CN1858937A - Automatic lattice dividing method for analyzing multiple antenna and scatterer structure by method of moment - Google Patents
Automatic lattice dividing method for analyzing multiple antenna and scatterer structure by method of moment Download PDFInfo
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- CN1858937A CN1858937A CN 200610042773 CN200610042773A CN1858937A CN 1858937 A CN1858937 A CN 1858937A CN 200610042773 CN200610042773 CN 200610042773 CN 200610042773 A CN200610042773 A CN 200610042773A CN 1858937 A CN1858937 A CN 1858937A
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Abstract
This invention discloses an automatic dividing method for networks to a multi-antenna-scattered structure with a moment method, which carries out three times of network partition to the dispersion surface on the basis of setting up geometrical models, firstly, it neglects antennas connected by the scatterer surfaces to apply a recursive dichotomy to divide the surface of the scatterer into triangles and quadrangles surface elements, secondly, it considers the antenna of the scatterer surface and divides the divided triangle and the quadrangle surface elements again into a square element with the line-surface link points at the center of the quadrangle, several triangles without line-surface link points and quadrangles in terms of different positions of the line-surface link points, thirdly, carries out network dividing to the narrow and long elements to get triangles and quadrangles even smaller than those of last two times.
Description
Technical field
The invention belongs to the electromagnetic compatibility technology field, relate to the used grid division methods of Numerical Calculation of Electromagnetic Field, specifically a kind of with the automatic mesh division methods of moment method to many antennas-scattering object structural analysis, can be used for the antenna degree of coupling, line current and surface current, field intensity and directional diagram calculating etc. vehicle-mounted, airborne, carrier-borne multiple antenna communication, to instruct and the assessment EMC Design.
Background technology
The antenna that has loaded different electronic equipment of various functions and various reception on Modern Communication System carrier such as vehicle, aircraft, the naval vessel and transmitted, these equipment and antenna are distributed in the comparison narrow space, as rationally not arranging, each electric room can produce very serious disturbance, and major part is to produce by the phase mutual interference between antenna separately, antenna is carried out rational deployment design can effectively solve phase mutual interference between antenna, whether reasonably the degree of coupling of calculating antenna can be used as estimates antenna arrangement foundation.Antenna and carrier surrounding space have electric field; this electric field exerts an influence to other communication equipments and the control electronics in the carrier surrounding space; when field intensity is strong, can burn out fragile electronic component or equipment; and stronger field intensity is harmful to health; calculate antenna electric current, calculate the electric current of carrier surface and then calculate field intensity, determine whether electronic equipment and personnel are taked safeguard measure according to the size of field intensity.
Vehicle-mounted, airborne, carrier-borne multiple antenna communication all can be summed up as many antennas-scattering object structure, and the antenna of the present invention's research is a whip antenna.For many antennas-scattering object structure, because antenna is thinner, can think that electric current only distributes along axis; Scattering object can be approximate with the metal guide dignity of sealing.When finding the solution this class problem, on lead, set up the field integral equation, on scattering surface, set up magnetic field integral equation, in the zone that antenna is connected with scattering surface, its limit of integration comprises straightway and conductor surface, need set up electric field and magnetic field mixing integral equation is found the solution.Find the solution these integral equations and can obtain the line current on the antenna and the surface current of scattering surface, and then can calculate the degree of coupling and the Electric Field Distribution of antenna.The numerical method of finding the solution these integral equations at present mainly is a moment method.The prerequisite that moment method is found the solution is that the grid of scattering surface is divided and the grid of antenna is divided, and the grid of antenna is divided and is easy to realize, and the division of the grid of scattering surface is difficult.
Because what the equation type of moment method and finite element model for solving was different, basic function and weight function are chosen is different, therefore, for electromagnetic problems, it is distinguishing dividing and divide based on the grid of finite element based on the grid of moment method.Be based on area-constrained grid as moment method and divide, promptly the area of grid bin size is relevant with wave frequency, and the bin size is that relative, antenna and the division of scattering surface junction have special requirement, adjacent bin node not necessarily hinged; And the finite element rule require adjacent bin node hinged, the absolute dimension of bin is had certain requirement.The grid of these two kinds of methods is divided also identical place, proper etc. as all having required preferably grid division quality, grid density.
At present more about the automatic mesh partitioning algorithm of finite element analysis, the grid partitioning technology is also comparatively ripe; And it is less based on the scattering surface grid division aspect automatically research of moment Method Analysis.Paper " grid that is used for communication command vehicle EMC design is divided and Display Technique " (computer engineering and design, the 24th the 12nd phase of volume, in December, 2003,58-61, author: Zhang Dengkui) with " grid of vehicle-mounted antenna system is divided simulation algorithm " (Computer Simulation, the 22nd the 1st phase of volume, in January, 2005,91-93, author: Guo Yuanyuan) the grid division methods of scattering surface has been done some researchs.The former paper is built the scattering object surface model and is made up of triangle and rectangle, and the face that connects antenna is limited to the horizontal rectangular face.For the rectangular surfaces that no antenna connects, the method that its grid is divided is several rectangle bin battle arrays for once divide equally this face by the area condition.For the rectangular surfaces that has antenna to connect, the method that its grid is divided is: at a certain line face binding site is the tie point of antenna and scattering surface, with this point is the center, with its distance to two nearest rectangular edges is the half of long rectangle of doing, wired binding site handled successively, and the part beyond the rectangle plane that comprises line face binding site is divided according to the conductor surface that no antenna connects.This division methods is only applicable to the situation of line face binding site near the rectangular surfaces edge.Latter's paper is built the scattering object surface model and is made up of triangle, rectangle and general quadrangle, and the face of connection antenna also is limited to the horizontal rectangular face.For the rectangular surfaces that no antenna connects, the method that its grid is divided is: from the midpoint of rectangle longest edge rectangle is divided into 2 little rectangles, circulation is carried out, and satisfies the area condition until the bin of dividing.For the general quadrilateral surface that no antenna connects, the method that its grid is divided is: connect short diagonal it is divided into two triangles, process by tessellation.For the rectangular surfaces that has antenna to connect, the method that its grid is divided is: the rectangular surfaces that connects by no antenna is divided earlier, obtain some rectangle bins, then separated time face binding site on rectangle bin summit, 3 kinds of situations are divided once more to relevant bin in rectangle bin inside, on rectangle bin limit, obtain a line face binding site rectangle bin and some other rectangle bins at the center.As can be seen, there is following problem in existing achievement in research: (1) line face binding site can not be on gore, the general quadrilateral surface; (2) surface location that connects antenna can not tilt; (3) bin that comprises line face binding site is not desirable square; (4) do not consider the processing of long and narrow bin.
The content of invention
The objective of the invention is to solve the problem that exists in the above-mentioned existing grid division, a kind of general grid division methods of scattering surface that is applicable to many antennas-scattering object structure moment Method Analysis is provided.
The object of the present invention is achieved like this:
It is to obtain meeting the grid bin that moment Method Analysis requires, i.e. triangle bin, quadrangle bin by three grids of scattering surface are divided on the geometrical model basis of being set up that grid of the present invention is divided.The principle that its grid is divided is: when setting up many antennas-scattering object construction geometry model, scattering object be the solid that the surface is sealed.Because curved surface can approach with the plane, so the scattering object surface finally can be represented with the plane.Suppose that scattering object is to be surrounded by some triangles, quadrangular plan sheet, because of the scattering surface magnetic field integral equation requires the surface normal vector outwardly, so the summit of triangle, quadrangular plan sheet should be counter clockwise direction in proper order during modeling.Grid is divided the division that comprises antenna and scattering surface, and antenna can be that 0.1 λ divides by line element length, realizes that than being easier to λ is electromagnetic wavelength.The grid of primary study scattering surface of the present invention is divided.Based on the requirement of moment method principle and consider the convergence of separating and the factor of accuracy two aspects, concrete principle is as follows:
(1) shape of bin adopts FInite Element triangle, quadrangle bin commonly used, so that calculate when dividing and the postposition processing of analysis result.Adopt single triangle or quadrilateral units increase sometimes grid quantity, influence the quality of unit.
(2) size of bin is moderate, if the bin area is excessive, the bin number of then dividing is just few, and computational accuracy is just low; If the bin area is too small, the bin number of then dividing is just many, and calculation scale and time just increase considerably, but the computational accuracy increase is very little, and reasonably the bin area is 0.01 λ
2
(3) bin of line face junction should be square, and makes line face binding site be in the center of square bin.
(4) bin can not be long and narrow, because moment method has adopted pulsed base and some apolegamy to find the solution integral equation, the electric current of whole like this bin is just used the electric current approximate representation at bin barycenter place, when bin is long and narrow, the electric current at barycenter place just can not be represented the electric current on this bin well, the result brings the error in the calculating, even can produce the singularity of separating.
Based on above principle, grid partition process of the present invention is as follows:
For the first time, ignore the antenna that the scattering object surface connects, adopt recursive bisection that the scattering object surface is divided into area and be less than or equal to 0.01 λ
2The triangle bin, the quadrangle bin that require;
For the second time, consider that the scattering object surface connects the structure of antenna, with the triangle bin divided, quadrangle bin diverse location by line face binding site, carry out grid more respectively and divide, obtain line face binding site at the square bin at quadrangle center with do not contain several triangles, the quadrangle bin of line face binding site;
For the third time, check and divided bin, grid for the first time and is for the second time divided long and narrow bin that the back occurs carries out grid again and divide, obtain the area comparison for the first time or for the second time grid divide littler triangle, the quadrangle bin of back area, to improve the quality of whole bin.
Above-mentioned automatic mesh division methods, wherein in the second time, grid was divided to the triangle bin divided, the quadrangle bin diverse location by line face binding site, carry out respectively again grid and divide, can further comprise; Grid to line face binding site position in the triangle bin or in the quadrangle bin is divided; The grid of line face binding site position in the common edge of two bins is divided; Line face binding site is divided at the grid of several bin public vertex positions; Line face binding site is in the inside on a bin limit, and the grid that overlaps again the position simultaneously with the summit of other bins is divided the grid division of four kinds of different situations.
Above-mentioned automatic mesh division methods, the grid of its center line face binding site position in the triangle bin or in the quadrangle bin is divided, and at first is to mark off an area less than 0.01 λ in described triangle or quadrangle bin
2Square, then remainder is divided, be that remainder is divided into a quadrangle and five triangles promptly for the triangle bin; For the quadrangle bin, be that remainder is divided into four quadrangles.
Above-mentioned automatic mesh division methods, the grid of its center line face binding site position in the common edge of two bins is divided, and comprises following three kinds of situations:
(1) grid of line face binding site in two quadrangle bin common edge divided, and is to mark off earlier an area less than 0.01 λ in described two quadrangle bins
2Square, then the remainder in two quadrangle bins is divided into six quadrangles;
(2) grid of line face binding site in the common edge of two triangle bins divided, and is to mark off an area earlier less than 0.01 λ in described two triangle bins
2Square, then the remainder in two triangle bins is divided into ten triangles;
(3) grid of line face binding site in the common edge of triangle and quadrangle two bins divided, and is to mark off earlier an area less than 0.01 λ in described triangle and two bins of quadrangle
2Square, then the remainder in described triangle and two bins of quadrangle is divided into five triangles and three quadrangles.
Above-mentioned automatic mesh division methods, its center line face binding site is divided at the grid of two bin public vertex positions at least, at first is to mark off an area less than 0.01 λ in these bins
2Square, ask difference to cut computing with each triangle in these bins or quadrangle bin respectively to this square then, after promptly triangle bin and square ask difference to cut the triangle bin is divided into a quadrangle or three triangles or a quadrangle and two triangles; After quadrangle bin and square ask difference to cut the quadrangle bin is divided into a quadrangle and triangle or two quadrangles or quadrangle and two triangles or five triangles.
Above-mentioned automatic mesh division methods, its center line face binding site are in the inside on a bin limit, and the grid that overlaps the position simultaneously again with the summit of other bins is divided, and comprises following two kinds of situations:
(1) line face binding site is in the inside on a quadrangle bin limit, and the grid that overlaps the position simultaneously again with the summit of other bins is divided, and at first finds out the opposite side mid point that comprises limit, line face binding site place in the described quadrangle bin, connecting line face binding site and this mid point; Then described quadrangle bin is divided into two quadrangles, these two quadrangles and summit have formed the situation of line face binding site at least two bin public vertex positions with the bin that line face binding site overlaps; Carrying out grid by line face binding site again in the grid division methods of at least two bin public vertex positions at last divides;
(2) line face binding site is in the inside on a triangle bin limit, the grid that overlaps simultaneously the position again with the summit of other bins is divided, at first comprise in connecting line face binding site and the described triangle bin line face binding site the limit right summit, described triangle bin is divided into two triangles, and these two triangles and summit have formed the situation of line face binding site at least two bin public vertex positions with the bin that line face binding site overlaps; Carrying out grid by line face binding site again in the grid division methods of at least two bin public vertex positions then divides.
Above-mentioned automatic mesh division methods is wherein carried out grid to the long and narrow bin that occurs after grid is divided for the first time and for the second time again and is divided, and comprises following two kinds of situations:
(1), finds out the diagonal angle α of longest edge, minor face and longest edge earlier for the triangle bin; Value m after the ratio of obtaining longest edge and minor face then rounds is if triangular shaped elongate ° is then thought in m 〉=3 or m＜3 and angle [alpha] 〉=120; Grid to the long and narrow bin of m 〉=3 is divided, and is with longest edge and vice-minister limit m five equilibrium, connects longest edge and the corresponding Along ent in vice-minister limit, is m-1 quadrangle and a triangle with this triangular shaped elongate binning; Grid to the long and narrow bin of m＜3 and angle [alpha] 〉=120 ° is divided, and is that this long and narrow bin is divided into two triangles along the longest edge center line, again these two triangles is carried out long and narrow judgement again by the condition that whether satisfies m 〉=3 and divides;
(2), find out longest edge earlier, the value m after the ratio of obtaining a longest edge and one adjacent side respectively rounds for the quadrangle bin
1, longest edge and its another adjacent side the value m of ratio after rounding
2, if m
1〉=3 and m
2〉=3, or m
1〉=3 and m
2＜3, or m
1＜3 and m
2Think that quadrangle is long and narrow for 〉=3; To m
1〉=3 and m
2The grid of 〉=3 long and narrow bin is divided, and at first finds out m
1, m
2The greater and be designated as k, should long and narrow tetragonal longest edge and opposite side k five equilibrium thereof, connect longest edge and the corresponding Along ent of opposite side thereof, obtain k quadrangle; To m
1〉=3 and m
2＜3, or m
1＜3 and m
2The grid of 〉=3 long and narrow bin is divided, and at first is that this quadrangle bin is divided into two triangles along short diagonal, these two triangles is judged with grid by the triangular shaped elongate bin again divided then.
The present invention compares with existing Meshing Method owing to adopted three grids to divide, and has following advantage:
(1) line face binding site can be on rectangular surfaces, gore, the general quadrilateral surface;
(2) connecting the surface location of antenna can level, vertically, tilt;
(3) bin that comprises line face binding site is desirable square;
(4) binning quality is preferably arranged.
Simulation analysis is the result show: general, reliable, the fast operation of grid division methods of the present invention.The scattering object surface mesh is divided and carried out parameters such as the antenna degree of coupling that moment Method Analysis draws, field strength distribution, directional diagram with method of the present invention and provide foundation for vehicle-mounted, airborne, carrier-borne communication system EMC Design.
Description of drawings
Fig. 1 is the triangle scattering surface grid division schematic diagram that the present invention does not have antenna.
Fig. 2 is the quadrangle scattering surface grid division schematic diagram that the present invention does not have antenna.
Fig. 3 is that the secondary grid of line face binding site of the present invention in the triangle bin divided schematic diagram.
Fig. 4 is that the secondary grid of line face binding site of the present invention in the quadrangle bin divided schematic diagram.
Fig. 5 is that line face binding site of the present invention is divided schematic diagram at the secondary grid of two quadrangle bin common edge.
Fig. 6 is that line face binding site of the present invention is divided schematic diagram at the secondary grid of two triangle bin common edge.
Fig. 7 is that the secondary grid of line face binding site of the present invention in triangle and quadrangle two bin common edge divided schematic diagram.
Fig. 8 is that line face binding site of the present invention is divided schematic diagram at the secondary grid of at least two bin public vertex.
Fig. 9 is that triangle bin of the present invention and the foursquare difference of asking are cut the division schematic diagram, wherein to be the triangle bin cut apart division schematic diagram with square intersects on one side to Fig. 9 a, Fig. 9 b be triangle bin and square both sides intersect and comprise a summit of square cut apart the division schematic diagram, Fig. 9 c be the triangle bin intersect and comprise square two summits with square both sides cut apart the division schematic diagram.
Figure 10 is that quadrangle bin of the present invention and the foursquare difference of asking are cut the division schematic diagram, wherein to be the quadrangle bin cut apart division schematic diagram with square intersects on one side to Figure 10 a, Figure 10 b be quadrangle bin and square both sides intersect and comprise a summit of square cut apart the division schematic diagram, Figure 10 c to be the quadrangle bin with square intersect on one side and comprise summit of square simultaneously by another summit of square cut apart the division schematic diagram, Figure 10 d be the quadrangle bin intersect and comprise square two summits with square both sides cut apart the division schematic diagram.
Figure 11 is that line face binding site of the present invention is divided schematic diagram at the secondary grid that the inside on quadrangle bin limit overlaps with the summit of other bins again simultaneously.
Figure 12 is that line face binding site of the present invention is divided schematic diagram at the secondary grid that the inside on triangle bin limit overlaps with the summit of other bins again simultaneously.
Figure 13 is the division schematic diagram of the long and narrow bin of diabolo of the present invention, and wherein Figure 13 a is the division schematic diagram of a kind of situation of triangular shaped elongate bin, and Figure 13 b is the division schematic diagram of the another kind of situation of triangular shaped elongate bin.
Figure 14 is the division schematic diagram of the present invention to the long and narrow bin of quadrangle, and wherein Figure 14 a is the division schematic diagram of a kind of situation of the long and narrow bin of quadrangle, and Figure 14 b is the division schematic diagram of the another kind of situation of the long and narrow bin of quadrangle.
Figure 15 is the instance graph that the present invention divides the rectangular pyramid model meshes, wherein Figure 15 a is the rectangular pyramid model of setting up, Figure 15 b is the rectangular pyramid model in frequency is the grid division figure of 80MHz when being wavelength X=3.75 meter, Figure 15 c is that antenna 1 is divided details drawing with the grid of scattering surface junction, Figure 15 d is that antenna 2 is divided details drawing with the grid of scattering surface junction, Figure 15 e is that antenna 3 is divided details drawing with the grid of scattering surface junction, and Figure 15 f is that antenna 4 is divided details drawing with the grid of scattering surface junction.
Figure 16 is the instance graph that the present invention divides the communication truck model meshes, wherein Figure 16 a is certain communication truck model of setting up, Figure 16 b is the communication truck model in tranmitting frequency is the grid division figure of 60MHz when being wavelength X=5 meter, Figure 16 c is that antenna 1, antenna 2 are the details drawings that the grid of antenna 3, antenna 4, antenna 5, antenna 6 and scattering surface junction is divided with the grid division of scattering surface junction and the details drawing of long and narrow binning, Figure 16 d.
Embodiment
Below in conjunction with accompanying drawing grid division methods of the present invention is described in further detail.
1. grid is divided for the first time
For the first time grid division connects by no antenna each surface of scattering object exactly and follows the area condition and carry out the grid division.The present invention has adopted the grid division methods of dichotomy, its basic thought is: for triangle, obtain the mid point of dough sheet longest edge earlier, connect mid point and relative summit thereof then, thereby the triangle that to obtain 2 areas are original dough sheet half of the area, so continuous recurrence is cut apart, and all meets area requirements until the bin of dividing, as shown in Figure 1.For quadrangle, obtain dough sheet longest edge and relative edge's thereof mid point earlier, connect two mid points then, thereby obtain 2 quadrangles, recurrence is cut apart constantly and is carried out like this, all meets area requirements until the bin of dividing.The advantage of dichotomy is: when not satisfying the area condition, the number that bin increases is original 2 times, and when reaching a certain frequency, the number of bin lacks than the number that additive method obtains, and can guarantee computational accuracy like this, can improve computational efficiency again.And the division processing procedure of this method diabolo and quadrilateral surface all is suitable for, and is easy to programming.
Grid for no antenna quadrangle scattering surface is divided as shown in Figure 2, and its process is as follows:
(1) reads in four apex coordinates of quad patch;
(2) judge tetragonal concavity and convexity,, otherwise change (3) if convex quadrangle then changes (4);
(3) find out this tetragonal concave crown point, connect concave crown point and relative summit thereof, obtain two triangles, and export its apex coordinate, call a grid that does not have sky thread triangle scattering surface then and divide algorithm, change (7) by inverse time pin mark preface;
(4) ask tetragonal area s, method is that this quadrangle is divided into two triangles, calculates two leg-of-mutton area sums and just can obtain tetragonal area, and triangle area can be pressed
Calculate, wherein a, b, c are the triangle length of side, and p is the triangle semi-perimeter;
(5) judge whether quadrangle satisfies area condition s≤0.01 λ
2If the quadrangle of dividing all satisfies the area condition, then change (7), otherwise change (6);
(6) find out the quadrangle longest edge that does not satisfy the area condition, calculate the mid point of longest edge and institute's opposite side thereof, quadrangle is divided into two little quadrangles, produce, change (4) by inverse time pin mark preface;
(7) export all bins after this dough sheet is divided.
Referring to Fig. 1, triangle A
1A
2A
3Scattering object surface when being Geometric Modeling, no antenna connects on it.This face is carried out for the first time grid divide namely that two minutes process is: find out triangle longest edge A
1A
2Mid point A
4, tie point A
3, A
4, with triangle A
1A
2A
3Be divided into two triangle A that area equates
1A
4A
3With A
2A
3A
4Calculate triangle A
1A
4A
3Area, it is worth greater than s, establishes s=0.01 λ
2, find out triangle A
1A
4A
3Longest edge A
1A
4Mid point A
5, tie point A
3, A
5, again with triangle A
1A
4A
3Be divided into two triangle A that area equates
1A
5A
3With A
3A
5A
4, in like manner again with triangle A
2A
3A
4Be divided into two triangle A that area equates
2A
6A
4With A
3A
4A
6Calculate triangle A
1A
5A
3Area, its value or greater than s, find out triangle A
1A
5A
3Longest edge A
1A
3Mid point A
7, tie point A
5, A
7, with triangle A
1A
5A
3Be further divided into two triangle A that area equates
1A
5A
7With A
3A
7A
5, in like manner with triangle A
3A
5A
4Be divided into two triangle A that area equates
3A
5A
8With A
4A
8A
5, again with triangle A
2A
6A
4Be divided into two triangle A that area equates
2A
6A
10With A
4A
10A
6, again with triangle A
3A
4A
6Be divided into two triangle A that area equates
3A
4A
9With A
4A
6A
9Calculate triangle A
1A
5A
7Area, it is worth less than s, output triangle bin A
1A
5A
7With A
3A
7A
5Calculate triangle A
3A
5A
8Area, it is worth less than s, output triangle bin A
3A
5A
8With A
4A
8A
5Calculate triangle A
2A
6A
10Area, it is worth less than s, output triangle bin A
2A
6A
10With A
4A
10A
6Calculate triangle A
3A
4A
9Area, it is worth less than s, output triangle bin A
3A
4A
9With A
4A
6A
9Triangle A
1A
2A
3Obtain A through the first time after the grid division
1A
5A
7, A
3A
7A
5, A
3A
5A
8, A
4A
8A
5, A
2A
6A
10, A
4A
10A
6, A
3A
4A
9, A
4A
6A
9Totally 8 little triangle bins.
Referring to Fig. 2, convex quadrangle A
1A
2A
3A
4Scattering object surface when being Geometric Modeling, no antenna connects on it.This face is carried out for the first time grid divide promptly that two minutes process is: find out quadrangle A
1A
2A
3A
4Longest edge A
1A
2Mid point A
5, its opposite side A
3A
4Mid point A
6, tie point A
5, A
6, with quadrangle A
1A
2A
3A
4Be divided into two quadrangle A
1A
5A
6A
4With A
2A
3A
6A
5Calculate quadrangle A
1A
5A
6A
4Area, it is worth greater than s, finds out quadrangle A
1A
5A
6A
4Longest edge A
1A
4Mid point A
7, its opposite side A
5A
6Mid point A
8, tie point A
7, A
8, with quadrangle A
1A
5A
6A
4Be divided into two quadrangle A
1A
5A
8A
7With A
4A
7A
8A
6, in like manner with quadrangle A
2A
3A
6A
5Be divided into two quadrangle A
2A
3A
10A
9With A
5A
9A
10A
6Calculate quadrangle A
1A
5A
8A
7Area, its value is found out quadrangle A still greater than s
1A
5A
8A
7Longest edge A
1A
5Mid point A
11, its opposite side A
7A
8Mid point A
12, tie point A
11, A
12, with quadrangle A
1A
5A
8A
7Be divided into two quadrangle A
1A
11A
12A
7With A
5A
8A
12A
11, in like manner with quadrangle A
4A
7A
8A
6Be divided into two quadrangle A
4A
7A
12A
13With A
6A
13A
12A
8, with quadrangle A
2A
3A
10A
9Be divided into two quadrangle A
2A
15A
14A
9With A
3A
10A
14A
15, with quadrangle A
5A
9A
10A
6Be divided into two quadrangle A
5A
9A
14A
8With A
6A
8A
14A
10Calculate quadrangle A
1A
11A
12A
7Area, it is worth less than s, output quadrangle bin A
1A
11A
12A
7In the same way and the like, export seven quadrangle bin: A
5A
8A
12A
11A
4A
7A
12A
13A
6A
13A
12A
8A
2A
15A
14A
9A
3A
10A
14A
15A
5A
9A
14A
8A
6A
8A
14A
10This convex quadrangle A
1A
2A
3A
4After the first time, grid was divided, finally obtain A
1A
11A
12A
7A
5A
8A
12A
11A
4A
7A
12A
13A
6A
13A
12A
8A
2A
15A
14A
9A
3A
10A
14A
15A
5A
9A
14A
8A
6A
8A
14A
10Totally 8 little quadrangle bins.
2. grid is divided for the second time
For the second time grid division is on the basis of dividing for the first time the bin that is connected with antenna once to be divided again.Consider that the scattering object surface connects the structure of antenna, divide for the second time is that the triangle bin that will divide, quadrangle bin are by the diverse location of line face binding site, carry out respectively again grid and divide, obtain line face binding site at a square bin at quadrangle center and do not contain several triangles, the quadrangle bin of line face binding site.Grid division to this diverse location comprises four kinds of different situations: the one, the grid of line face binding site position in the triangle bin or in the quadrangle bin is divided; The 2nd, the grid of line face binding site position in the common edge of two bins is divided; The 3rd, line face binding site is divided at the grid of several bin public vertex positions; The 4th, in the inside on a bin limit, the grid that overlaps the position simultaneously again with the summit of other bins is divided to line face binding site.
(1) grid of line face binding site position in the triangle bin or in the quadrangle bin is divided
Grid partition process to line face binding site position in the triangle bin or in the quadrangle bin is: at first construct one less than 0.01 λ
2The square of area condition is cut apart remainder then, is that remainder is divided into a quadrangle and five triangles for the triangle bin promptly; For the quadrangle bin, be that remainder is divided into four quadrangles.
Referring to Fig. 3, the grid partition process of line face binding site O in triangle bin ABC is: obtain the minimum range d of an O to triangle ABC three limits earlier; Be the origin of coordinates again with A, to be that X-axis is set up local coordinate system apart from the AB limit of minimum, will put O, A, B, the C Coordinate Conversion is a local coordinate to some O; Being the center of circle with O then, is that the structure length of side is in the circle of radius with d/2
Square EFGH, make the FG limit be parallel to X-axis; Then triangle bin ABC is divided into 1 square EFGH, 1 quadrangle ABGF, 5 triangle AFE, AEC, CEH, CHB, BHG; Coordinate Conversion with these 7 little bins is world coordinates and exports these bins at last, can realize the secondary grid division of line face binding site O in triangle bin ABC.
Referring to Fig. 4, the secondary grid partition process of line face binding site O in quadrangle bin ABCD is: ask the minimum range d of an O to quadrangle four limits, the AB limit is to the limit of an O apart from minimum, with A is that the origin of coordinates, AB limit are that X-axis is set up local coordinate system, will put O, A, B, C, the D Coordinate Conversion is a local coordinate; Be that the center of circle, d/2 are that the structure length of side is in the circle of radius with O
Square EFGH, make the FG limit be parallel to X-axis; Quadrangle bin ABCD is divided into 1 square EFGH, 4 quadrangle ABGF, BCHG, CDEH, AFED; The Coordinate Conversion of these 5 little bins is world coordinates and exports these bins and can realize the secondary grid division of line face binding site O in quadrangle bin ABCD.
(2) grid of line face binding site position in the common edge of two bins is divided
For the situation of line face binding site in the common edge of two bins, comprise three kinds: the one, the grid of line face binding site in two quadrangle bin common edge divided, the 2nd, the grid of line face binding site in the common edge of two triangle bins divided, and the 3rd, the grid of line face binding site in the common edge of triangle and quadrangle two bins divided.
Divide for the grid of line face binding site in two quadrangle bin common edge: be in described two quadrangle bins, to mark off an area earlier less than 0.01 λ
2Square, then the remainder in two quadrangle bins is divided into six quadrangles, as shown in Figure 5.
Referring to Fig. 5, line face binding site O is at two quadrangle bin A
1A
2A
3A
4, B
1B
2B
3B
4Common edge A
1A
4, B
1B
4In secondary grid partition process be: ask a minimum range d on O to two each limit of quadrangle, take O as the origin of coordinates, common edge A
1A
4For X-axis is set up local coordinate system, will put O, A
1, A
2, A
3, A
4, B
1, B
2, B
3, B
4Coordinate Conversion is local coordinate; Again take O as the center of circle, d/2 in the circle of radius the structure length of side as
Square EFGH, make the FG limit be parallel to X-axis; Then with two quadrangle bin A
1A
2A
3A
4, B
1B
2B
3B
4Be divided into 1 square EFGH, 6 quadrangle A
1A
2FP, A
2A
3GF, A
3A
4QG, B
1B
2HQ, B
2B
3EH, B
3B
4PE; Coordinate Conversion with these 7 little bins is world coordinates and exports these bins and can realize that line face binding site O is at two quadrangle bin A at last
1A
2A
3A
4, B
1B
2B
3B
4Common edge A
1A
4, B
1B
4Interior secondary grid is divided.Symbol P is the intersection point of EF limit and common edge, and Q is the intersection point of GH limit and common edge.
Dividing for the grid of line face binding site in the common edge of two triangle bins, is to mark off earlier an area less than 0.01 λ in described two triangle bins
2Square, then the remainder in two triangle bins is divided into ten triangles, as shown in Figure 6.
Referring to Fig. 6, line face binding site O is at two triangle bin A
1A
2A
3, B
1B
2B
3Common edge A
1A
3, B
1B
3In secondary grid partition process be: ask a minimum range d on O to two each limit of triangle, take O as the origin of coordinates, common edge A
1A
3For X-axis is set up local coordinate system, will put O, A
1, A
2, A
3, B
1, B
2, B
3Coordinate Conversion is local coordinate; Take O as the center of circle, d/2 in the circle of radius the structure length of side as
Square EFGH, make the FG limit be parallel to X-axis; Then with two triangle bin A
1A
2A
3, B
1B
2B
3Be divided into 1 square EFGH, 10 triangle A
1FP, A
1A
2F, A
2GF, A
2A
3G, A
3QG, B
1HQ, B
1B
2H, B
2EH, B
2B
3E, B
3PE; Coordinate Conversion with these 11 little bins is world coordinates and exports these bins and can realize that line face binding site O is at two triangle bin A at last
1A
2A
3, B
1B
2B
3Common edge A
1A
3, B
1B
3Interior secondary grid is divided.Symbol P is the intersection point of EF limit and common edge, and Q is the intersection point of GH limit and common edge.
Dividing for the grid of line face binding site in the common edge of triangle and quadrangle two bins, is to mark off earlier an area less than 0.01 λ in described triangle and two bins of quadrangle
2Square, then the remainder in described triangle and two bins of quadrangle is divided into five triangles and three quadrangles, as shown in Figure 7.
Referring to Fig. 7, line face binding site O is at triangle bin A
1A
2A
3, quadrangle bin B
1B
2B
3B
4Common edge A
1A
3, B
1B
4In secondary grid partition process be: ask a minimum range d on O to two each limit of bin, take O as the origin of coordinates, common edge A
3A
1For X-axis is set up local coordinate system, will put O, A
1, A
2, A
3, B
1, B
2, B
3, B
4Coordinate Conversion is local coordinate; Take O as the center of circle, d/2 in the circle of radius the structure length of side as
Square EFGH, make the FG limit be parallel to X-axis; Then with triangle bin A
1A
2A
3, quadrangle bin B
1B
2B
3B
4Be divided into 1 square EFGH, 5 triangle A
1HQ, A
1A
2H, A
2EH, A
2A
3E, A
3PE, 3 quadrangle B
1B
2FP, B
2B
3GF, B
3B
4QG; Coordinate Conversion with these 9 little bins is world coordinates and exports these bins and can realize that line face binding site O is at triangle bin A at last
1A
2A
3, quadrangle bin B
1B
2B
3B
4Common edge A
1A
3, B
1B
4Interior secondary grid is divided.Symbol Q is the intersection point of HG limit and common edge, and P is the intersection point of EF limit and common edge.
(3) line face binding site is divided at the grid of two bin public vertex positions at least
Dividing at the grid of at least two bin public vertex positions for line face binding site, at first is to mark off an area less than 0.01 λ in these bins
2Square, ask difference to cut computing with each triangle in these bins or quadrangle bin respectively to this square then, after promptly triangle bin and square ask difference to cut the triangle bin is divided into a quadrangle or three triangles or a quadrangle and two triangles; After quadrangle bin and square ask difference to cut the quadrangle bin is divided into a quadrangle and triangle or two quadrangles or quadrangle and two triangles or five triangles, as Fig. 8, Fig. 9, shown in Figure 10.
Referring to Fig. 8, line face binding site O is at 4 bin OABC, OA
1A
2A
3, OA
3A
4A
5, OA
6A
7The secondary grid partition process on A summit is: ask binding site O to the minimum range d of described these bin opposite side, this opposite side is and the unconnected limit of binding site; Have on the bin OABC of minimum range d take O as the origin of coordinates, limit OA sets up local coordinate system as X-axis, will put that all bin apex coordinates are converted to local coordinate in O and described these bins; Again take O as the center of circle, d/2 in the circle of radius the structure length of side as
Square EFGH, make the FG limit be parallel to X-axis; Described these bins are done with square EFGH respectively ask difference to cut computing, wherein bin OABC asks difference to cut and obtains quadrangle ABHP, BCQH, bin OA
1A
2A
3Ask difference to cut and obtain quadrangle A
1A
2EQ, A
2A
3RE, bin OA
3A
4A
5Ask difference to cut and obtain quadrangle A
3A
4FR, A
4A
5SF, bin OA
6A
7A asks difference to cut and obtains quadrangle A
6A
7GS, A
7APG; At last with square bin EFGH and 8 quadrangle facets unit ABHP, BCQH, A
1A
2EQ, A
2A
3RE, A
3A
4FR, A
4A
5SF, A
6A
7GS, A
7The Coordinate Conversion of APG is world coordinates and exports these bins, can realize that line face binding site O is at 4 bin OABC, OA
1A
2A
3, OA
3A
4A
5, OA
6A
7The secondary grid on A summit is divided.
Referring to Fig. 9, triangle bin ABO and the foursquare difference of asking are cut three kinds of situations: to be triangle bin ABO cut apart division with square intersects on one side to Fig. 9 a, is divided into 1 quadrangle bin ABQP after this triangle bin ABO is asked difference to cut; Fig. 9 b is the division of cutting apart that 1 summit of square is intersected and comprised on triangle bin ABO and square both sides, is divided into 3 triangle bin AA after triangle bin ABO is divided
1P, ABA
1, A
1BQ; Fig. 9 c is the division of cutting apart that 2 summits of square are intersected and comprised on triangle bin ABO and square both sides, is divided into 1 quadrangle bin ABA after triangle bin ABO is divided
2A
1With 2 triangle bin AA
1P, BQA
2Symbol P, Q are the intersection point on triangle edges and square limit.
Referring to Figure 10, quadrangle bin ABCO and the foursquare difference of asking are cut four kinds of situations: to be quadrangle bin ABCO cut apart division with square intersects on one side to Figure 10 a, is divided into 1 quadrangle bin ACQP and 1 triangle bin ABC after quadrangle bin ABCO is divided; Figure 10 b is the division of cutting apart that 1 summit of square is intersected and comprised on quadrangle bin ABCO and square both sides, is divided into 2 quadrangle bin ABA after quadrangle bin ABCO is divided
1P, BCQA
1Figure 10 c is that quadrangle bin ABCO intersects and comprise 1 summit of square on one side simultaneously by the division of cutting apart on another summit of square with square, is divided into 1 quadrangle bin ABA after quadrangle bin ABCO is divided
1P and 2 triangle bin BCA
1, CQA
1Figure 10 d is the division of cutting apart that 2 summits of square are intersected and comprised on quadrangle bin ABCO and square both sides, is divided into 5 triangle bin AA after quadrangle bin ABCO is divided
1P, ABA
1, BA
2A
1, BCA
2, CQA
2Symbol P, Q are the intersection point on quadrangle limit and square limit.
(4) line face binding site is in the inside on a bin limit, and the grid that overlaps the position simultaneously again with the summit of other bins is divided
Line face binding site is in the inside on a bin limit, and the grid that overlaps again the position simultaneously with the summit of other bins is divided, and comprises following two kinds of situations:
First kind of situation is: line face binding site is in the inside on a quadrangle bin limit, and the grid that overlaps the position simultaneously again with the summit of other bins is divided.The opposite side mid point that comprises limit, line face binding site place in the described quadrangle bin is at first found out in the division of this situation, connecting line face binding site and this mid point; Then described quadrangle bin is divided into two quadrangles, these two quadrangles and summit have formed the situation of line face binding site at least two bin public vertex positions with the bin that line face binding site overlaps; Carry out grid by above-mentioned line face binding site again in the grid division methods of at least two bin public vertex positions at last and divide, as shown in figure 11.
Referring to Figure 11, the secondary grid partition process when line face binding site O overlaps with the summit of other 2 bins again in the inside of quadrangle bin ABCD limit AB simultaneously is: obtain the mid point M of AB edge-to-edge CD, quadrangle ABCD is divided into two quadrangles of AOMD, BCMO; Two quadrangles of AOMD, BCMO and summit are continued to divide by the grid division methods of line face binding site at least two bin public vertex positions with other 2 bins that an O overlaps.
Second kind of situation is: line face binding site is in the inside on a triangle bin limit, the grid that overlaps simultaneously the position again with the summit of other bins is divided, the division of this situation at first comprise in connecting line face binding site and the described triangle bin line face binding site the limit right summit, again described triangle bin is divided into two triangles, these two triangles and summit have formed the situation of line face binding site at least two bin public vertex positions with the bin that line face binding site overlaps; Carry out grid by above-mentioned line face binding site again in the grid division methods of at least two bin public vertex positions at last and divide, as shown in figure 12.
Referring to Figure 12, the secondary grid partition process when line face binding site O overlaps with the summit of other 3 bins again in the inside of triangle bin ABC limit AB simultaneously is: tie point O and summit C are divided into two triangles of AOC, BCO with triangle ABC; Two triangles of AOC, BCO and summit are continued to divide by the grid division methods of line face binding site at least two bin public vertex positions with other 3 bins that an O overlaps.
3. grid is divided for the third time
For the third time grid division is after grid is divided for the first time and for the second time, the bin of having divided is checked, to checking that the long and narrow bin that occurs carries out grid again and divides, obtain Area Ratio to littler triangle, the quadrangle bin of area after grid is divided for the first time or for the second time, to improve the quality of whole bin.This time division comprises following two kinds of situations:
(1) for the division of long and narrow triangle bin, shown in Figure 13 a, Figure 13 b.
With reference to Figure 13 a, ABC is a long and narrow triangle bin, and finding out earlier longest edge is AB, and minor face is BC; Value m after the ratio of obtaining then longest edge AB and minor face BC rounds, i.e. m=3; With AB and vice-minister limit AC trisection, the result is divided into 2 quadrangle bin A with triangle ABC again
1A
2A
4A
3, A
2BCA
4With 1 triangle bin AA
1A
3
Referring to Figure 13 b, DEF is another long and narrow triangle bin, and finding out longest edge earlier is DF, and minor face is DE, diagonal angle α=135 of DF °; Value m after the ratio of obtaining longest edge DF and minor face DE then rounds, i.e. m=2; Obtain the mid point M of DF again, tie point E, M, the result is divided into 2 triangle DEM, EFM with triangle DEF.
(2) for the division of long and narrow quadrangle bin, shown in Figure 14 a, Figure 14 b.
With reference to Figure 14 a, ABCD is a long and narrow quadrangle bin, and finding out earlier longest edge is AB, and the adjacent side of AB is BC, AD, the value m after the ratio of obtaining then longest edge AB and adjacent side BC rounds
1, i.e. m
1=3, the value m after the ratio of obtaining longest edge AB and another adjacent side AD rounds
2, i.e. m
2=3; With AB and its opposite side CD trisection, the result is divided into 3 quadrangle bin AA with quadrangle ABCD again
1A
3D, A
1A
2A
4A
3, A
2BCA
4
Referring to Figure 14 b, EFGH is another long and narrow quadrangle bin, and finding out longest edge earlier is EF, and the adjacent side of EF is FG, EH, the value m after the ratio of obtaining longest edge EF and adjacent side FG then rounds
1, i.e. m
1=3, the value m after the ratio of obtaining longest edge EF and another adjacent side EH rounds
2, i.e. m
2=1; Again quadrangle EFGH is divided into 2 triangle bin EFH, FGH along short diagonal FH.
Simulation example 1
The present invention carries out emulation graticule to the rectangular pyramid model and divides, and process and result that this grid is divided are as follows.
(1) sets up the rectangular pyramid model
The pyramid of this rectangular pyramid model is formed by 4 gores, 1 quadrilateral surface envelope, bores high 4 meters; Respectively place 1 whip antenna on 4 incline faces of rectangular pyramid, the length of antenna is 3 meters, shown in Figure 15 a.
(2) institute's established model being carried out three grids respectively divides
Be that 80MHz carries out earlier first time grid to this model under the condition of wavelength X=3.75 meter to divide in the antenna transmission frequency, obtain 642 triangle bins and quadrangle bin; The triangle bin that then 4 antennas is connected carries out respectively the grid division second time again by the position difference of line face binding site, Figure 15 c is that antenna 1 is divided details drawing with the grid of scattering surface junction, and inner 1 the triangle bin that is generated by for the first time division that comprises line face binding site is divided into 1 square bin, 1 quadrangle bin and 5 triangle bins among this figure when dividing for the second time.Figure 15 d is that antenna 2 is divided details drawing with the grid of scattering surface junction, and 8 triangle bins that generated by for the first time division that public vertex overlaps with line face binding site position among this figure are divided into 1 square bin, 4 quadrangle bins and 12 triangle bins when dividing for the second time.Figure 15 e is that antenna 3 is divided details drawing with the grid of scattering surface junction, and common edge comprises 2 of line face binding site and is divided into 1 square bin and 10 triangle bins by dividing the triangle bins that generate for the first time when dividing for the second time among this figure.Figure 15 f is that antenna 4 is divided details drawing with the grid of scattering surface junction, and 4 triangle bins that generated by for the first time division that public vertex overlaps with line face binding site position among this figure are divided into 1 square bin and 12 triangle bins when dividing for the second time.For the second time grid division of bin by to 4 antenna line face binding site places obtains 675 triangle bins and quadrangle bin, at last shown in Figure 15 b.For the second time grid has been divided and rear these 675 triangle bins and quadrangle bin has been carried out long and narrow judgement, prepares to carry out for the third time grid and divides, and by judging the bin that satisfies long and narrow condition is not arranged, so the bin sum after three grids are divided still is 675.
Simulation example 2
The present invention carries out emulation graticule to the communication truck model and divides, and process and result that this grid is divided are as follows.
(1) sets up the communication truck model
This communication truck model is made up of car body and antenna, and the scattering surface of envelope car body has 8 triangles, 5 rectangles and 8 general quadrangles, and 6 whip antennas are arranged, wherein have 1 antenna tilt, on the non-rectangle face, shown in Figure 16 a.
(2) institute's established model being carried out three grids respectively divides
Be that 60MHz carries out earlier first time grid to this model under the condition of wavelength X=5 meter to divide in the antenna transmission frequency, obtain 528 triangle bins and quadrangle bin; The quadrangle bin that then 6 antennas is connected carries out respectively the grid division second time again by the position difference of line face binding site, Figure 16 c is that antenna 1, antenna 2 are divided details drawing with the grid of scattering surface junction, and inner 1 of comprising antenna 1 and scattering surface binding site divides the quadrangle bin that generates by the first time and be divided into 1 square bin and 4 quadrangle bins when dividing for the second time among this figure.The grid division second time of antenna 2 and scattering surface junction and antenna 1 are roughly the same.Figure 16 d is the details drawing that the grid of antenna 3, antenna 4, antenna 5, antenna 6 and scattering surface junction is divided, and inner 1 the quadrangle bin that is generated by division for the first time that comprises antenna 3 and scattering surface binding site is divided into 1 square bin and 4 quadrangle bins among this figure when dividing for the second time.The grid division second time of antenna 4, antenna 5, antenna 6 and scattering surface junction and antenna 3 are roughly the same.For the second time grid division of bin by to 6 antenna line face binding site places obtains 546 triangle bins and quadrangle bin, at last shown in Figure 16 b.For the second time grid has been divided and rear these 546 triangle bins and quadrangle bin has been carried out long and narrow judgement, for the third time grid division is carried out in preparation, find to have 1 long and narrow triangle bin by judging, shown in Figure 16 c, the label 7 among Figure 16 c refers to 1 the triangular shaped elongate bin that produces after grid is divided for the first time and be divided into 2 triangle bins and 4 quadrangle bins when for the third time grid division.Bin after three times grid has been divided adds up to 551.
Claims (7)
1. one kind with the automatic mesh division methods of moment method to many antennas-scattering object structural analysis, be by three grids of scattering surface are divided on the basis of foundation antenna-scattering object geometrical model, obtain meeting the grid bin that moment Method Analysis requires, its detailed process is as follows:
For the first time, ignore the antenna that the scattering object surface connects, adopt recursive bisection that the scattering object surface is divided into area and be less than or equal to 0.01 λ
2The triangle bin, the quadrangle bin that require;
For the second time, consider that the scattering object surface connects the structure of antenna, with the triangle bin divided, quadrangle bin diverse location by line face binding site, carry out grid more respectively and divide, obtain line face binding site at the square bin at quadrangle center with do not contain several triangles, the quadrangle bin of line face binding site;
For the third time, check and divided bin, grid for the first time and is for the second time divided long and narrow bin that the back occurs carries out grid again and divide, obtain the area comparison for the first time or for the second time grid divide littler triangle, the quadrangle bin of back area, to improve the quality of whole bin.
2. automatic mesh division methods according to claim 1, wherein in the second time, grid was divided to the triangle bin divided, quadrangle bin diverse location by line face binding site, carry out grid more respectively and divide, can further comprise: the grid to line face binding site position in the triangle bin or in the quadrangle bin is divided; The grid of line face binding site position in the common edge of two bins is divided; Line face binding site is divided at the grid of several bin public vertex positions; Line face binding site is in the inside on a bin limit, and the grid that overlaps the position simultaneously again with the summit of other bins is divided the grid division of four kinds of different situations.
3. automatic mesh division methods according to claim 1 and 2, the grid of its center line face binding site position in the triangle bin or in the quadrangle bin is divided, and at first is to mark off an area less than 0.01 λ in described triangle or quadrangle bin
2Square, then remainder is divided, be that remainder is divided into a quadrangle and five triangles promptly for the triangle bin; For the quadrangle bin, be that remainder is divided into four quadrangles.
4. automatic mesh division methods according to claim 1 and 2, the grid of its center line face binding site position in the common edge of two bins is divided, and comprises following three kinds of situations:
(1) grid of line face binding site in two quadrangle bin common edge divided, and is to mark off earlier an area less than 0.01 λ in described two quadrangle bins
2Square, then the remainder in two quadrangle bins is divided into six quadrangles;
(2) grid of line face binding site in the common edge of two triangle bins divided, and is to mark off an area earlier less than 0.01 λ in described two triangle bins
2Square, then the remainder in two triangle bins is divided into ten triangles;
(3) grid of line face binding site in the common edge of triangle and quadrangle two bins divided, and is to mark off earlier an area less than 0.01 λ in described triangle and two bins of quadrangle
2Square, then the remainder in described triangle and two bins of quadrangle is divided into five triangles and three quadrangles.
5. automatic mesh division methods according to claim 1 and 2, its center line face binding site is divided at the grid of two bin public vertex positions at least, at first is to mark off an area less than 0.01 λ in these bins
2Square, ask difference to cut computing with each triangle in these bins or quadrangle bin respectively to this square then, after promptly triangle bin and square ask difference to cut the triangle bin is divided into a quadrangle or three triangles or a quadrangle and two triangles; After quadrangle bin and square ask difference to cut the quadrangle bin is divided into a quadrangle and triangle or two quadrangles or quadrangle and two triangles or five triangles.
6. automatic mesh division methods according to claim 1 and 2, its center line face binding site are in the inside on a bin limit, and the grid that overlaps the position simultaneously again with the summit of other bins is divided, and comprises following two kinds of situations:
(1) line face binding site is in the inside on a quadrangle bin limit, and the grid that overlaps the position simultaneously again with the summit of other bins is divided, and at first finds out the opposite side mid point that comprises limit, line face binding site place in the described quadrangle bin, connecting line face binding site and this mid point; Then described quadrangle bin is divided into two quadrangles, these two quadrangles and summit have formed the situation of line face binding site at least two bin public vertex positions with the bin that line face binding site overlaps; Carrying out grid again by claim 5 at last divides;
(2) line face binding site is in the inside on a triangle bin limit, the grid that overlaps simultaneously the position again with the summit of other bins is divided, at first comprise in connecting line face binding site and the described triangle bin line face binding site the limit right summit, described triangle bin is divided into two triangles, and these two triangles and summit have formed the situation of line face binding site at least two bin public vertex positions with the bin that line face binding site overlaps; Carrying out grid again by claim 5 then divides.
7. automatic mesh division methods according to claim 1 is wherein carried out grid to the long and narrow bin that occurs after grid is divided for the first time and for the second time again and is divided, and comprises following two kinds of situations:
(1) for the triangle bin, find out longest edge, minor face and longest edge earlier diagonal angle α °; Value m after the ratio of obtaining longest edge and minor face then rounds is if triangular shaped elongate ° is then thought in m 〉=3 or m＜3 and angle [alpha] 〉=120; Grid to the long and narrow bin of m 〉=3 is divided, and is with longest edge and vice-minister limit m five equilibrium, connects longest edge and the corresponding Along ent in vice-minister limit, is m-1 quadrangle and a triangle with this triangular shaped elongate binning; Grid to the long and narrow bin of m＜3 and angle [alpha] 〉=120 ° is divided, and is that this long and narrow bin is divided into two triangles along the longest edge center line, again these two triangles is carried out long and narrow judgement again by the condition that whether satisfies m 〉=3 and divides;
(2), find out longest edge earlier, the value m after the ratio of obtaining a longest edge and one adjacent side respectively rounds for the quadrangle bin
1, longest edge and its another adjacent side the value m of ratio after rounding
2, if m
1〉=3 and m
2〉=3, or m
1〉=3 and m
2＜3, or m
1＜3 and m
2Think that quadrangle is long and narrow for 〉=3; To m
1〉=3 and m
2The grid of 〉=3 long and narrow bin is divided, and at first finds out m
1, m
2The greater and be designated as k, should long and narrow tetragonal longest edge and opposite side k five equilibrium thereof, connect longest edge and the corresponding Along ent of opposite side thereof, obtain k quadrangle; To m
1〉=3 and m
2＜3, or m
1＜3 and m
2The grid of 〉=3 long and narrow bin is divided, and at first is that this quadrangle bin is divided into two triangles along short diagonal, then these two triangles is carried out grid by (1) bar in the claim 7 and divides.
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| CN101976287A (en) * | 2010-10-29 | 2011-02-16 | 上海交通大学 | Hybrid mesh partition method with design of integrity of system-level packaging power supply |
| CN101689213B (en) * | 2007-06-29 | 2012-01-18 | 富士通株式会社 | Design support apparatus, and design support method |
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