CN102799750B - Method for quickly generating common side and non-common sides of geometry surface triangle - Google Patents
Method for quickly generating common side and non-common sides of geometry surface triangle Download PDFInfo
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- CN102799750B CN102799750B CN201210301738.2A CN201210301738A CN102799750B CN 102799750 B CN102799750 B CN 102799750B CN 201210301738 A CN201210301738 A CN 201210301738A CN 102799750 B CN102799750 B CN 102799750B
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Abstract
The invention provides a method for quickly generating a common side and non-common sides of geometry surface triangle and relates to a pretreatment technology for analyzing field problems by using computers. The method comprises the steps of: reading a surface-point incidence matrix of a triangular unit from data subdivided by a common mesh generator, and obtaining a point-surface incidence matrix through transposition; multiplying the surface-point incidence matrix by the point-surface incidence matrix to obtain a surface-surface adjacent matrix; and then sequentially traversing sides subdivided by a defined surface by using an adjacent relation of a discrete unit to obtain a side-point and side-surface incidence relation. The matrixes are stored by using a method of compressing a row main sequence by using a triple sequence list, and the transposition and multiplication operations adopt a corresponding sparse matrix algorithm. By using the method, a special mesh generator is avoided from developing, and side element information of the surface subdivision is quickly generated.
Description
Technical field
The present invention relates to a kind of fast geometric disposal route, belong to computer-aided analysis and design and software design arts, can be used in the Engineering Simulation analysis of the field problems such as electromagnetic field, stress field, thermal field, sound field, fluid.
Background technology
Based on the discrete engineering problem numerical analysis method of object subdivision because its applicability is wide, precision advantages of higher, widespread use in the Computer aided analysis of each engineering field.The most frequently used method of the discrete subdivision of usual body surface is triangle subdivision, and Geometric Modeling and subdivision can be completed by mesh generator, and the existing commercial copyright software of mesh generator also has free Open-Source Tools.For engineering problem, the discrete usual employing of integral equation divides territory basis function and point territory weight function.For vector field integral equation, general basis function and weight function are also defined in triangular element region unlike finite element method, but are defined in adjacent two triangular elements that leg-of-mutton common edge is associated.In actual computation, for face subdivision, need common edge and this two leg-of-mutton numberings of acquisition two adjacent triangle bins.
Conventional unit relation generation method is each limit by comparing discrete trigonometric shape unit between two, obtains common edge.The computation complexity of the method is
, wherein
for the number of Triangular patch.The method thinking is directly clear, but along with dimension of object increase, number of unit increases, and computing time will increase very fast.Therefore, a kind of computation complexity is needed to be that linear generation method is to improve treatment effeciency.
Summary of the invention
technical matters:the object of the invention is to propose a kind of common edge and not common limit rapid generation obtaining solid surface triangles subdivision from the data file that mesh generator subdivision obtains fast.By to the relationship analysis between point, line, surface different units, invent a kind of high efficiency generation method, to utilize existing mesh generator, realize general engineering vector field case study software, avoid the mesh generator that overlapping development is special, the computing cost that common edge and not common limit generate is down to minimum simultaneously.
technical scheme:for Surface Partition, the information that can directly obtain from mesh generator is: 3 node numbers of the coordinate figure that each node (distinguishing with node number) is corresponding and each triangular element (distinguishing with unit number) correspondence.Method proposed by the invention can complete the information extraction of discrete unit with minimum calculated amount, improve the pre-treatment speed of associated software.Concrete steps are as follows:
The first step, mesh generator is utilized to set up the geometric model of required simulation object, and carry out surface triangles mesh generation, derive the information of the grid cell of solid afterwards, comprise node coordinate message file and cell node message file and leg-of-mutton-some incidence matrix;
Second step, the data file obtained from mesh generator subdivision reads in a face-incidence matrix of node coordinate message file and triangle subdivision unit, and the method adopting tlv triple sequence list row-major order to compress stores a face-incidence matrix of triangle subdivision unit;
3rd step, a face-incidence matrix for diabolo utilizes sparse matrix transposition to obtain leg-of-mutton point-face incidence matrix;
4th step, leg-of-mutton-some incidence matrix is multiplied by point-face incidence matrix, and gained product divides exactly 2, and is set to 0 by diagonal line, obtains face-face adjacency matrix, adopts the method storage surface-face adjacency matrix of tlv triple sequence list row-major order compression;
5th step, the half of the off-diagonal non-zero entry number of face-face adjacency matrix is the number of common edge, according to bin number
, common edge number
with not common limit number
relation, by formula
not common limit unit number can be tried to achieve;
6th step, by bin number ergodic surface in turn-face adjacency matrix, generates limit-face incidence matrix and a limit-incidence matrix of common edge;
7th step, judges not common limit by bin number, if there is not common limit, is then stored in the limit-face incidence matrix on not common limit, record a limit-incidence matrix on not common limit simultaneously while generation common edge;
8th step, merges common edge metamessage and not common limit metamessage, obtains complete limit metamessage.
In the third step, be adopt sparse matrix transposition to obtain point-face incidence matrix, it is operating as the size prejudging out gained matrix, and accurate storage allocation, without the need to above quota distribution memory headroom, computation complexity is
.
Utilizing after sparse matrix transposition obtains point-face incidence matrix, the order of subsequent treatment is: first, generation face-face adjacency matrix, then each bin is traveled through in turn by bin number, to generate common edge metamessage and not common limit metamessage, be stored in one by one in a limit-association and limit-face incidence matrix, finally merge common edge metamessage and not common limit metamessage, obtain complete limit metamessage.
When generating face-face adjacency matrix, be adopt sparse matrix multiplication to carry out realization matrix to be multiplied; Be multiplied and adopt auxiliary one-dimension array, this one-dimension array is dividing exactly the non-zero element of gained after 2 stored in face-face adjacency matrix, and the computation complexity of this process and memory consumption are all
.
When obtaining complete limit metamessage, first judge common edge unit number according to face-face adjacency matrix, again by common edge unit number, not common limit unit's number and bin number relation, obtain not common limit unit number, then open and store common edge unit and the memory headroom needed for the unit of not common limit, without the need to above quota distribution memory headroom.
beneficial effect:the invention has the beneficial effects as follows, in field analysis, can directly utilize the data of mesh generator to obtain limit metamessage fast, and required memory cost and calculated amount little.Its advantage is: (1) avoids specially for edge element exploitation or the amendment mesh generator of face subdivision, decreases overlapping development; (2) obtain incidence matrix and adjacency matrix by sparse matrix compression storage, transposition and multiplication, it is all linear for storing with computation complexity
, be minimal complexity; (3) compared with openly fast method, the method that the present invention carries memory cost and calculated amount lower.
Accompanying drawing explanation
Fig. 1 is solid structural representation;
Fig. 2 is the schematic diagram that solid obtains through triangle subdivision;
Fig. 3 is figure computing time that the limit metamessage of one group of gore subdivision generates.
Embodiment
Below in conjunction with drawings and Examples, the invention will be further described.
The first step, mesh generator is utilized to set up the geometric model of required simulation object, and carry out surface triangles mesh generation, derive the information of the grid cell of solid afterwards, comprise node coordinate message file and cell node message file and leg-of-mutton-some incidence matrix;
Second step, the data file obtained from mesh generator subdivision reads in a face-incidence matrix of node coordinate message file and triangle subdivision unit, and the method adopting tlv triple sequence list row-major order to compress stores a face-incidence matrix of triangle subdivision unit;
3rd step, a face-incidence matrix transposition for diabolo obtains leg-of-mutton point-face incidence matrix;
4th step, leg-of-mutton-some incidence matrix is multiplied by point-face incidence matrix, and gained product divides exactly 2, and is set to 0 by diagonal line, obtains face-face adjacency matrix, adopts the method storage surface-face adjacency matrix of tlv triple sequence list row-major order compression;
5th step, the half of the off-diagonal non-zero entry number of face-face adjacency matrix is the number of common edge, according to bin number
, common edge number
with not common limit number
relation, by formula
not common limit unit number can be tried to achieve;
6th step, by bin number ergodic surface in turn-face adjacency matrix, generates limit-face incidence matrix and a limit-incidence matrix of common edge;
7th step, judges not common limit by bin number, if there is not common limit, is then stored in the limit-face incidence matrix on not common limit, record a limit-incidence matrix on not common limit simultaneously while generation common edge;
8th step, merges common edge metamessage and not common limit metamessage, obtains complete limit metamessage.
The concrete steps that the present invention generates limit metamessage to the solid shown in Fig. 1 are as follows:
Note: for sake of convenience, now specifies that leg-of-mutton element relation is as follows: leg-of-mutton, common edge, not common limit and dot element represent with f, lc, lb and n respectively, and its number is expressed as
,
,
with
; Common edge and not common be commonly referred to as while, be expressed as l;
,
,
,
with
presentation surface-Bian, limit-face, face-point, a point-face and limit-incidence matrix respectively;
for face-face adjacency matrix.
The first step, utilize mesh generator to set up the geometric model of spheroid, and carry out triangular mesh subdivision, as shown in Figure 2, derive the information of the grid cell of solid afterwards, comprise node coordinate message file and a cell node message file (i.e. gore-incidence matrix
).
Second step, reads in node coordinate message file and leg-of-mutton-some incidence matrix
, and the method storage surface-incidence matrix adopting tlv triple sequence list row-major order to compress
.
Compress the nonzero element storing and namely only store sparse matrix, except needing the value of storage nonzero element, store the position of its place row and column in addition
.A tlv triple order tableau format is
, it uniquely determines a nonzero element of matrix, wherein
be expressed as the position of its place row and column,
for the value of this nonzero element.Adopt the face-incidence matrix that row-major order compression stores
as follows, wherein the 1st row
iarrange with the 2nd
jbe respectively the line number of matrix non-zero element and row number, the 3rd row
vfor nonzero element value.
3rd step, a face-incidence matrix of diabolo
transposition obtains leg-of-mutton point-face incidence matrix
.
Obviously, point-face incidence matrix
non-zero entry number and a face-incidence matrix
non-zero entry number be the same.
Can realize this step by sparse matrix transposition, the transposition of sparse matrix is exactly change the row compression storage of original matrix into row compression to store, first by an ergodic surface-incidence matrix in fact
, find out the bin number corresponding to each point, set up array of indexes, again travel through unloading afterwards and just can obtain this point-face incidence matrix
, without the need to above quota distribution memory headroom.Adopt the point-face incidence matrix that row-major order compression stores
as follows, wherein the 1st row
iarrange with the 2nd
jbe respectively the line number of matrix non-zero element and row number, the 3rd row
vfor nonzero element value.
4th step, by leg-of-mutton-some incidence matrix
be multiplied by point-face incidence matrix
, gained product divides exactly 2, and is set to 0 by diagonal line, obtains face-face adjacency matrix
, adopt the method storage surface-face adjacency matrix of tlv triple sequence list row-major order compression
, shape as
Wherein the 1st row
iarrange with the 2nd
jbe respectively the line number of matrix non-zero element and row number, the 3rd row
vfor nonzero element value.
5th step, face-face adjacency matrix
the half of non-diagonal nonzero element number be the number of common edge
, and bin number, common edge and not common limit unit number meet as follows
.Not common limit unit number can be obtained thus
, be metamessage storage allocation space, limit below, and without the need to above quota distribution memory headroom.
6th step, by bin number ergodic surface-face adjacency matrix
, for certain bin, if adjacent bin number is greater than self, then records common edge, be stored in common edge-face incidence matrix, record a common edge-incidence matrix simultaneously, otherwise be recorded, skip.
7th step, judges not common limit by bin number, if current bin has 3 adjacent bins, shows that 3 limits in this face are all common edge, otherwise there is not common limit while generation common edge.The node ID of the common edge that 3 node ID comparing bin comprise with this bin, just obtains not common side information, is stored in the limit-face incidence matrix on not common limit, record a limit-incidence matrix on not common limit simultaneously.
8th step, merges common edge information and not common side information, obtains limit-face incidence matrix
with a limit-incidence matrix
.
Finally, in order to show validity of the present invention, giving the result of calculation of one group of triangle subdivision at Fig. 3, can find out that its computation complexity is
.
According to the above, just the present invention can be realized.
Claims (5)
1. the common edge of solid surface triangles subdivision and a not common limit rapid generation, is characterized in that the method realizes according to the following steps:
The first step, mesh generator is utilized to set up the geometric model of required simulation object, and carry out surface triangles mesh generation, derive the information of the grid cell of solid afterwards, comprise node coordinate message file and cell node message file and leg-of-mutton-some incidence matrix;
Second step, the data file obtained from mesh generator subdivision reads in a face-incidence matrix of node coordinate message file and triangle subdivision unit, and the method adopting tlv triple sequence list row-major order to compress stores a face-incidence matrix of triangle subdivision unit;
3rd step, a face-incidence matrix transposition for diabolo obtains leg-of-mutton point-face incidence matrix;
4th step, leg-of-mutton-some incidence matrix is multiplied by point-face incidence matrix, and gained product divides exactly 2, and is set to 0 by diagonal line, obtains face-face adjacency matrix, adopts the method storage surface-face adjacency matrix of tlv triple sequence list row-major order compression;
5th step, the half of the off-diagonal non-zero entry number of face-face adjacency matrix is the number of common edge, according to bin number N
f, common edge number N
lcwith not common limit number N
lbrelation, by formula 2N
lc+ N
lb=3N
fnot common limit unit number can be tried to achieve;
6th step, by bin number ergodic surface in turn-face adjacency matrix, for certain bin, if adjacent bin number is greater than self, then records common edge, be stored in common edge-face incidence matrix, record a common edge-incidence matrix simultaneously, otherwise be recorded, skip;
7th step, judges not common limit by bin number, if there is not common limit, is then stored in the limit-face incidence matrix on not common limit, record a limit-incidence matrix on not common limit simultaneously while generation common edge;
8th step, merges common edge metamessage and not common limit metamessage, obtains complete limit metamessage.
2. the common edge of solid surface triangles subdivision according to claim 1 and not common limit rapid generation, it is characterized in that, in the third step, adopt sparse matrix transposition to obtain point-face incidence matrix, its operation can prejudge out the size of gained matrix, and accurate storage allocation, without the need to above quota distribution memory headroom, computation complexity is O (N).
3. the common edge of solid surface triangles subdivision according to claim 1 and not common limit rapid generation, it is characterized in that, utilizing after sparse matrix transposition obtains point-face incidence matrix, the order of subsequent treatment is: first, generation face-face adjacency matrix, then each bin is traveled through in turn by bin number, to generate common edge metamessage and not common limit metamessage, be stored in a limit-association and limit-face incidence matrix one by one, finally merge common edge metamessage and not common limit metamessage, obtain complete limit metamessage.
4. the common edge of solid surface triangles subdivision according to claim 3 and not common limit rapid generation, it is characterized in that, when generating face-face adjacency matrix, adopt sparse matrix multiplication to carry out realization matrix to be multiplied, be multiplied and adopt auxiliary one-dimension array, this one-dimension array is dividing exactly the non-zero element of gained after 2 stored in face-face adjacency matrix, and the computation complexity of this process and memory consumption are all O (N).
5. the common edge of solid surface triangles subdivision according to claim 3 and not common limit rapid generation, it is characterized in that, obtaining in complete limit metamessage step, first judge common edge unit number according to face-face adjacency matrix, again by common edge unit number, not common limit unit's number and bin number relation, obtain not common limit unit number, then open and store common edge unit and the memory headroom needed for the unit of not common limit, without the need to above quota distribution memory headroom.
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| 导体磁场积分方程快速退化核算法的研究;许秀明;《中国优秀硕士学位论文全文数据库》;20120715;第9-13页 * |
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Application publication date: 20121128 Assignee: Jiangsu Nanyou IOT Technology Park Ltd. Assignor: NANJING University OF POSTS AND TELECOMMUNICATIONS Contract record no.: 2016320000209 Denomination of invention: Method for quickly generating common side and non-common sides of geometry surface triangle Granted publication date: 20150128 License type: Common License Record date: 20161111 |
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