CN105809735A - Topology maintenance method based on three-dimensional geometric body combination - Google Patents
Topology maintenance method based on three-dimensional geometric body combination Download PDFInfo
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Abstract
The invention discloses a topology maintenance method based on three-dimensional geometric body combination, and the method comprises the steps: Boolean operation is performed on three-dimensional boundary surfaces, so that a relation surface set is obtained; geometric operation is performed on intersecting lines, so that a new edge is generated, and the relations between the lines and surfaces are updated; surfaces comprising crossing relation and containing relation are divided; all common elements and divide elements are combined, and the uniqueness of topology element is ensured; geometrical elements are combined, and new lines, surfaces and bodies are generated; and combined internal topological relation is updated. According to the invention, the method makes up a defect of inconsistent topological relation after spatial operation for three-dimensional body in a three-dimensional space; the construction of partial topological relation is accelerated through dividing the common surfaces and recording and combining the corresponding relations of front and rear elements; moreover, the method provided by the invention is suitable for combining operation between two bodies and complex space operation between a plurality of bodies.
Description
Technical field
The invention belongs to the topological relation constructing technology field between solid in three dimensions, particularly relate to a kind of three-dimensional topology relationship safeguard method based on union operation.
Background technology
Three-dimensional topology relation is most important spatial relationship in three dimensions, is the theoretical basis of three-dimensional space data expression, inquiry, analysis and application.Brown (1988) elaborates the topology importance to scientific research from the general extent, and from broadly giving propinquity and successional idea directly perceived.Use topology solve one of problem analysis the earliest example be in the Euler in 1735 research to Konigsberg bridge problem.Three-dimensional data are processed topological relation and spatial analysis is significant: 1) can clearly reflect the logical structure relation between entity；2) a lot of actual application problem can be solved, for instance the Path Selection in emergency escape；3) geographical entity can be rebuild according to topological relation.
Progress along with three-dimensional space data collection and treatment technology, the growth of the quantity size of three-dimensional space data collection exponentially formula, three-dimensional topology has more and more important effect in the fields such as three-dimensional space data modeling, the visualization of three-dimensional data validity check, three-dimensional data, three-dimensional applications analysis.Carson (1987) proposes to use a kind of method based on simplex to generate figure layer to support the analysis of geological model；Ladner (2001) describes and utilizes how topology synthesizes three-dimensional hybrid environment, the problem solving three-dimensional visualization；Spikins (2002) describes the importance that historic site is positioned by three dimensional analysis；Barcelo (2003) describes after obtaining three-dimensional archaeology data, determines the importance of accurate topological relation when finding historical relic near particular substrate.Particularly in three-dimensional land deeds field, soil updates to be needed three-dimensional ancestor is split and union operation, safeguards that the topological relation between body and body advantageously ensures that integrity and the concordance of topological data.
The current support that three-dimensional topology research is only limitted to substantially its Formal Representation and data model, but the support of the Formal Representation model that can contain all scenario of a not unification and completely data model, the difficulty of topology constructing be mainly reflected in following some: (1) Formal Representation model can't well describe all scenario of three-dimensional topology；(2) logic data model also can only partly support the structure of three-dimensional topology, it is impossible to contains all, it is achieved the structure of full topology；(3) production of data can't realize the automatization of computer, and the foundation of many data models needs manual intervention.Existing three-dimensional topology is rebuild in research, and the reconstruction of external topology (topological relation between body and body) is often out in the cold, and a lot of researchs are only for simple rule, body that structure is consistent, and outer topology is to lose.Additionally, topology constructing good after, segmentation, to merge the maintenance to topology be also a challenge, and segmentation, merging the new topology element produced needs and already present topology element maintenance topological coherence.The research built currently, with respect to three-dimensional topology relation only has a few studies of the author such as Li Lin (2012), Guo Renzhong (2012), safeguards that research is then less based on the topological relation after spatial operation.
Summary of the invention
In order to solve the problems referred to above, the present invention proposes a kind of topological dimension maintaining method based on three-dimensional geometry body union operation, it is possible to ensure the topological data concordance and the integrity that ensure between single internal and solid after merging operation in three dimensions.
The technical solution adopted in the present invention is: a kind of topological dimension maintaining method merged based on three-dimensional geometry body, it is characterised in that comprise the following steps:
Step 1: the face in the boundary face set of two individualities to be combined is carried out Boolean operations between two, obtain having equal, cover, comprise the face collection with overlapping relation；
Step 2: all line elements of relation face collection in step 1 are sentenced friendship between two；
If two lines section is non-intersect, then do not deal with；
If two lines section intersects, then according to the intersection point sentencing friendship, it being interrupted process, record interrupts the relation between the new and old line segment in front and back；
Step 3: opposite is concentrated has the face employing Boolean operations subdivision intersected with inclusion relation；
Step 4: in range of tolerable variance, merges the common element in two individualities to be combined, including step 3 subdivision common element out；
Step 5: after element merges, all topology elements of two individualities are all unique, carry out the merging of geometric element；
Step 6: update local topology relation according to the corresponding relation on new and old and new and old limit, record the corresponding relation of new and old body.
As preferably, implementing of step 1 includes following sub-step:
Step 1.1: calculate the straight line that two planes intersect with the plane equation of two planar chips, using intersection as scanning line L；
Step 1.2: sentence friendship respectively with the border of two planar chips with scanning line L, calculate intersection point, obtain intersecting straight lines section；
Step 1.3: identify all intersecting straight lines sections and joining, it is judged that the straightway type between joining, including internal area straightway, foreign lands straightway, boundary straight line section, boundary point；Wherein internal area straightway refers to that straight line intersects with the border of dough sheet and passes internal section of sub-line section gone out of dough sheet, foreign lands straightway refers to that straight line intersects with the border of dough sheet and passes outside section of sub-line section gone out of dough sheet, boundary straight line section refers to that straight line is overlapping with certain straightway of patch boundaries, and boundary point refers to certain boundary node passing straight through on patch boundaries；
Step 1.4: judge the crossing type in three-dimensional two faces according to straightway type.
As preferably, in step 1.3, the method of internal area straightway and foreign lands straightway that identifies is for behind given scanning line L direction, find first limit intersected with outer shroud by sequence with this direction, the vector that the edge-vector on this limit obtains with the direction vector multiplication cross of scanning line L is made comparisons with the normal vector in face, determine that it is positive and negative, and as benchmark；Outer annular edge edge-vector is every identical with benchmark with the result of scanning line L multiplication cross, must be the starting point of internal area straightway, if contrary with benchmark, must be the terminal of internal area straightway, the result contrast of the result of internal ring and outer shroud.
As preferably, if two lines section described in step 2 intersects, then according to the intersection point sentencing friendship, it being interrupted process, record interrupts the relation between the new and old line segment in front and back, and it implements process and includes following sub-step:
Step 2.1: if two line segments are parallel, it is judged that two line segments whether conllinear；If conllinear, it is judged that whether two line segments have intersection point；If not conllinear, it is judged that whether two line segments intersect in threshold range；
Step 2.2: if two line segments are not parallel, it is judged that whether two lines section is in threshold range relief area.
As preferably, judging that two lines section is whether in threshold range relief area described in step 2.2, it implements process and is: using Article 1 line segment as reference line segment, calculates two end points of Article 2 line segment to the mapping distance of reference line segment and mapping point；If the mapping distance of two end points is both less than threshold value, two end points mapping limit are all mapping points；If the mapping distance of an end points is less than threshold value, the mapping distance of another end points is more than threshold value, then the end points mapping limit is mapping point, and another end points is the initial point of Article 2 line segment；If Article 1 line segment is come to nothing as reference line segment, then using Article 2 line segment as reference line segment, carry out the calculating of mapping distance and mapping point；Obtain judging after mapping line segment the relationship type of itself and reference line segment.
As preferably, step 5 implements and includes following sub-step:
Step 5.1: point merges；
Relatively whether the coordinate figure of two points is equal in range of tolerable variance, if equal, indicates them for same point；Concrete grammar be according to arrange threshold value build corresponding three-dimensional grid, match closest grid according to a location, according to coupling mesh point uniquely change a little；
Step 5.2: line merges；
Relatively whether the coordinate figure of the beginning and end on two limits is equal in range of tolerable variance, if equal, indicates them for same limit；
Step 5.3: face is merged；
Compare the limit on two face outer shrouds and internal ring whether equal in range of tolerable variance, if equal, indicate them for same.
As preferably, step 6 implements and includes following sub-step:
Step 6.1: the preliminary merging of two individualities, deletes the common sides element between two individualities；
Step 6.2: process to merge and internal is connected with each other coplanar dough sheet, it is judged that whether two faces merged are shared face with the 3rd individuality, if then can not merge, if not then can be merged into a face；
Step 6.3: process and merge the internal line segment being connected with each other conllinear, if the line segment of conllinear is positioned at the limit on merging face, is merged into the same line.
Technical scheme provides after three-dimensional geometry body is merged operation, safeguards a kind of method of its internal and external topological relation, compensate for and said three-dimensional body carries out defect that topological relation after spatial operation is inconsistent in three dimensions.The core of the present invention is to find the common element of two individualities, and by common element, the topological relation of in vitro and in vivo after union operation safeguarded in record.By subdivision common sides the corresponding relation recording merging front and back element, accelerate the structure of local topology relation.Further it is proposed that method be applicable not only to the union operation between two individualities, and be applicable to the complex space operation between many individualities.
Accompanying drawing explanation
Fig. 1 is the flow chart of the embodiment of the present invention；
Fig. 2 is the union operation intersecting straight lines section schematic diagram of the embodiment of the present invention；
The union operation topology that Fig. 3 is the embodiment of the present invention safeguards result schematic diagram.
Detailed description of the invention
Understand for the ease of those of ordinary skill in the art and implement the present invention, below in conjunction with drawings and Examples, the present invention is described in further detail, should be appreciated that enforcement example described herein is merely to illustrate and explains the present invention, be not intended to limit the present invention.
Union operation carries out topology maintenance, if the number of merging body is more than 2, then merges between two, then merges with the 3rd individuality, and before union operation, the topological relation in single internal portion should be complete.
Ask for an interview Fig. 1, a kind of topological dimension maintaining method merged based on three-dimensional geometry body provided by the invention, comprise the following steps:
Step 1: the face in the boundary face set of two individualities to be combined is carried out Boolean operations between two, obtains having between two individualities the face of relation (equal, cover, comprise, overlapping relation) by the algorithm of computational geometry；
Step 1.1: calculate the crossing straight line of two planes as scanning line with the plane equation of two planar chips；
Step 1.2: sentence friendship respectively with the border of two planar chips with this scanning line, calculate intersection point；
Step 1.3: identify all intersecting straight lines sections and joining, it is judged that the straightway type between joining, as shown in Figure 2.Wherein internal area straightway refers to that straight line intersects with the border of dough sheet and passes internal section of sub-line section gone out of dough sheet, foreign lands straightway refers to that straight line intersects with the border of dough sheet and passes outside section of sub-line section gone out of dough sheet, boundary straight line section refers to that straight line is overlapping with certain straightway of patch boundaries, and boundary point refers to certain boundary node passing straight through on patch boundaries.In identifying, the method for foreign lands straightway is for after given scan-line direction, find first limit intersected with outer shroud by sequence with this direction, the vector that the edge-vector on this limit obtains with the direction vector multiplication cross of scanning line is made comparisons with the normal vector in face, it is determined that it is positive and negative, and as benchmark.Outer annular edge edge-vector is every identical with benchmark with the result of scanning line multiplication cross, must be the starting point of internal area straightway, if contrary with benchmark, must be the terminal of internal area straightway, the result of internal ring is exactly contrary with the result of outer shroud；
Step 1.4 judges the crossing type in three-dimensional two faces according to straightway type.
Step 2: all line elements of relation face collection in step 1 are sentenced friendship between two；
If two lines section is non-intersect, then do not deal with；
If two lines section intersects, then according to the intersection point sentencing friendship, it being interrupted process, record interrupts the relation between the new and old line segment in front and back；
Step 2.1: if two line segments are parallel, it is judged that two line segments whether conllinear；If conllinear, it is judged that whether two line segments have intersection point；If not conllinear, it is judged that whether two line segments intersect in threshold range；
Step 2.2: if two line segments are not parallel, it is judged that whether two lines section is in threshold range relief area；Using Article 1 line segment as reference line segment, calculate two end points of Article 2 line segment to the mapping distance of reference line segment and mapping point；If the mapping distance of two end points is both less than threshold value, two end points mapping limit are all mapping points；If the mapping distance of an end points is less than threshold value, the mapping distance of another end points is more than threshold value, then the end points mapping limit is mapping point, and another end points is the initial point of Article 2 line segment；If Article 1 line segment is come to nothing as reference line segment, then using Article 2 line segment as reference line segment, carry out the calculating of mapping distance and mapping point；Obtain judging after mapping line segment the relationship type of itself and reference line segment.
Step 3: after line is disposed, uses Boolean operations subdivision to the face having overlapping relation and inclusion relation, is unique by the common portion of subdivision in new face；
Step 4: in range of tolerable variance, merges the common element in two individualities to be combined, including step 3 subdivision common element out；
Step 4.1: point merges；
Relatively whether the coordinate figure of two points is equal in range of tolerable variance, if equal, indicates them for same point；Concrete grammar be according to arrange threshold value build corresponding three-dimensional grid, match closest grid according to a location, according to coupling mesh point uniquely change a little；
Step 4.2: line merges；
Relatively whether the coordinate figure of the beginning and end on two limits is equal in range of tolerable variance, if equal, indicates them for same limit；
Step 4.3: face is merged；
Compare the limit on two face outer shrouds and internal ring whether equal in range of tolerable variance, if equal, indicate them for same.
Step 5: after element merges, all topology elements of two individualities are all unique, carry out the merging of geometric element；
Step 5.1: the preliminary merging of two individualities, deletes the common sides element between two individualities；
Step 5.2: process to merge and internal is connected with each other coplanar dough sheet, it is judged that whether two faces merged are shared face with the 3rd individuality, if then can not merge, if not then can be merged into a face；
Step 5.3: process and merge the internal line segment being connected with each other conllinear, if the line segment of conllinear is positioned at the limit on merging face, is merged into the same line.
Step 6: update local topology relation according to the corresponding relation on new and old and new and old limit, record the corresponding relation of new and old body.
Ask for an interview Fig. 3, being that the union operation topology of the embodiment of the present invention safeguards result schematic diagram, in figure, two solids have common sides, and after being merged by geometry, common sides is deleted, new line segment is merged on the limit of conllinear, new and old topological relation record and merge after internal portion topological relation complete.
It should be appreciated that the part that this specification does not elaborate belongs to prior art.
Should be understood that; the above-mentioned description for preferred embodiment is comparatively detailed; therefore the restriction to scope of patent protection of the present invention can not be thought; those of ordinary skill in the art is under the enlightenment of the present invention; under the ambit protected without departing from the claims in the present invention; can also making replacement or deformation, each fall within protection scope of the present invention, the scope that is claimed of the present invention should be as the criterion with claims.
Claims (7)
1. the topological dimension maintaining method merged based on three-dimensional geometry body, it is characterised in that comprise the following steps:
Step 1: the face in the boundary face set of two individualities to be combined is carried out Boolean operations between two, obtain having equal, cover, comprise the face collection with overlapping relation；
Step 2: all line elements of relation face collection in step 1 are sentenced friendship between two；
If two lines section is non-intersect, then do not deal with；
If two lines section intersects, then according to the intersection point sentencing friendship, it being interrupted process, record interrupts the relation between the new and old line segment in front and back；
Step 3: opposite is concentrated has the face employing Boolean operations subdivision intersected with inclusion relation；
Step 4: in range of tolerable variance, merges the common element in two individualities to be combined, including step 3 subdivision common element out；
Step 5: after element merges, all topology elements of two individualities are all unique, carry out the merging of geometric element；
Step 6: update local topology relation according to the corresponding relation on new and old and new and old limit, record the corresponding relation of new and old body.
2. the topological dimension maintaining method merged based on three-dimensional geometry body according to claim 1, it is characterised in that implementing of step 1 includes following sub-step:
Step 1.1: calculate the straight line that two planes intersect with the plane equation of two planar chips, using intersection as scanning line L；
Step 1.2: calculate intersection point with two planar chips respectively with scanning line L, obtain intersecting straight lines section；
Step 1.3: identify all intersecting straight lines sections and joining, it is judged that the straightway type between joining, including internal area straightway, foreign lands straightway, boundary straight line section, boundary point；Wherein internal area straightway refers to that straight line intersects with the border of dough sheet and passes internal section of sub-line section gone out of dough sheet, foreign lands straightway refers to that straight line intersects with the border of dough sheet and passes outside section of sub-line section gone out of dough sheet, boundary straight line section refers to that straight line is overlapping with certain straightway of patch boundaries, and boundary point refers to certain boundary node passing straight through on patch boundaries；
Step 1.4: judge the crossing type in three-dimensional two faces according to straightway type.
3. the topological dimension maintaining method merged based on three-dimensional geometry body according to claim 2, it is characterized in that: in step 1.3, the method of internal area straightway and foreign lands straightway that identifies is for behind given scanning line L direction, find first limit intersected with outer shroud by sequence with this direction, the vector that the edge-vector on this limit obtains with the direction vector multiplication cross of scanning line L is made comparisons with the normal vector in face, determine that it is positive and negative, and as benchmark；Outer annular edge edge-vector is every identical with benchmark with the result of scanning line L multiplication cross, must be the starting point of internal area straightway, if contrary with benchmark, must be the terminal of internal area straightway, the result contrast of the result of internal ring and outer shroud.
4. the topological dimension maintaining method merged based on three-dimensional geometry body according to claim 1, it is characterized in that: if two lines section described in step 2 intersects, then according to the intersection point sentencing friendship, it is interrupted process, record interrupts the relation between the new and old line segment in front and back, and it implements process and includes following sub-step:
Step 2.1: if two line segments are parallel, it is judged that two line segments whether conllinear；If conllinear, it is judged that whether two line segments have intersection point；If not conllinear, it is judged that whether two line segments intersect in threshold range；
Step 2.2: if two line segments are not parallel, it is judged that whether two lines section is in threshold range relief area.
5. the topological dimension maintaining method merged based on three-dimensional geometry body according to claim 1, it is characterized in that, judge described in step 2.2 that two lines section is whether in threshold range relief area, it implements process: using Article 1 line segment as reference line segment, calculates two end points of Article 2 line segment to the mapping distance of reference line segment and mapping point；If the mapping distance of two end points is both less than threshold value, two end points mapping limit are all mapping points；If the mapping distance of an end points is less than threshold value, the mapping distance of another end points is more than threshold value, then the end points mapping limit is mapping point, and another end points is the initial point of Article 2 line segment；If Article 1 line segment is come to nothing as reference line segment, then using Article 2 line segment as reference line segment, carry out the calculating of mapping distance and mapping point；Obtain judging after mapping line segment the relationship type of itself and reference line segment.
6. the topological dimension maintaining method merged based on three-dimensional geometry body described in claim 1, it is characterised in that step 5 implements and includes following sub-step:
Step 5.1: point merges；
Relatively whether the coordinate figure of two points is equal in range of tolerable variance, if equal, indicates them for same point；Concrete grammar be according to arrange threshold value build corresponding three-dimensional grid, match closest grid according to a location, according to coupling mesh point uniquely change a little；
Step 5.2: line merges；
Relatively whether the coordinate figure of the beginning and end on two limits is equal in range of tolerable variance, if equal, indicates them for same limit；
Step 5.3: face is merged；
Compare the limit on two face outer shrouds and internal ring whether equal in range of tolerable variance, if equal, indicate them for same.
7. the topological dimension maintaining method merged based on three-dimensional geometry body described in claim 1, it is characterised in that step 6 implements and includes following sub-step:
Step 6.1: the preliminary merging of two individualities, deletes the common sides element between two individualities；
Step 6.2: process to merge and internal is connected with each other coplanar dough sheet, it is judged that whether two faces merged are shared face with the 3rd individuality, if then can not merge, if not then can be merged into a face；
Step 6.3: process and merge the internal line segment being connected with each other conllinear, if the line segment of conllinear is positioned at the limit on merging face, is merged into the same line.
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