CN103817938A - Rapid bridging method of polygonal area containing plurality of holes - Google Patents

Rapid bridging method of polygonal area containing plurality of holes Download PDF

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CN103817938A
CN103817938A CN201410064160.2A CN201410064160A CN103817938A CN 103817938 A CN103817938 A CN 103817938A CN 201410064160 A CN201410064160 A CN 201410064160A CN 103817938 A CN103817938 A CN 103817938A
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polygon
outline
bridge
array
polygons
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傅建中
林志伟
贺永
沈洪垚
甘文峰
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Zhejiang University ZJU
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Zhejiang University ZJU
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Abstract

The invention discloses a rapid bridging method of a polygonal area containing plurality of holes. The method comprises the following steps: inputting an outer-contour polygon and several inner-contour polygons; copying and storing coordinate of vertexes of each polygon and simultaneously recording serial number of each vertex on corresponding polygon and serial number of the polygon in the polygon array so as to obtain a planar point cloud; carrying out Delaunay triangularization on the point cloud to obtain a plane triangle array; deleting useless triangles in the plane triangle array; establishing an initial bridge inside each triangle remaining to connect two corresponding polygons so as to obtain an initial bridge array; finding out several useful bridges in the array and using the bridges to bridge all inner-contour polygons to the outer-contour polygon; and finally outputting an unified polygon containing the inner-contour polygons and the outer-contour polygon. According to the invention, a plurality of inner-contour polygons on a plane domain can be bridged to an outer-contour polygon within approximate linear time. Rough-machining path generation efficiency is raised.

Description

The quick bridging method of a kind of polygonal region that comprises multiple holes
Technical field
The present invention relates to three-dimensional printing technology field, specifically relate to the quick bridging method of a kind of polygonal region that comprises multiple holes.
Background technology
In layer cutting method roughing path planning, first go to cut part and blank model by a variable plane of floor height, obtain the some machining areas on this layer plane.These machining areas are formed by the nested encirclement of a series of polygons.Take one of them machining area as example, this region is surrounded by a polygon that represents profile in the polygon of outline and zero or multiple expression, and wherein outline polygon direction is generally expressed as counterclockwise, and interior outline polygon direction is generally expressed as clockwise.In machining area, conventional cutter path form has parallel and annular two kinds.Parallel path generating algorithm is comparatively simple, but adds frequently cutter lifting in man-hour, and may have the inhomogeneous situation of cutting force at two paths joining places.Circular path generating algorithm is comparatively complicated, but cutter lifting is less and cutting force is even, is therefore widely used in the roughing process of all kinds of parts.
The process of generation circular path is exactly the process that the polygon to representing machining area carries out continuous biasing, and in machining area, the existence of profile (hole) has increased the difficulty that polygon is setovered greatly.In document, the processing method of setovering with Cave polygon region is mainly contained to two kinds at present:
The one, internal, outline is setovered first respectively, wherein outline is inwardly setovered, interior profile is outwards setovered, and then all offset lines that obtain is asked and is handed over and according to the logical relation between each intersection point, offset line carried out to cutting, finally obtains some sealing offset lines.The representative document of adopting in this way has: Lee CS, Phan TT, Kim DS, 2D curve offset algorithm for pockets with islands using a vertex offset, The International Journal of Precision Engineering and Manufacturing, 2009,10 (2): 127-135.
The 2nd, first all interior outline polygons are bridged on outline polygon, obtain the polygon that a unification has comprised inside and outside profile, then this polygon is setovered, generate some offset lines.Kim K, Jeong J and Choi BK, Park SC has all adopted the biasing problem of this method processing with Cave polygon in their article, but their article all focuses on polygonal biasing problem, and interior profile bridges to the process of outline by realizing (referring to Kim KJeong J manually, Tool path generation for machining free-form pockets with islands, Computers & Industrial Engineering, 1995, 28 (2): 399-407 and Choi BK, Park SC, A pair-wise offset algorithm for2D point-sequence curve, Computer-Aided Design, 1999, 31 (12): 735-745).Wong TN, Wong KW in their article, studied in region in the automatic bridging method of profile, but the time complexity of the method is a square magnitude, on the more or interior profile of profile number, put in region when more, adopt the interior profile of the method bridge joint consuming time large (referring to Wong TN, Wong KW, NC toolpath generation for arbitrary pockets with Islands, The International Journal of Advanced Manufacturing Technology, 1996,12 (3): 174-179).
In sum, for the bridge joint problem of the polygon machining area that comprises multiple holes, prior art is complete not, still rests on manual bridge joint or has in the automatic bridge joint rank of square magnitude time complexity.Roughing circular path generative process need badly a kind of can be approaching the method that completes profile bridge joint process in region in linear session.
Summary of the invention
In order to solve the deficiency that in the generation of roughing circular path, prior art exists in bridging strip Cave polygon region, improve bridging efficiency, the invention provides the quick bridging method of a kind of polygonal region that comprises multiple holes.The Delaunay trigonometric ratio technology of this method based on planar point cloud, can bridge to the interior outline polygon in input plane region on outline polygon approaching in linear session, obtains a unified polygon that has comprised inside and outside outline polygon.
The quick bridging method of polygonal region that comprises multiple holes, comprising:
Step 1, one of input represent the polygon array of plane domain, and the wherein outline in first For Polygons Representation region, is defined as outline polygon, profile in all the other For Polygons Representation regions, i.e. and the profile in each hole, is defined as interior outline polygon;
Step 2, copy and store the each apex coordinate of above-mentioned polygon, record sequence number and this polygon sequence number in polygon array of each summit on corresponding polygon simultaneously, obtain one group of planar point cloud;
Step 3, above-mentioned planar point cloud is carried out to the processing of Delaunay trigonometric ratio, obtain a plane triangle array;
Step 4, delete useless triangle in above-mentioned plane triangle array, these triangles comprise that three summits are all on same polygon or three summit triangles on three polygons respectively;
Step 5, in each triangle, set up initial bridge to connect two corresponding polygons, obtain an initial bridge array;
Step 6, in initial bridge array, find the useful bridges of some seats and all interior outline polygons are bridged to outline polygon with these bridges;
Step 7, one of output have comprised all interior outline polygons and the polygonal unified polygon of outline.
The quick bridging method of the polygonal region that comprises multiple holes of the present invention, the time complexity of bridge joint and the number in hole are irrelevant, for O (nlogn) (approaching bridge joint in linear session completes), wherein n is the number of vertices sum in all polygons of inputting; After bridge joint completes, between any two bridges, can not intersect, and can not intersect between any bridge and interior profile.
In described step 1, the polygon of input is generally simple polygon, there is no the polygon of self intersection.To representing the polygon of outline, its direction gage is decided to be counterclockwise; To representing the polygon of interior profile, its direction is defined as clockwise.In a region, represent that the polygon of outline must have and only have one, in representing in outline, the polygon of profile can have zero or multiple.For the model area with multiple outlines, can adopt and repeatedly adopt method of the present invention, the present invention is only explanation to only having the bridging method in a polygonal region of outline in detail, but does not affect the scope that comprises of the present invention.
The data structure that copies the polygon vertex obtaining in described step 2 for preserving can be (x, y, pIdx, cIdx), and wherein x, y are type real, for savepoint coordinate figure in the plane; PIdx, cIdx are integer type, and pIdx is for preserving this sequence number at its corresponding polygon, and cIdx is for preserving the sequence number of corresponding polygon in polygon array.As point (1.2,3.5,47,6) represents this point, coordinate is for (1.2,3.5) in the plane, and it is the 47th point on the 6th polygon in polygon array.The all polygon vertexs of copying and saving can obtain one group of planar point cloud successively.
In described step 3, can be the various effective ways that existing document is mentioned to planar point cloud Delaunay Triangulation Algorithm, but time complexity must not be higher than O (nlogn), wherein n counts in planar point cloud.
As preferably, in step 3, described planar point cloud is carried out to the processing of Delaunay trigonometric ratio before, need upset at random the some order in planar point cloud.To eliminate each point impact of summit rule ordering on polygon in step 2 reproduction process, its object is to improve the efficiency of Delaunay trigonometric ratio.In order to identify each out of order particular location on former polygon, before upsetting an order, step 2 at an internal record point in polygonal some order of correspondence and corresponding polygon the point order in polygon array.
After having deleted useless triangle in described step 4 in triangle array, to the triangle array after upgrading, each triangle must connect two polygons, and leg-of-mutton one of them summit is dropped on a polygon, and two other summit is dropped on another polygon.
As preferably, in step 5, the process of setting up initial bridge in each triangle is as follows: setting A, B, C are arbitrary leg-of-mutton three summits, this triangle connects two polygons, wherein summit A is on first polygon, summit B, C, on second polygon, connect one of them end points E of first polygon, two polygonal bridges 1on the A of summit, another one end points E 2on summit B or C.In order to shorten bridge E 1e 2length, described end points E 2get in B, C and make E 1e 2on the less point of length.
The bridge E setting up in triangle ABC 1e 2two-end-point except having inherited the coordinate of triangle respective vertices, also inherited sequence number and corresponding polygon sequence number in polygon array, i.e. pIdx and the cIdx of summit in corresponding polygon.
As preferably, in step 6, useful bridge is found and the detailed process of profile bridge joint is:
Step 6.1, search for the bridge that in initial bridge array, all one end are connected with outline polygon, therefrom find out that the shortest bridge, be designated as bridge b, two end points of bridge b are respectively E 1' and E 2', wherein E 1' be the bridge b end points on outline polygon outside, E 2' be another end points of bridge b;
Step 6.2, find and bridge b other end E 2' that connected interior outline polygon;
Step 6.3, copy and extract bridge b, and delete the bridge that in initial bridge array, all and above-mentioned interior outline polygons and outline polygon are connected;
Step 6.4, this interior outline polygon is bridged on outline polygon with bridge b, in outline polygon become the polygonal part of outline;
Step 6.5, judging whether that all interior outline polygons have all been bridged on outline polygon, is to exit; Otherwise, upgrade interior outline polygon signal and outline polygon information in initial bridge array, skip to step 6.1.
Wherein in step 6.1, step 6.2, searching for specific bridge or specific polygon is specifically inherited from pIdx and the cIdx variate-value of triangular apex and is realized by every bridge in the initial bridge array of comparison.
As further preferred, in described step 6.4, interior outline polygon is bridged to the polygonal step of outline as follows:
Step 6.4.1, find out on outline polygon and the E of bridge b 1that point that ' end points connects, is designated as P 1;
Step 6.4.2, outline polygon are at P 1place disconnects, and is connected and is entered interior outline polygon by bridge b, and inlet point is on the polygon row of interior profile and the E of bridge b 2that point that ' end points connects, is designated as P 2;
Step 6.4.3, from P 2start, in a clockwise direction traversal copy and add in the institute of profile on polygon a little to outline polygon;
Step 6.4.4, from P 2point out, is connected to P 1, obtain closed polygon.
The quick bridging method of a kind of polygonal region that comprises multiple holes of the present invention, the useful effect having is:
Can within the time of O (nlogn), the multiple interior outline polygon on plane domain be bridged on outline polygon, the number of vertex sum that wherein n is inside and outside outline polygon, irrelevant with the number in hole, and can self intersection between connecting bridge, also can not intersect with polygon; Thereby provide part solution for roughing circular path generates, improve roughing path formation efficiency.
Accompanying drawing explanation
Fig. 1 is the quick bridging method flow chart of polygonal region that the present invention comprises multiple holes.
Fig. 2 is one group of polygon of the expression plane domain of input.
Fig. 3 is for carrying out result after Delaunay trigonometric ratio to planar point cloud.
Fig. 4 deletes useless triangle result after Delaunay trigonometric ratio.
Fig. 5 is that useful bridge is found and interior profile bridges to outline process.
Fig. 6 is that inside and outside contour polygon bridge joint and circular path generate example.
The specific embodiment
Below in conjunction with drawings and Examples, technical solution of the present invention is described in further details, following examples do not form limitation of the invention.
As shown in Figure 1, concrete implementation step is as follows for the flow chart of the quick bridging method of polygonal region that the present invention comprises multiple holes:
Step 101, one of input represent the polygon array of plane domain, comprise an outline and multiple interior profile.
A machining area 202 in the polygon array representation plane of input, as shown in gray area in Fig. 2, in array, first element is outline polygon 201, all the other elements are the interior outline polygon in outline, it is respectively the polygon 203 in hole 1, the polygon 204 in hole 2, the polygon 205 in hole 3.Outline polygon 201 must have and only have one, and interior outline polygon number is indefinite, can have any number ofly, can be also zero; In Fig. 2, be three.Inside and outside outline polygon opposite direction, general provision outline polygon direction is that interior outline polygon direction is clockwise counterclockwise.
Step 102, copy and store each apex coordinate in above-mentioned polygon successively, record sequence number and this polygon sequence number in polygon array of each summit on corresponding polygon simultaneously, obtain one group of planar point cloud.
Particularly, be used for preserving the data structure that copies the polygon vertex obtaining and can be designed to (x, y, pIdx, cIdx), wherein x, y are type real, for savepoint coordinate in the plane; PIdx, cIdx are integer type, and pIdx is for preserving this sequence number at its corresponding polygon, and cIdx is for preserving the sequence number of corresponding polygon in polygon array.The all polygon vertexs of copying and saving can obtain one group of planar point cloud successively.With point (1.2,3.5,47,6), for example, this some coordinate is in the plane (1.2,3.5), and it is the 47th point on the 6th polygon in polygon array.How to change without argument (1.2,3.5,47,6) sequence number in array, its total energy is the own detail location in input polygon array in location accurately.
Step 103, above-mentioned planar point cloud is carried out to the processing of Delaunay trigonometric ratio, obtain a plane triangle array.
Can be the various effective ways that existing document is mentioned to the Delaunay Triangulation Algorithm of planar point cloud, but time complexity must not be higher than O (nlogn), wherein n counts in planar point cloud.Fig. 3 has provided the Delaunay trigonometric ratio result of inputting polygon form point cloud in Fig. 2.In the present embodiment, adopt random method of addition to carry out the processing of Delaunay trigonometric ratio to planar point cloud, its time complexity is O (nlogn).(referring to Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars, Computional Geometry:Algorithms and Applications, 2008).
It should be noted that the operation efficiency in order to improve Delaunay trigonometric ratio, before starting trigonometric ratio processing, need upset at random a cloud mid point order, eliminate each point impact of summit rule ordering on polygon in step 102 reproduction process.In order to identify each out of order particular location on former polygon, before upsetting an order, step 102 at an internal record point in polygonal some order of correspondence and corresponding polygon the point order in polygon array.
Step 104, delete the useless triangle in the triangle array that obtains, comprise three summits all on same polygon or three summit triangles on three polygons respectively.
As shown in Figure 4, deleted useless triangle in triangle array after, there is not any triangle in interior outline polygon inside; To the triangle array after upgrading, each triangle must connect two polygons, and leg-of-mutton one of them summit is dropped on a polygon, and two other summit is dropped on another polygon.
Step 105, in remaining each triangle, set up initial bridge to connect two corresponding polygons, obtain an initial bridge array.
As shown in Figure 4, the explanation as an example of arbitrary triangle ABC wherein example, ABC has connected two polygons, and wherein summit A is on the polygon 203 in hole 1, and summit B, C on outline polygon, connect one of them end points E of these two polygonal bridges outside 1on the A of summit, another one end points E 2be taken on summit B or C; In order to shorten bridge E 1e 2length, E 2get in B, C and make E 1e 2on the less point of length.
The bridge E setting up in above-mentioned triangle ABC 1e 2two-end-point E 1, E 2same with the preservation of (x, y, pIdx, cIdx) structure, they have also inherited sequence number and corresponding polygon sequence number in polygon array, i.e. pIdx and the cIdx of summit in corresponding polygon except having inherited the coordinate of triangle respective vertices.
Step 106, in initial bridge array, find the useful bridges of some seats and all interior profiles are bridged to outline polygon with these bridges.
Particularly, the step of useful bridge searching and profile bridge joint is as follows:
Step 106.1, search for all one end (E in initial bridge array 1' or E 2') bridge that is connected with outline polygon, therefrom find out that the shortest bridge, be designated as bridge b;
Step 106.2, find and the bridge b other end (E 2' or E 1') that connected interior outline polygon;
Step 106.3, copy and extract bridge b, and delete the bridge that in initial bridge array, all and above-mentioned interior outline polygons and outline polygon are connected;
Step 106.4, this interior outline polygon is bridged on outline polygon with bridge b, in profile become the part of outline;
Step 106.5, judging whether that all interior outline polygons have all been bridged on outline polygon, is to exit, otherwise, upgrade initial bridge array China and foreign countries' outline polygon information and interior outline polygon information, skip to step 106.1.
Wherein in step 106.1, step 106.2, searching for specific bridge or specific polygon is specifically inherited from pIdx and the cIdx variate-value of triangular apex and is realized by every bridge in the initial bridge array of comparison.
Further, in step 106.4, interior profile is bridged to the step of outline as follows:
Step 106.4.1, find out on outline polygon and the E of bridge b 1' end points connect that point, be designated as P 1;
Step 106.4.2, outline polygon are at P 1place disconnects, and is connected and is entered interior outline polygon by bridge b, and inlet point is on the polygon row of interior profile and the E of bridge b 2' end points connect that point, be designated as P 2;
Step 106.4.3, from P 2start, in a clockwise direction traversal copy and add in the institute of profile on polygon a little to outline polygon;
Step 106.4.4, from P 2point out, is connected to P 1, obtain closed polygon.
Fig. 5 has provided by above-mentioned steps circulation and has found out 3 useful bridge b 1, b 2, b 3, wherein in Fig. 5 (a), b 1bridge joint outline and hole 2 polygons, formed new outline polygon 501; In Fig. 5 (b), b 2bridge joint hole 2 and hole 3 polygons, formed new outline polygon 502; In Fig. 5 (c), b 3bridge joint hole 2 and hole 1 polygon, formed new outline polygon 503.As shown in Figure 5, when interior profile bridge is received after outline by useful bridging, in fact comprise the line segment of two coincidences on every bridge, wherein one for repeatedly kicking into line segment, and another is for connecting line segment.
In the present invention, characteristic that can be not crossing between any two useful bridges by Delaunay trigonometric ratio after the characteristic that converges at infinity of any two triangles guarantee; Any useful bridge can be not crossing with interior profile characteristic maximize and guarantee by all triangle Minimum Internal Angles after Delaunay trigonometric ratio.The operation time of this bridging method is mainly by determining the operation time of Delaunay trigonometric ratio, and Delaunay trigonometric ratio can complete in the time at O (nlogn) at present, wherein n counts in planar point cloud, and therefore the time complexity of this bridging method is O (nlogn).
Step 107, a unified polygon that has comprised inside and outside outline polygon of output.
A typical embodiment of the present invention is as follows:
The rough machined part of needs of selecting in this example is a cavity part, on a certain cutting lay, needs the region of processing as shown in gray area in Fig. 6 (a).Complicated outline polygon of this district inclusion and central 15 by rectangle, circle, ellipse and the randomly shaped interior outline polygon forming, wherein outline polygon comprises 500 points, interior outline polygon does not comprise 4 to 500 points not etc., and all polygonal always counting are 2191.
At Duo double-core CPU@2.53GHz, on the computer platform of 2GB internal memory, in bridge test program by above-mentioned polygon group input with C Plus Plus establishment, the total about 25ms consuming time of bridge joint process, the wherein Delaunay trigonometric ratio 22ms that is about consuming time, the total about 3ms consuming time of operation such as point copies, the deletion of useless triangle, the searching of useful bridge, contour linkage.If with the bridging method of square magnitude of mentioning in document, this example of bridge joint needs about 672ms consuming time.In this example contrast, the inventive method can improve approximately 25 times by profile bridging efficiency in polygon.
Fig. 6 (b) deletes the result after useless triangle after having provided Delaunay trigonometric ratio; Fig. 6 (c) has provided 15 interior outline polygons has been bridged to the result after outline, only comprises a polygon in this figure; Fig. 6 (d) has provided the result in the annular roughing of the continuous biasing path generating in the machining area shown in Fig. 6 (c), and as known in the figure, the machining area of the For Polygons Representation that above bridge joint obtains is accurate.
The above is only the preferred embodiment of the present invention, it should be pointed out that the those skilled in the art for the art, and the present invention can also have various modifications and variations.Under the premise without departing from the principles of the invention, any modification of doing, be equal to replacement, improvement etc., within protection scope of the present invention all should be included in.

Claims (7)

1. the quick bridging method of polygonal region that comprises multiple holes, is characterized in that, comprising:
Step 1, one of input represent the polygon array of plane domain, and the wherein outline in first For Polygons Representation region, is defined as outline polygon, profile in all the other For Polygons Representation regions, i.e. and the profile in each hole, is defined as interior outline polygon;
Step 2, copy and store the each apex coordinate of above-mentioned polygon, record sequence number and this polygon sequence number in polygon array of each summit on corresponding polygon simultaneously, obtain one group of planar point cloud;
Step 3, above-mentioned planar point cloud is carried out to the processing of Delaunay trigonometric ratio, obtain a plane triangle array;
Step 4, delete useless triangle in above-mentioned plane triangle array, these triangles comprise that three summits are all on same polygon or three summit triangles on three polygons respectively;
Step 5, in each triangle, set up initial bridge to connect two corresponding polygons, obtain an initial bridge array;
Step 6, in initial bridge array, find the useful bridges of some seats and all interior outline polygons are bridged to outline polygon with these bridges;
Step 7, one of output have comprised all interior outline polygons and the polygonal unified polygon of outline.
2. the quick bridging method of the polygonal region that comprises multiple holes according to claim 1, is characterized in that, in step 3, described planar point cloud is carried out to the processing of Delaunay trigonometric ratio before, need upset at random the some order in planar point cloud.
3. the quick bridging method of the polygonal region that comprises multiple holes according to claim 1, it is characterized in that, in step 5, the process of setting up initial bridge in each triangle is as follows: setting A, B, C are arbitrary leg-of-mutton three summits, this triangle connects two polygons, wherein summit A is on first polygon, and summit B, C, on second polygon, connect one of them end points E of first polygon, two polygonal bridges 1on the A of summit, another one end points E 2on summit B or C.
4. the quick bridging method of the polygonal region that comprises multiple holes according to claim 3, is characterized in that, described end points E 2get in B, C and make E 1e 2on the less point of length.
5. the quick bridging method of the polygonal region that comprises multiple holes according to claim 1, is characterized in that, in step 6, detailed process is:
Step 6.1, search for the bridge that in initial bridge array, all one end are connected with outline polygon, therefrom find out that the shortest bridge, be designated as bridge b, two end points of bridge b are respectively E 1' and E 2',, wherein E 1' be the bridge b end points on outline polygon outside, E 2' be another end points of bridge b;
Step 6.2, find and bridge b other end E 2' that connected interior outline polygon;
Step 6.3, copy and extract bridge b, and delete the bridge that in initial bridge array, all and above-mentioned interior outline polygons and outline polygon are connected;
Step 6.4, this interior outline polygon is bridged on outline polygon with bridge b, in outline polygon become the polygonal part of outline;
Step 6.5, judging whether that all interior outline polygons have all been bridged on outline polygon, is to exit; Otherwise, upgrade interior outline polygon information and outline polygon information in initial bridge array, skip to step 6.1.
6. the quick bridging method of the polygonal region that comprises multiple holes according to claim 5, is characterized in that, in described step 6.4, interior outline polygon is bridged to the polygonal step of outline as follows:
Step 6.4.1, find out on outline polygon and the E of bridge b 1that point that ' end points connects, is designated as P 1;
Step 6.4.2, outline polygon are at P 1place disconnects, and is connected and is entered interior outline polygon by bridge b, and inlet point is on the polygon row of interior profile and the E of bridge b 2that point that ' end points connects, is designated as P 2;
Step 6.4.3, from P 2start, in a clockwise direction traversal copy and add in the institute of profile on polygon a little to outline polygon;
Step 6.4.4, from P 2point out, is connected to P 1, obtain closed polygon.
7. the quick bridging method of the polygonal region that comprises multiple holes according to claim 1, is characterized in that, in described step 1, the polygon of input is simple polygon, there is no the polygon of self intersection.
CN201410064160.2A 2014-02-25 2014-02-25 Rapid bridging method of polygonal area containing plurality of holes Pending CN103817938A (en)

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Application publication date: 20140528