram of a circuit for executing the graphic data processing method according to the present invention. The apparatus of this example includes a CPU 11, a ROM 12, a RAM 13, and an input / output I / F circuit 14, which are connected to each other via an internal bus 15 and can communicate data with each other. The CPU 11 controls the entire apparatus. Each processing method constituting the present invention is stored in the ROM 12 in the form of a program, and the RAM 13 stores data used by each processing method. The input / output I / F circuit 14 is connected to the external storage device 16. The apparatus of this example receives data from the external storage medium via the external storage device 16 and outputs data processed by the apparatus of this example to the external storage medium.

  FIG. 2 shows the entire procedure of graphic data processing by this apparatus. First, in step S10, data is read from the external storage medium and stored in the RAM 13. In step S11, it is determined whether the processing has been completed for all the plane area data. If not, the data is extracted from the data stored in the RAM 13 in units of the plane area in step S20. . In step S21, self-intersecting polygon division processing is performed. In step S22, multiple polygon deduplication processing is performed. In step S23, nested polygon vertex row direction adjustment processing is performed. In step S24. And post-processing. If it is determined in step S11 that these processes have been completed for all plane area data, the processed data is stored in an external storage medium in step S30.

Hereinafter, the graphic data processing method in the present invention will be described in detail.
(1) Self-intersecting polygon division processing Japanese Patent Application Laid-Open No. 10-154237 proposes a method of dividing a self-intersecting polygon at a self-intersection for a polygon convex in the y-axis direction. However, since the polygon targeted by the present invention is an object to be processed by the geographic information system and is a general polygon with no constraint on the shape, the method of Japanese Patent Laid-Open No. 10-154237 cannot be applied.

  With reference to FIG. 3, the outline of the self-intersecting polygon division processing according to the present invention will be described. In the polygon of FIG. 3A, the vertex p1 is in contact with the side p3p4, and the side p3p4 and the side p5p0 intersect. FIG. 3 (b) shows the positions of the self-contact as c1 and the self-intersection as c2. First, the coordinate value of the contact c1 (in this case, equal to the coordinate value of the vertex p1) and the coordinate value of the intersection c2 are obtained. A vertex having the same coordinate value is inserted into each of the sides where the contact point c1 and the intersection point c2 exist. That is, a vertex equal to the coordinate value of the contact c1 and a vertex equal to the coordinate value of the intersection c2 are inserted into the side p3p4, and a vertex equal to the coordinate value of the intersection c2 is inserted into the side p5p0. Hereinafter, the contact points and intersections are referred to as cut points.

  FIG. 3 (c) shows the result of inserting vertices in the original polygon and renumbering them. In the polygon vertex row after such processing, there are two or more vertices equal to the coordinate value for each cut point.

  Next, when the combination of two vertices of this polygon is examined in order from the smallest number, it is found that the coordinate values of the vertices p1 and p4 are equal, that is, they are equal to the cut point. Therefore, if the polygon is divided into two at the cut points p1 and p4, the two polygons shown in FIGS. 3 (d) and 3 (e) are obtained. Further, the vertex numbers in FIG. 3 (d) are re-assigned to FIG. 3 (f). In FIG. 3 (f), if the combination of two vertices is examined in the same manner, it is found that the vertices p2 and p5 are equal to the cut point, so if the polygon is divided into two there, FIG. 3 (g) and FIG. Two polygons of (h) are obtained.

  As described above, the division method proposed by the present invention inserts a vertex that is equal to the cut point into the target polygon, and then searches for two vertices having the same coordinate value in the vertex row and the vertex row at the vertex. By repeating the above two divisions by recursive processing, it is possible to divide even when there are a plurality of cut points.

Hereinafter, a specific processing procedure for realizing this method will be described.
(1-1) If a plurality of consecutive vertices in the vertex row are equal, only one of them is left and the others are deleted.
As can be seen from the above description, in the dividing method according to the present invention, when the coordinate values of two vertices are equal, it is determined that the cut point is a cut point. If the coordinate values (including the combination of the end point and the start point of the vertex row, and so on) are equal, it cannot be determined correctly.

  Therefore, as a pre-processing, when multiple consecutive vertices in the vertex row are equal, in advance, only one of them is deleted and the others are deleted, so that the two consecutive vertices are converted into a non-overlapping vertex row. .

(1-2) A cut point is searched, and a vertex equal to the coordinate value of the searched cut point is inserted into a corresponding portion of the vertex row.
For all combinations of two sides of the polygon, the cut point is searched by checking whether the two sides intersect or whether the end point of one side is on the other side. If there is a cut point, a vertex equal to the coordinate value of the cut point is inserted into the corresponding portion of the vertex row.

  With reference to FIG.4 and FIG.5, the procedure of the process of searching a cut point and inserting the vertex equal to a cut point into a vertex row | line | column is demonstrated. In step S400, a polygon vertex row {p0, p1,..., Pn-1} is selected. In step S401, an associative container M for temporarily storing information on the insertion position of the vertex to be inserted into the vertex row and its coordinate value is prepared.

  The key of the associative container M is the vertex number immediately before the position at which the vertex is inserted as information on the vertex insertion position. The data stored in the associative container M is a set of vertices to be inserted at the position. M [i] represents a set of vertices to be inserted between the points pi and pi + 1, and M [j] represents a set of vertices to be inserted between the points pj and pj + 1.

  Steps S401 to S412 and steps S420 to S426 are cut point search processing. In steps S402 to S406, n vertices are processed one by one, and it is determined whether the processing has been completed for all vertices. If the processing has not been completed for all vertices, the process proceeds to step S407.

In step S407, it is determined whether the slopes of ei and ej are equal. ei is a side whose end points are vertices pi and pi + 1, and ej is a side whose end points are vertices pj and pj + 1 (p0 when j = n-1).
If the slopes of the side ei and ej are equal, the process proceeds to steps S408 to S412. If the slopes of the side ei and side ej are not equal, the process proceeds to steps S420 to S426.

  In steps S408 to S412, if the side ei and the side ej are in the same line and the vertex pj is on the side ei, a vertex equal to the vertex pj is added to M [i], and the vertex pi is the side If it is on ej, add a vertex equal to vertex pi to M [j]. In steps S420 to S423, if the slopes of the side ei and the side ej are not the same and the vertex pj is on the side ei, a vertex equal to the vertex pj is added to M [i], and the vertex pi is a side. If it is on ej, add a vertex equal to vertex pi to M [j]. In steps S424 and S425, when the side ei and the side ej intersect, a vertex equal to the intersection of the side ei and the side ej is added to M [i] and M [j].

  Please refer to FIG. Steps S4300 to S4304 are processes for inserting a vertex equal to the cut point into the vertex row. In step S4301, it is determined whether processing has been completed for all data stored in the associative container M. If processing has not been completed for all data, the process advances to step S4302 to determine whether vertex data is stored in M [i]. If the vertex data is stored in M [i] (not empty), the process proceeds to step S4304, and the vertex data stored in M [i] between the vertices pi and pi + 1 is converted to the vertex pi. Insert in ascending order of distance from.

(1-3) Divide the polygon at the cut points.
The cut point is searched from the polygon after the above processing is performed, and when the cut point exists, the polygon is divided there. The cut point is searched by checking whether there are two or more vertices having the same coordinate value in the vertex row. A procedure for dividing a polygon using this will be described with reference to the flowchart of FIG.

  With reference to FIG. 6, a procedure for searching for a cut point from a polygon and dividing the polygon will be described. In step S500, a polygon vertex row V0 {p0, p1,..., Pn-1} is selected. In steps S501 to S508, processing for checking whether there are two vertices having the same coordinate value is sequentially performed on the n vertices, and it is determined whether the processing has been completed for all the vertices. If two vertices pi and pj having the same coordinate value are found in step S507, it can be determined that they are vertices equal to the cut point, and the process proceeds to step S510. If two vertices having the same coordinate value are not found, the process proceeds to step S509, where it is determined that there is no cut point in the polygon, the vertex row V0 is added to the updated data, and the process ends. Here, the post-update data is to store and hold the processed vertex string data until the division process is completed for all the vertex strings representing the planar area.

  In step S510, the partial vertex sequence {p0, ..., pi-1} from the start point p0 of the vertex sequence V0 to the vertex pi-1 immediately before pi, and the end point pn-1 of the vertex sequence V0 starting from pj Create a vertex sequence {p0, ..., pi-1, pj, ..., pn-1} by connecting the partial vertex sequences {pj, ..., pn-1} up to V1 , Let V2 be a partial vertex sequence {pi, ..., pj-1} from the vertex pi to the vertex pj-1 immediately before pj. These are polygonal vertex rows obtained by dividing the vertex row V0 into two by the cut points pi and pj.

  In steps S511 and S512, the vertex rows V1 and V2 created in this way are read as vertex rows V0, respectively. Next, by repeating the process of FIG. 6, the division into two is repeated until there are no more cut points. When the recursion process is completed, the vertex sequences of the polygons divided at all the cut points are updated. Stored in the data.

  The process of step S501 will be described. When two continuous sides overlap in the polygon before processing on the same straight line, the overlapping part is separated in the process of the above processing, and a vertex sequence consisting of only two vertices at both ends is generated. Since this is a line segment with no area and is unnecessary as data representing a plane area, in step S501, if the number of vertices in the divided vertex row is less than 3, it is excluded by not storing.

  (1-4) By applying the processes (1-1) to (1-3) above to all vertex sequences in the original planar area data, it is converted into a plurality of polygon vertex sequences that do not self-intersect. Since the data is stored as updated data, the original plane area data is finally replaced with the updated data.

(2) Deduplication processing for multiple polygons
To eliminate the overlap of two polygons, you can convert them to multiple polygons. As such a polygon conversion method, a method by vertex tracking is conventionally known. A method using vertex tracking will be described with reference to FIG. For example, when two polygons A and B in FIG. 7 (a) overlap as shown in FIG. 7 (b), those vertex rows are reorganized and shown in FIGS. 7 (c) to 7 (e). It is necessary to convert them into a plurality of polygons, and use what is necessary according to the purpose.

  First, as shown in FIG. 7B, the directions of the vertex rows of the polygons A and B are unified clockwise, and the intersection points p1, p2, p3, and p4 of the polygons A and B are obtained. Next, the vertex line of polygon A is traced according to the direction from intersection point p1 as the starting point.When another intersection point p4 is reached, the vertex line of polygon B is changed in the same manner, and when returning to starting point p1, As shown in FIG. 7 (c), a polygon is obtained that surrounds an area obtained by combining the areas of polygons A and B (hereinafter referred to as “combined area”).

  In this way, the vertex line of polygon A is traced starting from a certain intersection, and when another intersection is reached, it is transferred to the vertex line of polygon B, and when the next intersection is reached, that is the starting point. If not, change to the vertex row of polygon A again and follow the vertex row. In this way, the procedure of creating a polygon by alternately switching the vertex rows of polygons A and B at the intersection and returning to the starting point is followed by tracing all the sides of polygons A and B once. Can be converted into a plurality of polygons. These polygons are the clockwise ones shown in FIG. 7 (c), the largest one enclosing the combined area of polygons A and B, and the other clockwise ones shown in FIG. 7 (d) are polygons. A polygon surrounding a region where A and B overlap (hereinafter referred to as “overlapping region”), and a counterclockwise region shown in FIG. Can be classified into polygons surrounding a hole area). Of course, depending on the positional relationship between the polygons A and B, the hole region may not be generated. One or a plurality of polygons are selected as necessary from the plurality of polygons thus obtained.

  When the directions of the vertex rows of the polygons A and B are both counterclockwise, the orientation of the vertex rows in the classification is reversed for the polygons generated by the same procedure as described above. The same result will be obtained if it is read.

  In the multi-polygon deduplication processing in the present invention, by this vertex row tracking method, among the plurality of polygons representing one plane area, the overlapping polygons are converted into a polygon surrounding the combined area and a polygon surrounding the hole area. Perform the conversion process. A specific processing procedure will be described below.

(2-1) Vertex row direction determination processing and vertex row direction unification processing As is clear from the above description, in order to obtain the expected result by the vertex tracking method, the direction of the vertex row of the target polygon is It must be unified either clockwise or counterclockwise. Therefore, as a pre-processing, first, the direction of all the vertex rows constituting the planar area is determined, and the vertex row order is reversed for the vertex rows that are determined to be counterclockwise. Unify the direction of.

  Conventionally, as a method of determining the direction of a polygonal vertex row, a method of calculating the outer product of vectors and determining the direction based on the sign of the outer product is known. In this method, first, select one of the vertices with the smallest x coordinate value, the vertex with the largest x coordinate value, the vertex with the smallest y coordinate value, and the vertex with the largest y coordinate value (referred to as p2). Then, the vertex immediately before vertex p2 (referred to as p1) and the vertex immediately subsequent to vertex (referred to as p3) in the vertex row are selected. Next, the cross product G of the vectors p2p1 and p2p3 is calculated, and the sign of the cross product G is determined.

  Specifically, for polygons in a coordinate system in which the positive x-axis direction is right and the positive y-axis direction is upward, the coordinate values of the vertices p1, p2, and p3 selected as described above are (x1, If y1), (x2, y2), and (x3, y3), the outer product G is obtained by Equation 1, and if the outer product G is positive, the direction of the vertex row of the polygon is clockwise, and if it is negative, it is counterclockwise It can be determined to be clockwise.

  G = p2p1 × p2p3 = (x1 − x2) × (y3 − y2) − (y1 − y2) × (x3 − x2) (Equation 1)

  However, this method has a problem that it cannot be determined when the outer product G becomes zero. In general, the cross product of vectors p2p1 and p2p3 is 0 when points p1, p2, and p3 are all on the same straight line (including the case where any two or three points are equal). . Here, assuming that the points p1, p2, and p3 are the vertices of the polygon after the above-described self-intersecting polygon division processing, the three points p1, p2, and p3 are not equal to each other. Also, it is guaranteed that side p1p2 and side p2p3 do not overlap. In determining the direction of the vertex row, if the vertex having the smallest x coordinate value is p2, the immediately preceding vertex is p1, and the immediately following vertex is p3, the x coordinate value of the point p2 is the points p1 and p3 It cannot be larger than the x coordinate value of. Therefore, here, assuming that the calculation result of the outer product is 0, the three points p1, p2, and p3 are arranged in the order of {p1, p2, p3} or {p3, p2, p1} on the straight line parallel to the y-axis. You only need to consider the case. From the above consideration, it is found that this problem can be solved by an elementary geometric method.

  With reference to FIG. 8, a procedure for determining the direction of the vertex row of the polygon and changing it in the clockwise direction when it is counterclockwise will be described. In step S700, a polygon vertex row V0 is prepared. In step S701, a vertex p2 having the smallest x coordinate value is selected from the polygon vertex row, and in step S702, the immediately preceding vertex p1 and the immediately following vertex p3 in the vertex row are selected. In step S703, the outer product G of the vectors p2p1 and p2p3 is calculated. In steps S704 to S707, if the outer product G is non-zero, the determination is performed by the conventional method. That is, if the outer product G is positive, it is determined to be clockwise, and if the outer product G is negative, it is determined to be counterclockwise. When the outer product G is 0, it can be determined from the above consideration that the vertex rows {p1, p2, p3} or {p3, p2, p1} are arranged in the order on the same straight line parallel to the y axis. Accordingly, in step S706, the y coordinate value of the vertex p3 is compared with the y coordinate value of the vertex p2. If the y coordinate value of the vertex p3 is larger than the y coordinate value of the vertex p2, it can be determined that the direction of the vertex row of the polygon is clockwise, and if it is smaller, it is counterclockwise. It goes without saying that the same determination can be made by comparing the y-coordinate values of the vertex p2 and the vertex p1. If it is counterclockwise, the order of the polygonal vertex row is reversed in step S707.

(2-2) Search for intersections between two polygons and insert vertices.
Next, the vertex rows Va and Vb of the two polygons A and B are extracted from the plane area data, and an intersection or contact point (hereinafter referred to as “intersection or the like”) between the two polygons A and B is searched. It is examined whether all combinations of the sides of the two polygons A and B intersect or whether the end point of one side is on the other side. If there is an intersection or the like, a vertex equal to the intersection or the like is inserted into the corresponding portion of the vertex rows Va and Vb.

  With reference to FIG. 9 and FIG. 10, a procedure for searching for an intersection between two polygons and inserting a vertex will be described. In step S800, two polygon vertex rows Va {pa0, pa1, ..., pana-1} and Vb {pb0, pb1, ..., pbnb-1} are selected. The vertex rows Va and Vb represent polygons A and B having na and nb vertices, respectively. In step S801, associative containers Ma and Mb for temporarily storing information on the insertion positions of the vertices to be inserted into the vertex rows Va and Vb and their coordinate values are prepared.

The keys of the associative containers Ma and Mb are the number of the vertex immediately before the position where the vertex is inserted, as information on the insertion position of the vertex. The data stored in the associative containers Ma and Mb is a set of vertices to be inserted at the positions.
Ma [i] represents a set of vertices to be inserted between the points pai and pai + 1, and Mb [j] represents a set of vertices to be inserted between the points pbj and pbj + 1.

  Steps S802 to S812 and steps S820 to S826 are search processing for intersections and the like. These processes are the same as steps S402 to S412 and S420 to S426 in FIG. 4. In the example of FIG. 4, the cut points in the same polygon are searched. However, in the example of FIG. The point of searching for intersections between polygons is different. Therefore, in this example, ei is the side of the polygon A whose endpoints are the points pai and pai + 1 (pa0 when i = na-1), and ej is the points pbj and pbj + 1 (j = nb-1 Is the side of polygon B whose end point is pb0).

  Please refer to FIG. Steps S8300 to S8304 and steps S8400 to S8404 are processes for inserting vertices that are equal to intersections or the like into the vertex row. In step S8304, the vertex data stored in Ma [i] is inserted between the vertices pai and pai + 1 of the vertex row Va in ascending order of the distance from the vertex pai. In step S8404, the vertex data stored in Mb [j] is inserted between the vertices pbj and pbj + 1 of the vertex row Vb in ascending order of the distance from the vertex pbj.

  By performing this process for all combinations of vertex rows that make up the planar area, if there are intersections between any two polygons, both of the two polygons must be equal to the intersections, etc. Will have vertices.

  (2-3) After performing the above processing, extract the vertex sequence representing the two overlapping polygons from the planar area data, and enclose the polygon and hole area surrounding the combined area by the method of vertex tracking described above. By repeating the process of converting to polygons and updating the plane area data until there is no overlap in all combinations of vertex rows belonging to the updated plane area data, the overlapping of the polygons in the plane area data is repeated. Eliminate.

  With reference to FIG. 11, the procedure for eliminating the overlapping of a plurality of polygons will be described. In step S900, a set {V0, V1,..., Vn-1} of n vertex rows is prepared as plane area data. In steps S901 to S907, whether or not the two polygons represented by the two vertex rows overlap each other is sequentially performed on the n vertex rows, and the processing is completed for all the vertex rows. Determine. If it is determined in step S905 that the two polygons represented by the two vertex rows Vi and Vj overlap, the process proceeds to step S908.

  In step S908, a copy Va of the vertex row Vi and a copy Vb of the vertex row Vj are created, and the vertex rows Vi and Vj are deleted from the plane area data. In step S909, the vertex rows Va and Vb are converted into a polygon surrounding the combined region and a polygon surrounding the hole region by the vertex tracking method. In step S910, the converted polygon vertex row is added to the plane area data. In step S911, recursion processing is performed on the updated planar area data.

  (2-4) Processing for determining whether or not two polygons overlap in step S905 in FIG. 11 will be described. Here, it is determined whether or not there is an intersection between the two polygons. If there is an intersection, it is determined that they overlap, and if there is no intersection, it is determined that they do not overlap. In the planar area data after processing (2-2), if there are intersections or contact points between two polygons, be sure to set the same coordinate value to the two vertex rows representing those polygons. It is guaranteed that there are vertices with. Therefore, the coordinate value of each vertex is examined for two vertex rows, and if a vertex having the same coordinate value is found, it can be determined that it is an intersection or a contact point.

  With reference to FIG. 12, when it is determined that the vertex is an intersection or a contact, a method for determining whether the vertex is an intersection or a contact will be described. First, assume that two polygons are A and B, and the coordinate values of those vertices are examined, and vertices equal to point p exist in both polygons A and B, that is, point p is in polygons A and B. Suppose that it is an intersection or point of contact. In the polygon A, an arbitrary point m1 on the side connecting the vertex equal to the point p and the immediately preceding vertex, and an arbitrary point m2 on the side connecting the vertex equal to the point p and the immediately following vertex are selected.

  If either point m1 or m2 is inside polygon B and the other is outside polygon B, point p is an intersection, and both points m1 and m2 are outside or inside polygon B. If there is, it is determined that the point p is a contact point. For example, in the case of FIG. 12 (a), point m1 is inside polygon B and point m2 is outside, so p is an intersection, and in FIG. 12 (b), both points m1 and m2 are many. Since it is outside the square B, it can be determined that the point p is a contact point.

  Further, for the purpose of the present invention, when the sides of two polygons overlap each other, they must be subjected to the deduplication processing. For example, the sides of the polygons A and B overlap as shown in FIG. It is necessary to treat the point p as an intersection. In the case of FIG. 12C, when the positional relationship between the points m1 and m2 selected as described above and the polygon B is seen, the point m1 is outside the polygon B and the point m2 is on the side of the polygon B. . Here, if the point on the side of the polygon is defined to be inside the polygon, it can be said that the point m2 in the case of FIG. 12C is inside the polygon B. Therefore, FIG. Similarly to the case of FIG. 12, the point p in the case of FIG. 12C can be determined to be an intersection.

  From this, in the graphic data processing method according to the present invention, the point on the side of the polygon is defined as being inside the polygon, and the point equal to the vertex of the polygon is also the point corresponding to the consistency with it. Defined as inside a polygon. In addition, as a method of selecting the points m1 and m2 in the above description, a method of selecting a midpoint of a side connecting the point p and the vertex immediately before or after it can be considered in consideration of the ease of processing.

  In order to determine whether or not it is an intersection by the above method, it is necessary to determine whether or not an arbitrary point is inside the polygon. Conventionally, as a method for determining whether or not an arbitrary point is inside a polygon, an interior point determination method using a vertical line algorithm is known.

  The interior point determination method based on the vertical line algorithm is a method in which a half line is drawn in an arbitrary direction from a point to be determined (hereinafter referred to as a determination target point), and the number of times the half line intersects the target polygon is counted. If it is an even number (including 0), the determination target point is outside the polygon, and if it is an odd number, it is determined to be inside.

  With reference to FIG. 13, the specific procedure of the interior point determination method by the vertical line calculation will be described. First, half straight lines L1, L2, and L3 are drawn from the determination target points p1, p2, and p3. Next, the number of intersections between the polygon and the half lines L1, L2, and L3 is calculated. When calculating the number of intersections between the polygon and the half line L1, first, the initial value of the number of intersections is set to 0, and the six sides are examined in turn for the presence or absence of intersection between the side and the half line L1. In some cases, increase the number of crossings by one. For example, the side ab intersects the half line L1, so the number of intersections is increased by 1, and the side bc, cd, de, and ef do not intersect the half line L1, so the number of intersections is not changed, and the side fa is again the half line L1 Increase the number of crossings by 1. Eventually, the intersection number 2 (even number) is obtained, and it can be determined that the determination target point p1 is outside the polygon. By the same procedure, the number of intersections 1 (odd number) is obtained for the half line L2, and it can be determined that the determination target point p2 is inside the polygon.

The half line L3 passes through the vertex b and the vertex f. In such a case, a special determination procedure is required to determine whether the half line intersects or touches the polygon.
Specifically, when the side ab is examined, it is stored that the half line L3 passes through the end point b of the side ab and that the start point a of the side ab is on the left side in the direction of the half line L3. Next, when the side bc is examined, it is stored that the half line L3 passes through the start point b of the side bc and that the end point c of the side bc is on the right side in the direction of the half line L3. Thereby, it is found that the vertex a and the vertex c before and after the vertex b through which the half line L3 passes are divided into the left side and the right side in the direction of the half line L3. Therefore, it is determined that the half line L3 intersects this polygon at the vertex b, and the number of intersections is increased by one.

  Similarly, when the side ef is examined, it is stored that the half line L3 passes through the end point f of the side f and that the start point e of the side ef is on the left side in the direction of the half line L3. Next, when the side fa is examined, it is memorized that the half line L3 passes through the start point f of the side fa and that the end point a of the side fa is on the left side in the direction of the half line L3. Thereby, it is found that the vertex e and the vertex a before and after the vertex f through which the half line L3 passes are on the same side in the direction of the half line L3. Accordingly, it is determined that the half line L3 is in contact with the polygon at the vertex f, and the number of intersections is not changed.

  In order to avoid such a special determination procedure, for example, in Japanese Patent Application Laid-Open No. 61-180378, when a half line used for determination passes through the apex, a position slightly parallel to the half line, Alternatively, a method is provided in which a second half line that does not pass through any vertex of the polygon is provided at a position rotated by a slight angle around the determination target point, and the number of intersections between the second half line and the side of the polygon is counted. Has been proposed.

  As described above, in the graphic data processing method according to the present invention, the points on the sides of the polygon and the points equal to the vertices are defined to be inside the polygon. Here, this is verified by an interior point determination method using a conventional vertical line calculation method.

This will be described with reference to FIG. The determination target points p4 and p5 are both on the sides of the polygon, and half lines L4 and L5 are drawn from them. The number of intersections between the half line L4 and the sides of the polygon is 2 including the intersection at the point to be judged p4, and the number of intersections between the half line L5 and the sides of the polygon is only the intersection at the point to be judged p5. Times. Therefore, the determination target point p4 is determined to be outside the polygon, and the determination target point p5 is determined to be inside the polygon. Also, if it is defined that the judgment target point is not included in the half line, the number of intersections of the half line L4 and the polygon side is 1, and the number of intersections of the half line L5 and the polygon side is 0. Is reversed.
Furthermore, considering the case where the direction of drawing the half-line is variously changed, it is clear that the determination results for the determination target points p4 and p5 are indefinite.

  From the above considerations, in the conventional method, no matter how the determination target point is included in the half line or how the half line is drawn, there are many points on the side. It can be seen that it cannot be determined that it is inside the square. It is obvious that the method proposed in Japanese Patent Application Laid-Open No. 61-180378 does not solve this problem.

(2-5) Therefore, in the present invention, based on the principle of the interior point determination method based on the vertical line algorithm, as described below, points on the sides of the polygon and points that are equal to the vertices are set inside the polygon. Provided is an interior point determination method including a procedure for determining that
First, a procedure for counting the number of intersections between the half line drawn from the determination target point and the circumference of the polygon based on the principle of the inner point determination method based on the vertical line calculation will be described.

  The point to be judged is pt (xt, yt), the number of vertices of the polygon is n, the vertex sequence is {p0, p1, ... pi, ... pn-1}, and is used for inner point judgment by vertical line algorithm A half line Lt is drawn from the determination target point pt in parallel to the y axis and in the positive direction along the y axis.

  The initial value of the number of intersections is set to 0, the vertex pn-1 is set as the starting point, the entire circumference of the polygon is examined in principle in units of edges, and the half straight line Lt is determined by the intersection determination method described below. The number of intersections is counted by increasing the number of intersections by 1 when it is determined that the perimeters of the polygons intersect.

The above-mentioned determination of the intersection of the half-line Lt and the circumference of the polygon is based on a straight line x = xt parallel to the y-axis passing through the determination target point pt when both vertices of the side of the polygon are viewed If it is not (hereinafter referred to as “Case A”), it is determined by determining whether or not the corresponding side of the half-line Lt intersects, and one of the vertices at both ends of the side is on the line x = xt In the case (hereinafter referred to as “Case B”), a range of a plurality of continuous sides with a vertex on the straight line x = xt in between and a vertex not on the straight line x = xt as a start point and an end point is defined. Basically, the selection is performed by determining whether or not the circumference of the half line Lt and the polygon intersect in the range of the side.
However, it is assumed that the determination target point pt is not equal to any vertex of the polygon and is not on a side parallel to the y-axis of the polygon.

  If the point to be judged pt is equal to one of the vertices of the polygon, or if it is on a side parallel to the y-axis of the polygon, the intersection judgment procedure based on the above basic policy is not applicable. This process will be described later as case C.

Case A
Case A is a case where when a side pipi + 1 with a polygon is viewed, none of its vertices are on the straight line x = xt.
In this case, whether or not the half line Lt intersects the circumference of the polygon between the vertices pi and pi + 1 is determined depending on whether or not the half line Lt and the side pipi + 1 intersect.

  The method will be described with reference to FIGS. 15 (a) and 15 (b). First, it is checked whether or not the x coordinate value xt of the determination target point pt is within the range of the x coordinate value xi of the start point pi of the side and the x coordinate value xi + 1 of the end point pi + 1 of the side.

If the x coordinate value xt of the judgment target point pt is outside the range of the x coordinate value xi of the start point pi of the side and the x coordinate value xi + 1 of the end point pi + 1, the half line Lt and the side pipi + 1 intersect Since it can be determined that there is no such thing, the process proceeds to the intersection determination for the next side pi + 1pi + 2 without changing the number of intersections.
If the x coordinate value xt of the judgment target point pt is within the range of the x coordinate value xi of the start point pi of the side and the x coordinate value xi + 1 of the end point pi + 1, the half line Lt and the side pipi + 1 can intersect. It can be determined that there is sex.

  15 (a) and 15 (b), the x coordinate value xt of the judgment target point pt is within the range of the x coordinate value xi of the start point pi and the x coordinate value xi + 1 of the end point pi + 1. This is an example of a case where it can be determined that there is a possibility that the half line Lt and the side pipi + 1 intersect.

  Thus, if it is determined that there is a possibility that the half line Lt and the side pipi + 1 intersect, then the straight line x = xt passing through the determination target point pt and the side pipi + 1 The y coordinate value yc of the intersection pc of is obtained, and the magnitude relationship between it and the y coordinate value yt of the determination target point is examined.

  As shown in FIG. 15 (a), if the y-coordinate value yc of the intersection pc is larger than the y-coordinate value yt of the determination target point, that is, if yc> yt, it is determined that the half line Lt intersects the side pipi + 1. Increase the number of intersections by 1 and move to the intersection determination for the next side pi + 1pi + 2.

  As shown in FIG. 15 (b), if the y-coordinate value yc of the intersection pc is smaller than the y-coordinate value yt of the determination target point, that is, if yc <yt, it is determined that the half line Lt does not intersect the side pipi + 1. Without changing the number of intersections, the process proceeds to the intersection determination for the next side pi + 1pi + 2.

  The y coordinate value yc of the intersection pc is equal to the y coordinate value yt of the judgment target point, that is, when yc = yt, the judgment target point pt is on the side pipi + 1, so pt is on the side of the polygon Judge that there is.

  Here, in the present invention, as described above, since the point on the side of the polygon is defined as being inside the polygon, when the determination target point pt is determined to be on the side of the polygon, Determines that the determination target point pt is inside the polygon, and ends the inner point determination process.

Case B
Case B is a case where when one side pipi + 1 of a polygon is viewed, one of its vertices is on the straight line x = xt.
First, consider the case where the end point pi + 1 of the side pipi + 1 is on the straight line x = xt, that is, the x coordinate value xt of the determination target point pt is equal to the x coordinate value xi + 1 of the end point pi + 1. .

  In this case, there is a possibility that the half-line Lt intersects the circumference of the polygon at the vertex pi + 1, but just examining the relative positional relationship between the half-line Lt and the side pipi + 1 just touches or intersects It cannot be determined.

  Therefore, if the x-coordinate value xt of the judgment target point pt is equal to the x-coordinate value xi + 1 of the end point pi + 1, that is, if xt = xi + 1, the vertex pi is taken as the starting point and the starting point is the vertex pi + 1. Then, the vertexes are advanced one by one, and first, a plurality of continuous sides with the vertex deviating from the straight line x = xt as the end point are selected, and the half line Lt It is determined whether or not intersects with the circumference of the polygon.

  Here, the single side in case A and a plurality of continuous sides selected as described above are part of the circumference of the polygon to be determined as to whether or not the half line Lt intersects. In the following description, both are collectively referred to as “a range of sides to be determined”.

  With reference to FIG. 15 (c), FIG. 15 (d), FIG. 15 (e), FIG. 15 (f), in the case of Case B, the selection procedure of the end point of `` the range of the side to be determined '' and the `` A procedure for determining whether or not the half line Lt intersects the circumference of the polygon in the “range of sides to be determined” will be described.

  When looking at the side pipi + 1 in Fig. 15 (c), Fig. 15 (d), Fig. 15 (e), Fig. 15 (f), since xt = xi + 1, one by one starting from the vertex pi + 1 The vertex is moved forward, and the vertex that deviates from the straight line x = xt is first selected as the end point of the “side range to be judged”.

  Hereinafter, the end point of the “side range to be determined” selected in this way is represented by pe. For example, the vertex pi + 2 is selected as the end point pe in FIGS. 15 (c) and 15 (d), and the vertex pi + 3 is selected in FIGS. 15 (e) and 15 (f).

Next, it is checked whether or not the x coordinate value xt of the determination target point pt is within the range of the x coordinate value xi of the start point pi and the x coordinate value xe of the end point pe of “the range of the determination target side”.
As shown in FIG. 15 (f), if the x coordinate value xt of the determination target point pt is not within the range of the x coordinate value xi of the start point pi and the x coordinate value xe of the end point pe, the half line Lt is the start point pi and the end point pe. Since it can be determined that there is no possibility of intersecting with the circumference of the polygon between, the intersection determination for the next "range of sides to be judged" starting from the end point pe at this time without changing the number of intersections Move on.

  As shown in FIGS. 15 (c), 15 (d), and 15 (e), the x coordinate value xt of the determination target point pt is within the range of the x coordinate value xi of the start point pi and the x coordinate value xe of the end point pe. If there is, it can be determined that there is a possibility that the half straight line Lt may intersect the circumference of the polygon between the “range of sides to be determined” pipe.

  As shown in FIG. 15 (c), FIG. 15 (d), and FIG. 15 (e), it is determined that there is a possibility that the half line Lt may intersect the circumference of the polygon in the “side range to be determined” pipe. In this case, the magnitude relationship between the y coordinate value of the vertex (on the straight line x = xt) between the start point pi and the end point pe and the y coordinate value yt of the determination target point pt is examined.

In the example of FIGS. 15 (c) and 15 (d), since there is only one vertex pi + 1 between the start point pi and the end point pe (= pi + 2), the y coordinate value yi + of the vertex pi + 1 What is necessary is just to investigate the magnitude relationship between 1 and the y coordinate value yt of the determination target point pt.
In the example of FIG. 15 (e), there are two vertices, pi + 1 and pi + 2, between the start point pi and the end point pe (= pi + 3). The y-coordinate value y is uniform.

  Furthermore, it can be assumed that there are three or more vertices between the start point pi and the end point pe, but even in that case, the vertex pi + 1 is always one of those vertices, and y of those vertices The magnitude relationship between the coordinate value and the y coordinate value yt of the determination target point pt is uniform.

  Therefore, even when there are a plurality of vertices between the start point pi and the end point pe, the vertex pi + 1 represents them, and the y coordinate value yi + 1 of the vertex pi + 1 and the y coordinate value yt of the determination target point pt Investigate the magnitude relationship.

  As a result of examining the magnitude relationship between the y coordinate value yi + 1 of the vertex pi + 1 and the y coordinate value yt of the determination target point pt, as shown in FIGS. 15 (c) and 15 (e), if yi + 1> yt For example, the half straight line Lt can be determined to intersect with the circumference of the polygon in the “side range to be determined” pipe, so the number of intersections is increased by 1, and the next “determination target to be determined” starting from the end point pe at this time The process proceeds to the intersection determination for “side range”.

As in the example of Fig. 15 (d), if yi + 1 <yt, the straight line Lt can be determined not to intersect the circumference of the polygon in the "range of sides to be judged" pipe, so the number of intersections is changed Without proceeding, the process proceeds to the intersection determination for the next “range of sides to be determined” starting from the end point pe at this time.
Here, it is guaranteed that the end point of the “determined side range” selected as described above is not on the straight line x = xt.

  Also, the start point of the “determination target side range” is the end point of the “determination target side range” in the immediately preceding process. Therefore, in principle, it can be seen that the starting point of the “range of sides to be judged” is not on the straight line x = xt.

  However, only the starting point pn-1 when starting the counting process may be on the straight line x = xt. Therefore, the case where pn-1 is on the straight line x = xt is treated as a special case of Case B. In that case, the procedure for setting the "side range to be judged" and the "range of the side to be judged" A procedure for determining whether or not the half line Lt intersects the circumference of the polygon will be described.

First, start from the starting point pn-1, go back one vertex at a time, and first select a vertex that deviates from the straight line x = xt. For example, if the vertex pn-2 is not on the straight line x = xt, select the vertex pn-2, and if the vertex pn-2 is also on the straight line x = xt, repeat the process of going back one vertex. Good.
The vertex selected in this way is the start point of “the range of the side to be determined” when the start point pn-1 is on the straight line x = xt, and is represented by ps hereinafter.
In this case, the starting point of the counting process of the number of intersections between the circumference of the polygon and the half line Lt is also changed to ps.

  The end point of the first “range of sides to be judged” when the vertex pn-1 is on the straight line x = xt will be described. As described above, when the start point ps of the first “range of sides to be determined” is selected, the end point is assumed to be the vertex p0. If the vertex p0 is not on the straight line x = xt, the vertex p0 is determined as the end point pe of the first “range of sides to be determined”.

  However, if the vertex p0 is also on the straight line x = xt, the procedure for selecting the end point of the above-mentioned “range of sides to be judged” starts the vertex p0 and advances the vertex one by one. A vertex deviating from the straight line x = xt may be selected as the end point pe of the first “range of sides to be judged”.

  Next, the procedure for determining whether or not the half line Lt and the circumference of the polygon intersect in the first “range of sides to be determined” pspe set as described above will be described.

  First, it is checked whether or not the x coordinate value xt of the determination target point pt is within the range of the x coordinate value xs of the start point ps and the end point pe.

  If the x-coordinate value xt of the judgment target point pt is not within the range of the x-coordinate value xs of the start point ps and the x-coordinate value xe of the end point pe, the half line Lt intersects the circumference of the polygon between the start point ps and the end point pe Since it can be determined that there is no possibility of making an intersection, without changing the number of intersections, the process proceeds to the intersection determination for the next “range of sides to be determined” starting at the end point pe at this time.

  If the x-coordinate value xt of the judgment target point pt is within the range of the x-coordinate value xs of the start point ps and the x-coordinate value xe of the end point pe, the half line Lt is a polygon between the "side range of judgment target" pspe It can be determined that there is a possibility of intersecting with

  In this way, when it is determined that the half line Lt may intersect the circumference of the polygon in the “range of sides to be determined” pspe, the vertex between the start point ps and the end point pe (straight line x = on xt) and the y-coordinate value yt of the determination target point pt is examined.

  Here, as can be seen from the above selection procedure of the start point ps, the vertex pn-1 is one of the vertices between the “range of sides to be judged” pspe. Let us suppose that the vertex in the range of “side” pspe is represented, and examine the magnitude relationship between the y coordinate value yn-1 of the vertex pn-1 and the y coordinate value yt of the determination target point pt.

  As a result of examining the magnitude relationship between the y-coordinate value yn-1 of the vertex pn-1 and the y-coordinate value yt of the determination target point pt, if yn-1> yt, the half line Lt is the first " Since it can be determined that the area “pspe” intersects the circumference of the polygon, the number of intersections is increased by 1, and the process proceeds to the intersection determination for the next “range of determination target sides” starting from the end point pe at this time.

  If yn-1 <yt, it can be determined that the half-line Lt does not intersect with the circumference of the polygon in the first "range of sides to be judged" pspe, so the end point pe at this time can be changed without changing the number of intersections. The process proceeds to the intersection determination for the next “range of sides to be determined” starting from.

  As described above, even if the start point pn-1 of the first side when the counting process is started is on the straight line x = xt, the first “range of sides to be judged” is set by going back to the start point. This makes it possible to determine the intersection with the half line Lt.

  Based on the examination of Case A and Case B so far, if the target point pt is not equal to any vertex of the polygon and is not on a side parallel to the y-axis of the polygon, the vertical line algorithm By applying the principle, it is possible to count the number of intersections between the half-line Lt drawn in parallel with the y-axis from the judgment target point pt and in the positive direction of the y-axis and the circumference of the polygon, and integrated with it. In a typical procedure, the determination can be made even when the determination target point is on the side.

Case C
Case C is a case where the determination target point pt is equal to one of the vertices of the polygon, and a case where the determination target point pt is on a side parallel to the y axis of the polygon.
As described above, in the present invention, the point on the vertex of the polygon and the point on the side are defined to be inside the polygon. Therefore, in the case C, the determination target point pt is a polygon. It must be determined that it is inside.

  In case C, the interior point determination process based on the application of the principle of the vertical line algorithm described above cannot be performed correctly. Therefore, before performing the interior point determination process based on the application of the principle of the vertical line algorithm, the polygon It is determined whether or not the case C is satisfied by performing the following determination process for each side while tracing all the sides in order.

First, it is determined whether the determination target point pt is equal to the start point of the side. Here, if it is determined that the determination target point pt is equal to the start point of the side, it is determined that the determination target point pt is inside the polygon, and the interior point determination process is terminated.
If the determination target point pt is not equal to the start point of the side, it is determined whether or not the side is parallel to the y axis and the determination target point pt is on the side.

Here, when it is determined that the side is parallel to the y-axis and the determination target point pt is on the side, the determination target point pt is determined to be inside the polygon, The point determination process ends.
Even if the side is not parallel to the y-axis or is parallel to the y-axis, if it is determined that the determination target point pt is not on the side, the above processing for the next side is repeated.

  Even if the above processing is performed on all sides of the polygon, if it is not determined that the target point pt is inside the polygon, it does not fall under Case C, so the above-mentioned principle of the vertical line algorithm is applied. What is necessary is just to move to the inner point determination process.

  (2-6) The procedure of the process of converting the vertex strings Va and Vb of two overlapping polygons in step S909 of FIG. 11 will be described with reference to the example of FIG. A and B are polygons each having 11 vertices, and their vertex arrays Va and Vb are {a0, a1, a2, .... a10}, {b0, b1, b2, ..., b10, respectively. } And overlapping as shown in the figure. In addition, these polygons are the ones that have completed the processing of (2-1) and (2-2), and the directions of the vertex rows are both unified in the clockwise direction. It is assumed that a vertex equal to is already inserted. In terms of the symbols in the figure, the vertexes a3 and b7, a5 and b5, a7 and b3, and a9 and b1 are equal to each other, and the vertex is equal to the intersection.

First, from the vertex rows Va and Vb, a set of the following vertex rows with the vertices equal to the intersection as the start and end points is created.
Sa = {Va0 {a3, a4, a5}, Va1 {a5, a6, a7}, Va2 {a7, a8, a9}, Va3 {a9, a10, a0, a1, a2, a3}}
Sb = {Vb0 {b1, b2, b3}, Vb1 {b3, b4, b5}, Vb2 {b5, b6, b7}, Vb3 {b7, b8, b9, b10, b0, b1}}

  Next, one vertex row, for example, Va0 is selected from the set Sa, and then an element of the set Sb having a start point equal to the end point a5 is selected. Here, since the vertices a5 and b5 are equal, the vertex row Vb2 starting from the vertex b5 is selected. At this time, the end point b7 of the vertex row Vb2 is equal to the start point a3 of the vertex row Va0.

  The vertex trains Va0 and Vb2 selected in this way are connected after deleting their end points to obtain a vertex train V0 {a3, a4, b5, b6}. Thereafter, the vertex rows Va1, Va2, Va3 are sequentially selected and processed in the same manner, whereby the vertex rows V1 {a5, a6, b3, b4}, V2 {a7, a8, b1, b2}, V3 {a9, a10 , a0, a1, a2, b7, b8, b9, b10, b0}.

For the vertex rows obtained in this way, the vertex rows V0, V2, and V3 are classified clockwise and the vertex row V1 is classified counterclockwise using the above-described vertex row direction determination method.
Among the clockwise vertices, the area of the area that they enclose is the largest, in this case the vertices V3 is the polygon data that surrounds the combined area, the counterclockwise vertices V1 is the polygon that surrounds the hole area Since this is data, these are polygons after the conversion of the vertex rows Va and Vb.

  Note that when a vertex row is generated by such a procedure when two polygon sides before conversion overlap, a vertex row composed of only two vertices at both ends of the side is generated. This is a line segment with no area and does not need to be included in the data representing the planar area, so if the number of vertices in the converted vertex row is less than 3, do not add it to the updated planar area data Can be eliminated.

(3) Nested polygon vertex row direction adjustment When there are polygons that are nested in the polygons forming the planar area, the vertex row direction is adjusted by the following process.
First, the storage order of vertex rows representing n polygons existing in the planar area is rearranged in descending order of polygon area. The areas A0, A1, ..., An-1 of the n rearranged polygons P0, P1, ..., Pn-1 have the relationship A0≥A1≥ ... ≥An-1 . First, the polygon P0 having the largest area is selected, and the inclusion relation between the polygon P0 and the polygon having a smaller area is examined. The vertex row of the polygon P0 is turned clockwise, the vertex rows of all polygons contained in the polygon P0 are turned counterclockwise, and the vertex rows of all polygons not contained in the polygon P0 are turned clockwise.

  Next, the polygon P1 having the second largest area is selected, and the inclusion relation between the polygon P1 and the polygon having the smaller area is examined. The vertex sequence of the polygon P1 is left as it is, the direction of the vertex sequence of all polygons contained in the polygon P1 is reversed, and the polygon vertex sequence that is not contained in the polygon P1 and has a smaller area than the polygon P1 is leave it as it is.

  Thereafter, the process is repeated up to n-2 while increasing the subscript number by one. When the processing is finished for the polygon Pn-2 having the second smallest area, the directions of the vertex rows of all the polygons are determined. When the process is completed, the direction of the vertex row of the inner polygon is opposite to the direction of the vertex row of the polygon just outside the inner relation, that is, the nested polygon. Therefore, in all polygons, the right side in the direction of the vertex row is an internal region.

  A specific example will be described with reference to FIG. As shown in FIG. 17 (a), the size relationship of the areas A0, A1, A2, A3, A4, and A5 of the six polygons P0, P1, P2, P3, P4, and P5 is expressed as A0 ≧ A1 ≧ A2 ≧ A3 ≧ A4 ≧ A5. As shown in FIG. 17B, first, the polygon P0 having the largest area is selected, and its vertex row is turned clockwise. Next, as shown in FIG. 17C, the inclusion relation between the polygon P0 and a polygon having a smaller area is examined. Polygon P2 that is not contained in polygon P0 and has a smaller area than polygon P0, while the vertex row of polygon P0 is left as it is, and the vertex rows of polygons P1, P3, and P5 contained in polygon P0 are counterclockwise. , P4 vertex sequence is clockwise. As shown in FIG. 17D, the polygon P1 having the next largest area after the polygon P0 is selected, and the inclusion relation between the polygon P1 and the polygon having the smaller area is examined. Polygon P1, P3, P4, polygon polygon P1, which is not contained in polygon P1 and has a smaller area than polygon P1 Leave the vertex row of P5 as it is. In the example of FIG. 17D, there is no polygon included in the polygon P1.

  As shown in FIG. 17E, the polygon P2 having the next largest area after the polygon P1 is selected, and the inclusion relationship between the polygon P2 and the polygon having the smaller area is examined. Leave the vertex row of the polygon P2 as it is, reverse the direction of the vertex row of the polygon P4 contained in the polygon P2, and the vertexes of the polygons P3 and P5 that are not contained in the polygon P2 and have a smaller area than the polygon P2 Leave the column as it is. As shown in FIG. 17F, the polygon P3 having the next largest area after the polygon P2 is selected, and the inclusion relation between the polygon P3 and the polygon having the smaller area is examined. The vertex row of the polygon P3 is left unchanged, the direction of the vertex row of the polygon P5 contained in the polygon P3 is reversed, and the vertex row of the polygon P4 that is not contained in the polygon P3 and has a smaller area than the polygon P3 is leave it as it is.

  As shown in FIG. 17 (g), the polygon P4 having the next largest area after the polygon P3 is selected, and the inclusion relation between the polygon P4 and the polygon having the smaller area is examined. Leave the vertex row of polygon P4 as it is, invert the direction of the vertex row of the polygon contained in polygon P4, and leave the vertex row of polygon P5 that is not contained in polygon P4 and has a smaller area than polygon P4 as it is To. In the example of FIG. 17 (g), there is no polygon included in the polygon P4. Polygon P4 has the second smallest area. Therefore, the directions of the vertex rows of all the polygons are determined by the processing so far. As shown by the oblique lines in FIG. 17H, the right side in the direction of the vertex row is the internal region.

  The above-described processing includes processing for determining the inclusion relation between two polygons. The method is as follows. Here, the target polygon has been subjected to the above-described multi-polygon deduplication processing, and is guaranteed not to overlap. Thus, for example, if the larger area of two polygons is A and the smaller one is B, then if one vertex of B is outside of A, B will be represented by A It can be said that it is not included in the square.

Therefore, it examines the vertices of B in order, determines that it is not included when vertices outside A are found, and if no vertices outside are found when all vertices are examined, A It is determined that the contents are included. In this procedure, the above-described interior point determination method is used to determine whether the vertex of B is inside or outside A.
(4) Post-processing As is clear from the above processing procedure, the vertex row in the planar area data subjected to the processing so far is not closed. For this reason, as a post-process, a process of adding vertex data having the same coordinate value as the start point to the end point is performed on all the vertex rows.

It is a figure which shows the structure of the apparatus which performs the figure data processing method by this invention. It is a figure which shows the procedure of the whole figure data processing method by this invention. It is explanatory drawing for demonstrating the outline | summary of the self-intersection polygon division | segmentation process by this invention. It is explanatory drawing for demonstrating the procedure which searches a cut point from a polygon among the self-intersection polygon division | segmentation processes by this invention, and inserts the vertex equal to a cut point into a vertex row | line | column. It is explanatory drawing for demonstrating the procedure following the procedure of FIG. It is explanatory drawing for demonstrating the procedure which searches a cut point from a polygon among the self-intersection polygon division processes by this invention, and divides | segments a polygon. It is explanatory drawing for demonstrating the conventional vertex tracking method among the duplication elimination processes of a several polygon. It is explanatory drawing for demonstrating the procedure which determines the direction of the vertex row | line | column of a polygon and changes it clockwise in the case of counterclockwise among the duplication elimination processing of the multiple polygon by this invention. It is explanatory drawing for demonstrating the procedure of a search of the intersection etc. between two polygons, and vertex insertion among the deduplication removal processing of the several polygon by this invention. It is explanatory drawing for demonstrating the procedure following the procedure of FIG. It is explanatory drawing for demonstrating the procedure which eliminates the overlap of a some polygon among the duplication elimination processing of the some polygon by this invention. It is explanatory drawing for demonstrating the method of determining whether it is an intersection or a contact, when an intersection or a contact is found between two polygons in the process of FIG. It is explanatory drawing for demonstrating the interior point determination method by the conventional vertical line arithmetic. It is explanatory drawing for demonstrating the problem when the determination target point exists on the edge | side of a polygon in the interior point determination method by a perpendicular line method. It is explanatory drawing for demonstrating the interior point determination method by this invention. It is explanatory drawing for demonstrating the procedure of the process which converts the vertex row | line | column of two polygons which overlap in step S909 of FIG. It is a figure for demonstrating the nested polygon vertex row | line | column direction adjustment process by this invention. It is a figure which shows the specific example of the self-intersection polygon division | segmentation process by this invention. It is a figure which shows the specific example of the duplication elimination process of the multiple polygon by this invention. It is a figure which shows the specific example of the nested polygon vertex row | line | column direction adjustment process by this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 11 ... CPU, 12 ... ROM, 13 ... RAM, 14 ... Input / output I / F circuit, 15 ... Internal bus, 16 ... External storage device

Claims (17)

Using a computer having a storage device for storing graphic data and a program, a RAM for temporarily storing the graphic data, and a CPU for executing the program using the graphic data, a planar area is divided into a plurality of plane areas. In a graphic data processing method for processing graphic data represented by a square,
Reading polygonal graphic data from the storage device and storing the graphic data in the RAM;
A self-intersecting polygon dividing step of dividing the self-intersecting polygon into self-intersecting polygons or self-intersecting polygons and converting them into a plurality of polygons without self-intersection;
A multi-polygon deduplication step of converting a plurality of intersecting polygons into a plurality of non-intersecting polygons;
Nested polygon vertices that adjust vertex rows so that the directions of the vertex rows of two polygons that are inclusive relations and are adjacent in the order of the size of the nested polygons are opposite to each other A column direction adjustment step;
Is executed by the above CPU,
The self-intersecting polygon division step includes
A vertex insertion step for inserting a vertex equal to a self-intersection or self-contact into a vertex array of self-intersecting polygons;
A combination search step of searching for a combination of two vertices having the same coordinate value from the vertex array of polygons intersecting with each other;
A polygon dividing step of dividing the polygon into two at the vertex when two vertices having the same coordinate value are found;
Repeating the combination search step and the polygon division step until there is no self-intersection for each of the polygons after the two divisions;
A graphic data processing method comprising: 2. The graphic data processing method according to claim 1, wherein the deduplication step of the plurality of polygons sets the direction of the vertex sequence of the polygons for all of the non-self-intersecting polygons obtained by the self-intersecting polygon division step. Vertex row direction determination processing step for determining,
Vertex row direction unification processing step for unifying the direction of the vertex row of the polygon clockwise or counterclockwise,
A combination of two polygons in which one side of the polygon intersects a side of the other polygon, or a combination of two polygons in which the vertex of one polygon touches the side of the other polygon. Intersection search processing step to search;
Vertex insertion processing step for inserting a vertex equal to the coordinate value of the intersection or contact point into the two polygonal vertex rows detected in the intersection search processing step;
A polygon superposition search processing step for searching for two polygons intersecting each other;
A polygon conversion step of converting two intersecting polygons into a polygon surrounding a connected region and a polygon surrounding a hole region by the principle of vertex tracking;
A graphic data processing method characterized by repeating the polygon superposition search processing step and the polygon conversion step until there is no combination of two intersecting polygons. 3. The graphic data processing method according to claim 2, wherein the vertex row direction determination processing step includes:
Selecting a vertex p2 having a minimum x coordinate value and a vertex p1 immediately before and a vertex p3 immediately after it in the vertex sequence of the polygon, and calculating an outer product G of the vectors p2p1 and p2p3;
When the outer product G is non-zero, determining the rotation direction of the vertex row by its positive / negative,
When the outer product G is zero, determining the rotation direction of the vertex row based on the magnitude relationship of the y coordinate values of the vertex p2 and the vertex p3, or the vertex p2 and the vertex p1,
A graphic data processing method comprising: 3. The graphic data processing method according to claim 2, wherein the polygon superposition search processing step includes:
In two polygonal vertex rows in which vertices with the same coordinate value obtained in the vertex insertion processing step are inserted, the line segment connecting the vertexes in the vertex row of one polygon and the vertices immediately before and after it A two-point selection step to select any two points on top,
If one of the two points selected in the above two-point selection step is inside the other polygon and the other two points are outside the other polygon, the vertex is an intersection. An intersection determination step for determining that there is,
A graphic data processing method comprising: a contact determination step of determining that the vertex is a contact when the intersection is not determined to be an intersection in the intersection determination step. 5. The graphic data processing method according to claim 4, wherein, in the intersection determination step, one of the two points is inside the other polygon and the other of the two points is outside the other polygon. The process of determining that
A half-line step that draws a half-line with the judgment target point as an end;
Any two adjacent vertices are selected as a start point candidate and an end point candidate, it is determined whether or not the start point candidate and the end point candidate are on a straight line including the half line, and the start point candidate and the end point candidate are the half point. If not on a straight line including a straight line, a start point end point selection step for selecting the start point candidate and the end point candidate as a start point and an end point; and
When it is determined in the start point / end point selection step that the start point candidate is on a straight line including the half line, the vertices are sequentially retreated one by one from the start point candidate, and the start point candidate is on the straight line including the half line. When a first non-existent vertex is found, a starting point selection step starting from that point, and
In the start point / end point selection step, when it is determined that the end point candidate is on a straight line including the half line, the apexes are sequentially advanced one by one from the end point candidate, and then on the straight line including the half line. If the first non-existent vertex is found, the end point selection step will be the end point.
A range selection step of a determination target side that selects a range between the start point and the end point selected in the start point end point selection step or the start point selection step and the end point selection step as a range of a determination target side;
An intersection determination step for determining whether or not the half line intersects a polygon in the range of the determination target side;
In the intersection determination step, when it is determined that the half line intersects with the polygon, the number of intersections is increased by 1, and when it is determined that the intersection does not intersect, an intersection counting step for leaving the number of intersections as it is.
Repeating step of sequentially repeating the start point / end point selection step, the start point selection step, the end point selection step, the edge range selection step, the intersection determination step, and the intersection counting step over the entire circumference of the polygon. When,
If the number of intersections counted in the intersection counting step is an even number, it is determined that the determination target point is outside the polygon. If the number of intersections is an odd number, the determination target point is inside the polygon. A determination target point determination step for determining that the
A graphic data processing method comprising: The graphic data processing method according to claim 1, wherein the nested polygon vertex row direction adjusting step includes:
The plurality of polygons are n polygons, a polygon having the largest area among the n polygons is selected, and the polygon having the largest area and all polygons having a smaller area are selected. A first inclusion relationship search step for examining an inclusion relationship between
The vertex row representing the polygon with the largest area is clockwise or counterclockwise, and the vertex rows of all the polygons included in the polygon with the largest area are the direction of the vertex row representing the polygon with the largest area. In the opposite direction, the first step is to make the vertex rows of all the polygons not included in the polygon with the largest area the same direction as the direction of the vertex row representing the polygon with the largest area;
A polygon having the kth (k = 2 to n-1) th largest area is selected from the n polygons, and the kth largest polygon and all polygons having a smaller area are selected. A second inclusion relationship search step for examining the inclusion relationship between the two,
The vertex array of the polygon with the kth largest area is left as it is, the directions of the vertex arrays of all the polygons included in the polygon with the largest area are reversed, and the kth largest area is A second step of leaving a vertex row of a polygon that is not enclosed in a polygon and smaller in area than the k-th largest polygon as it is,
A graphic data processing method characterized in that the second inclusion relation retrieval step and the second step are repeated up to n-1 while increasing the index k from 2 to 1. The graphic data processing method according to claim 6, wherein the first and second inclusion relation search steps of the nested polygon search step include:
Setting two polygons that do not intersect with each other as the target for examining the inclusive relationship;
Determining the polygon with the smaller area and the polygon with the larger area of the two polygons;
If at least one vertex of the polygon with the smaller area is outside the polygon with the larger area, determine that the polygon with the smaller area is not included in the polygon with the larger area. When,
When all the vertices of the polygon with the smaller area are inside the polygon with the larger area, it is determined that the polygon with the smaller area is included in the polygon with the larger area. ,
A graphic data processing method comprising: Claim 1-7 readable program by a computer for executing the graphic data processing method according to any one of the computers. A computer-readable medium storing the program according to claim 8 . Using a computer having a storage device for storing graphic data and a program, a RAM for temporarily storing the graphic data, and a CPU for executing the program using the graphic data, a self-intersecting polygon is obtained. In the graphic data processing method for dividing,
Reading polygonal graphic data from the storage device and storing the graphic data in the RAM;
When there are a plurality of continuous vertices whose coordinate values are equal to each other from a vertex sequence representing a polygon, a redundant vertex deletion step of deleting one vertex from the plurality of continuous vertices and deleting the other vertices;
A coordinate point detection step for calculating a coordinate value of a self-intersection where a side of the polygon intersects from a vertex row representing the polygon and a self-contact point where the vertex contacts the side; and
A vertex insertion step of inserting a vertex equal to the coordinate value of the self-intersection point and the self-contact point into a polygon vertex row;
A combination search step for searching for a combination of two vertices having the same coordinate value from the vertex sequence;
When two vertices having the same coordinate value are found, a two-dividing step of dividing the polygon into two at the vertices;
Repeating the combination search step and the two division step until there is no self-intersection for each of the polygons after the division into two,
Is executed by the CPU . A computer-readable program for causing a computer to execute the graphic data processing method according to claim 10 . A computer-readable medium storing the program according to claim 11 . It is represented by a vertex sequence using a computer having a storage device for storing graphic data and a program, a RAM for temporarily storing the graphic data, and a CPU for executing the program using the graphic data. In the graphic data processing method for determining whether the determination target point is inside or outside the polygon when the polygon and the determination target point are given,
Reading polygonal graphic data from the storage device and storing the graphic data in the RAM;
A half-line step that draws a half-line with the judgment target point as an end;
Any two adjacent vertices are selected as a start point candidate and an end point candidate, it is determined whether or not the start point candidate and the end point candidate are on a straight line including the half line, and the start point candidate and the end point candidate are the half point. If not on a straight line including a straight line, a start point end point selection step for selecting the start point candidate and the end point candidate as a start point and an end point; and
When it is determined in the start point / end point selection step that the start point candidate is on a straight line including the half line, the vertices are sequentially retreated one by one from the start point candidate, and the start point candidate is on the straight line including the half line. When a first non-existent vertex is found, a starting point selection step starting from that point, and
In the start point / end point selection step, when it is determined that the end point candidate is on a straight line including the half line, the apexes are sequentially advanced one by one from the end point candidate, and then on the straight line including the half line. If the first non-existent vertex is found, the end point selection step will be the end point.
A range selection step of a determination target side that selects a range between the start point and the end point selected in the start point end point selection step or the start point selection step and the end point selection step as a range of a determination target side;
An intersection determination step for determining whether or not the half line intersects a polygon in the range of the determination target side;
In the intersection determination step, when it is determined that the half line intersects with the polygon, the number of intersections is increased by 1, and when it is determined that the intersection does not intersect, an intersection counting step for leaving the number of intersections as it is.
Repeating step of sequentially repeating the start point / end point selection step, the start point selection step, the end point selection step, the edge range selection step, the intersection determination step, and the intersection counting step over the entire circumference of the polygon. When,
If the number of intersections counted in the intersection counting step is an even number, it is determined that the determination target point is outside the polygon. If the number of intersections is an odd number, the determination target point is inside the polygon. A determination target point determination step for determining that the
Is executed by the CPU . 14. The graphic data processing method according to claim 13, wherein the intersection determination step includes:
X-coordinate to determine whether the x-coordinate value of the judgment target point is between the x-coordinate value of the start point and the x-coordinate value of the end point when setting the direction of the half line to the positive direction of the y-axis A value determination step;
When it is determined in the x coordinate value determining step that the x coordinate value of the determination target point is not between the x coordinate value of the start point and the x coordinate value of the end point, the end of the intersection determination step is ended. Steps,
In the x coordinate value determining step, when it is determined that the x coordinate value of the determination target point is between the x coordinate value of the start point and the x coordinate value of the end point, the start point and the end point are polygonal. When there are two consecutive vertices, the y-coordinate value of the intersection of the straight line connecting the start point and the end point and the straight line including the half line is compared with the y-coordinate value of the determination target point, and the start point or the end point is Y coordinate value comparison that compares the y coordinate value of the vertex between the start point and the end point with the y coordinate value of the judgment target point when the vertex is selected at the start point selection step or the end point selection step Steps,
From the comparison result in the y coordinate value comparison step, a comparison result intersection determination step for determining whether or not the half line intersects a polygon in the range of the side to be determined;
A graphic data processing method characterized by comprising : 14. The graphic data processing method according to claim 13, wherein in the second and subsequent loops, the start point / end point selection step selects an end point in the previous loop as a start point, and selects a vertex obtained by advancing the vertex by one from the start point. And determines whether the end point candidate is on a straight line including the half line. If the end point candidate is not on the straight line including the half line, the end point candidate is set as the end point, and the end point is determined. If the candidate is on a straight line including the half line, the vertices are sequentially advanced one by one from the end point candidate, and if the first vertex that is not on the straight line including the half line is found, it shall be the end point. Characteristic graphic data processing method . A computer-readable program for causing a computer to execute the graphic data processing method according to any one of claims 13 to 15 . A computer-readable medium storing the program according to claim 16 .

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