CN102831648A - Fixed node discharge curve approximation and curved surface mesh generation optimizing technology - Google Patents
Fixed node discharge curve approximation and curved surface mesh generation optimizing technology Download PDFInfo
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- CN102831648A CN102831648A CN2012102496303A CN201210249630A CN102831648A CN 102831648 A CN102831648 A CN 102831648A CN 2012102496303 A CN2012102496303 A CN 2012102496303A CN 201210249630 A CN201210249630 A CN 201210249630A CN 102831648 A CN102831648 A CN 102831648A
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Abstract
The invention relates to a fixed node discharge curve approximation and curved surface mesh generation optimizing technology which obviously improves the quality of a curved surface mesh and can be applied to the boundary discrete optimization and visualization technology when generating a body-fitted mesh. The technology comprises the following steps of: (1.1) establishing a curved surface model by a computer according to the curved surface to be analyzed, and determining the curved surface boundary, shape, mesh number and mesh step; (1.2) projecting the curved surface to a plane, generating a two-dimensional body-fitted mesh according to the projection area, and projecting the body-fitted mesh to the original curved surface; (1.3) optimizing the boundary node of the curved surface mesh according to the length maximization rule; (1.4) optimizing the internal node of the curved surface mesh according to the area maximization rule; and (1.5) optimizing the mesh step according to the optimization algorithm defining the mesh step, and finally generating a high-quality curved surface mesh. The technology provided by the invention realizes the boundary discrete optimization in generation of a body-fitted mesh of a complicated boundary as well as the mesh optimization in the visualization technology.
Description
Technical field
The invention belongs to computational geometry, computer graphics, visualization technique, numerical simulation, geology imaging and medical imaging field, its purpose comprises two aspects: the first, high-quality divergent boundary is provided when generating body fitted grids; The second, show grid true to nature is provided in visualization technique.The space curve that is specifically related to the length maximal criterion approaches, the surface mesh optimization of area maximal criterion, minor increment revised law, limit the contents such as optimized Algorithm of mesh spacing.
Background technology
Finite element, limited bulk, the finite difference numerical evaluation of grading requires on discrete grid node, to calculate, and grid just is in these discrete grid block node distributions in the The whole calculations zone.The suitable grid of definition is a serious thing in given zoning, and is not nonsensical, and the process that defines such grid is called grid and generates.It is the core technology of numerical simulation that grid generates, and grid generates the proportion of workload in the The whole calculations process and is about 60%, even more, and mesh quality will directly influence numerical analysis result's precision.Structured grid is because advantages such as reserves are little, simple in structure, easy operating are used widely it in numerical simulation.Body fitted grids is a kind of structured grid that occurs for adaptation complex geometry border, and body fitted grids is widespread use in Flight Vehicle Design manufacturing, water conservancy construction, water-sediment movement and the discharge of river are analyzed, also in geophysical modeling, is able at present use.Body fitted grids generation method mainly contains algebraic approach, method of interpolation, conformal transformation and differential equation method, when these methods generate body fitted grids, and must at first given discrete boundary condition.
The information that the mankind obtain comes from vision more than 83%, so visualization technique has very important significance.Visualization technique computer-aided design (CAD), space science, Machine Design manufacturing, hazard forecasting analysis, learn fields such as space, numerical simulation aftertreatment and be widely used.Visualization technique mainly is divided into image viewing technology and geometric figure visualization technique.The geometric figure visualization technique is the gordian technique of technology such as the analysis of mineral reserve reserves, seismic data analysis, spacecraft manufacture and design.The geometric figure visualization technique is divided into based on surperficial visualization technique with based on the visualization technique of body; Use model and have the polygonal mesh of the quadrilateral mesh of the triangle gridding of non-structure, structure, non-structure etc. based on the visualization technique on surface, use model and have the hexahedral mesh of structure, tetrahedral grid, and the polyhedron grid of non-structure etc. based on the visualization technique of body.
In numerical simulation and visualization technique, curve and curved surface go to approach with broken line and polygon respectively.Though a lot of scholars approach with surface mesh optimization to curve and have done many researchs; Most of research all is the Modeling Technology of the free curve curved surface of indefinite node amount, though theoretical curve ripe and that be not suitable for given geometric configuration and node amount approaches and surface mesh generates and optimization.
Curve is as the border of plane and curved surface, and it is discrete when two-dimentional body fitted grids generates, must to accomplish curve according to the node amount earlier, approximating curve shape as much as possible when discrete curve.Batten, circular arc and straight-line segment approximating curve commonly used.Though body fitted grids is as the border with curve on physical domain; But, grid can't be concerned about the curve shape between adjacent node when generating; Seldom use in body fitted grids generates with the method for SPL section or arc section approximating curve, we come approximating curve with straight-line segment during generating mesh in real work.The method of straight-line segment approximating curve mainly contains: equidistantly method, etc. step-length method, equal error method.Equidistantly method can't automatically realize approaching of complicated shape curve, and the equal error method can't limit number of nodes, and the curve that the step-length method such as has only to be fit to given node amount approaches.Implement simply etc. the step-length method, efficient is high, but it does not consider curve shape in implementation process.
Curved surface carries out curved surface with triangle and quadrilateral surface usually and disperses as the border of three-dimensional geometry body.The three dimensional body fitted grids border is discrete with the quadrilateral structure grid configuration, usually discrete method have that interpolation algorithm, nurbs surface approach, differential equation method etc.These methods all do not contain the optimizing process to grid, and at present main grid optimization method has: the Laplacian method for fairing, etc. the parameter graduation.The Laplacian method for fairing moves to the mean value place that is adjacent the conllinear node coordinate with internal node, is the mean value that the coordinate of grid internal node is revised as the adjacent coplanar node coordinate etc. the parameter smooth.These two kinds of optimization methods all do not consider to optimize the influence to the surface mesh shape.
Summary of the invention
Grid optimization problem in border discrete optimization problem and the visualization technique when technical matters that the present invention solves is the body fitted grids generation.The Laplacian method for fairing with etc. the consideration optimization useless of parameter graduation to the influence of curve and surface shape, can't to describe curve and surface shape direction true to nature near; Optimisation technique in the curve and surface Modeling Technology can not satisfy the requirement of deciding the node amount, can't be applicable to the border discrete optimization when body fitted grids generates.Border discrete optimization when the length maximal criterion that proposes among the present invention, area maximal criterion and the optimized Algorithm that limits mesh spacing can realize that body fitted grids generates makes the description border that the border grid also can be maximum when satisfying the border step-length and requiring; The length maximal criterion can be used for approaching of curve, is used in the broken line fairing more of approximating curve; The area maximal criterion can be used for the optimization of surface mesh, and the curved surface that grid is described is more true to nature.
Technical scheme of the present invention is described as follows.
A kind ofly decide that the node discharge curve approaches and surface mesh generates optimisation technique, it is characterized in that may further comprise the steps:
(1.1) utilize computing machine to set up surface model; Confirm the quantity and the mesh spacing of curve form, border, generating mesh;
(1.2),, generate the body fitted grids of two dimension according to the curved surface projection zone with curved surface projection to a plane according to curve form and border; This body fitted grids is mapped on the former curved surface, forms the initial mesh of curved surface;
(1.3) optimize the surface mesh boundary node according to the length maximal criterion;
(1.4) optimize the surface mesh internal node according to the area maximal criterion;
(1.5) optimize mesh spacing according to the optimized Algorithm that limits mesh spacing.
In the said step (1.3), the length maximal criterion is meant that the position of node makes node form broken line length maximum on the optimal curve, and its process is:
(2.1) the node on the curve be created as a set that order point arranged
P i |
I=0,1,
N;
(2.2) from
iNode is sought in=1 beginning
P I-1
With node
P I+1
Between point in the curve regions
P, make a little
PFrom node
P I-1
And node
P I+1
Maximum apart from sum, use a little
PCoordinate replace node
P i Coordinate, up to
I=N-1 finishes;
(2.3) repeat (2.2), the broken line length of forming up to node on the curve does not finish to optimize when changing, and accomplishes the optimization of length maximal criterion to curve.
Comprised in the said step (2.2) and sought node
P I-1
With node
P I+1
Between point in the curve regions
P, make a little
PFrom node
P I-1
With node
P I+1
The algorithm maximum apart from sum, its algorithm is:
(3.1) initialization data memory
M, the memory decay factor
D, the memory enhancer
E, be provided with and judge to revise finish the factor
K=0;
(3.2)
P i Coordinate give assignment
P
(3.3) ask for random number with computing machine
R, the scope of random number be [
-b,
b], (
bFor the point
P i From adjacent node
P I-1
And node
P I+1
Apart from sum 1/10th), calculate a little
PMovable length
Z i , its computing formula is:
Z i ?=?
R+E*M （1）
(3.4) basis
Z i Value calculates a little
PThe position, the direction that sign representative is different;
(3.5) calculate
PPosition change before and after point
PFrom node
P I-1
And node
P I+1
Apart from sum;
(3.6) if point
PPosition change after become big apart from sum, then use
PThe coordinate of point upgrades
P i Coordinate is used
Z i Upgrade
MValue, be provided with
k=0, and forward (3.3) step to;
(3.7) if point
PPosition change after diminish apart from sum, then be provided with
M=M/D,
k++;
(3.8) if
kLess than 3, then forward (3.3) step to.
In the said step (1.4), the area maximal criterion is to make its surface mesh area maximum through optimizing surface mesh internal node position, and its process is:
(4.1) characteristic according to surface mesh is divided into two families with the grid curve, mutually disjoints with the curve of gang, is defined as respectively
XThe curve of direction with
YThe curve of direction;
(4.2) optimize according to the length maximal criterion
YThe curve of direction;
(4.3) optimize according to the length maximal criterion
XThe curve of direction;
(4.4) according to minor increment revised law correction surface mesh;
(4.5) repeat (4.2) to (4.4) step, up to satisfying convergent requirement.
The algorithm that has comprised the minor increment revised law in the said step (4.4), its algorithm purpose are to make to revise the minimum apart from sum of node and adjacent conllinear node, and its algorithm steps comprises:
(5.1) initialization surface mesh node subscript
i=1
(5.2) initialization surface mesh node subscript
j=1;
(5.3) calculate with node on the surface mesh
Q (
i,
j)
Be the summit, with line segment
Q (
i,
j)
Q (
i-1,
j)
With
Q (
i,
j)
Q (
i+ 1,
j)
Angle for the limit
α 1Value;
(5.4) calculate with node on the surface mesh
Q (
i,
j)
Be the summit, with line segment
Q (
i,
j)
Q (
i,
j-1)
With
Q (
i,
j)
Q (
i,
j+ 1)
Angle for the limit
α 2Value;
(5.5) if
α 1Less than
α 2, then at segment of curve
Q (
i,
j-1)
Q (
i,
j+ 1)
On ask a little
Q,Make straight-line segment
QQ (
i-1,
j)
,
QQ (
i+ 1,
j)
,
QQ (
i,
j-1)
With
QQ (
i,
j+ 1)
Length and minimum, otherwise at curve
Q (
i-1,
j)
Q (
i+ 1,
j)
On ask a little
Q, make straight-line segment
QQ (
i-1,
j)
,
QQ (
i+ 1,
j)
,
QQ (
i,
j-1)
With
QQ (
i,
j+ 1)
Length and minimum;
(5.6) with point
QThe coordinate assignment give
Q (
i,
j)
(5.7) if
jLess than maximum dimension
j Max , then
j++, and forward (5.2) to;
(5.8) if
iLess than maximum dimension
i Max , then
i++, and forward (5.1) to.
The optimized Algorithm of the qualification mesh spacing in the said step (1.5), this algorithm are to accomplish mesh spacing optimization through the step-length of optimizing every mesh lines, and the step of its every mesh lines step-length optimized Algorithm comprises:
(6.1) the maximum step-length coefficient of initialization grid length of curve
α Max With the minimum step coefficient
α Min
(6.2) initialization node subscript
I=1, and the judgement correction end factor is set
K=0;
(6.3) computing grid length of a curve, and computing grid average step length
L Ave
(6.4) the maximum step-length of computing grid qualification
L Max =
α Max* L Ave And minimum step
L Min =
α Min* L Ave
(6.5) computing node
I-1 and node
iAir line distance
L i-1
, i
(6.6) if
iGreater than 1 and less than
N-1, then jump to (6.8) step, otherwise continue down to carry out;
(6.7) if
iEqual
N, then be designated as under the node of optimal curve section:
j 1=
N-2,
j 2=
N-1,
j 3=
N, otherwise
j 1=0,
j 2=1,
j 3=2, and jump to (6.12) step;
(6.8) calculated line distance
L i-2,
i-1
With
L i,
i+ 1
(6.9) if
L i-2,
i-1
Greater than
L i,
i+ 1
Then continue down to carry out, otherwise jump to (6.11) step;
(6.10) if
L i-1
, i Less than
L Min , then
j 1=
i-2,
j 2=
i-1,
j 3=
i, otherwise
j 1=
i-1,
j 2=
i,
j 3=
i+ 1, and jump to (6.12) step;
(6.11) if
L i-1
, i Greater than
L Max , then
j 1=
i-2,
j 2=
i-1,
j 3=
i, otherwise
j 1=
i-1,
j 2=
i,
j 3=
i+ 1;
(6.12) if
L i-1
, i Less than
L Min , then at segment of curve
j 1 j 3Last searching node
j 2Coordinate, make
L i-1
, i Equal
L Min , and be provided with
k=1;
(6.13) if
L i-1
, i Greater than
L Max , then at segment of curve
j 1 j 3Last searching node
j 2Coordinate, make
L i-1
, i Equal
L Max , and be provided with
k=1;
(6.14) if
iLess than the node number
NValue, then
i++, and forward (6.3) to;
(6.15) if
kEqual 1, then be provided with
i=1 draw
k=0, and forward (6.3) to.
The present invention mainly contains 4 contributions: the first, the method for length maximal criterion approximating curve has been proposed, this method can best description go out the virgin curve shape under the condition of confirming the node amount, for two-dimentional body fitted grids with the space curved surface grid generation lay a good groundwork; The second, area maximal criterion optimization method has been proposed, the former curve form of the surface mesh fine maintenance of ability that this method is optimized, and grid fairing; The 3rd, the minor increment revised law has been proposed, be used for the fairing smoothing processing of net surfaces ruling, to eliminate the zigzag deformity grid in the grid; The 4th; For solving the uncontrollable problem of surface mesh step-length that maximal criterion is optimized; The optimized Algorithm of restriction mesh spacing has been proposed; Through the surface mesh that this algorithm optimization maximal criterion is optimized, realized that grid also can maximum maintenance curve form when the assurance step-length is in claimed range.
Description of drawings
Fig. 1 decides the node discharge curve and approaches the main flow line that generates optimisation technique with surface mesh.
The body fitted grids that Fig. 2 curved surface projection generates behind the two dimensional surface.
Fig. 3 two dimension body fitted grids projects to the curved surface initial mesh that the back forms on the curved surface.
Fig. 4 optimizes the grid behind the surface mesh border according to the length maximal criterion.
The zigzag deformity grid that Fig. 5 occurs when optimizing surface mesh with the maximum method of mesh lines length sum.
Fig. 6 adopts the surface mesh behind the minor increment revised law correction deformity grid.
Surface mesh after Fig. 7 optimizes according to the area maximal criterion.
Surface mesh after Fig. 8 optimizes based on the optimized Algorithm that limits mesh spacing.
Embodiment
Body fitted grids is a kind of structured grid under the body-fitted coordinate system, so-called body-fitted coordinate system be meant in the flow field object plane shape and computation bound can with some or the whole coordinate lines coordinate systems that match in calculating.Body-fitted coordinate system can adopt suitable coordinate Mapping to realize.The basic ideas of structure body-fitted coordinate system are: pass through certain coordinate Mapping to object plane border on the physical plane and computation bound curve (can be that simply connected region also can be a multiply connected region); Be mapped as the coordinate line that calculates on the plane, be mapped to the rectangular area to them generally speaking.In order to guarantee physical plane and to calculate complete mapping relations between the plane, the most basic condition below border (being generally curved surface) the discrete optimization technology of generation three dimensional body fitted grids must satisfy:
(1) transformational relation between physical plane interior nodes and the calculating plane interior nodes must be an one-to-one relationship;
(2) physical plane all is continuous and smooth with the coordinate line that calculates in the plane, and derivative is continuous during with the assurance changes in coordinates.Can not intersect with gang's coordinate line (mesh lines), coordinate line not of the same clan (mesh lines) can only intersect once; Each node must be the intersection point of coordinate line not of the same clan (mesh lines) in the coordinate system in the grid, with guarantee physical plane with calculate plane Intranet lattice point and do not overlap and interlock;
(3) in order to improve computational accuracy, require physical plane and calculate plane internal coordinate line (mesh lines) quadrature or basic quadrature, avoid physical plane and calculating horizontal areal coordinate line too to tilt;
(4) grid generation technique will be easy to control physical plane and calculate plane Intranet lattice density degree.
Body fitted grids generation method all need be carried out the border discrete optimization.The objective of the invention is to: utilize the optimized Algorithm of length maximal criterion, area maximal criterion, qualification mesh spacing to propose a kind of optimization method that satisfies body fitted grids border discrete optimization technology pacing items; Decide promptly that the node discharge curve approaches and surface mesh generates optimisation technique, the grid after the optimization is in the shape that guarantees description curved surface that also can be maximum when step-length is in claimed range.
Below in conjunction with accompanying drawing and embodiment, the present invention is further specified.
Fig. 1 approaches the process flow diagram that generates optimisation technique with surface mesh for deciding the node discharge curve.According to shown in Figure 1, decide the node discharge curve and approach with the flow process of surface mesh generation optimisation technique following: set up surface model, confirm surface boundary, shape; The quantity and the mesh spacing of the discrete grid block of record input; Curved surface projection to the plane, is generated the body fitted grids of two dimension according to the zone of projection plane; Show consideration for mesh mapping to the two dimension that generates to former curved surface, form initial surface mesh; Optimize the node on the surface boundary according to the length maximal criterion, make border fairing more, describe more boundary shape; Optimize the inner node of surface mesh according to the area maximal criterion, make grid smoothly true to nature, and describe maximum curve forms; Optimize mesh spacing according to the optimized Algorithm that limits mesh spacing, mesh spacing is distributed in requires in the step-length scope, and the shape of description curved surface as much as possible; So far the generation and the optimization of the surface mesh of deciding the node amount have been accomplished.
Decide in order to be illustrated more clearly in that the node discharge curve approaches and surface mesh generates the process of optimisation technique and the effect of each step thereof, next with instance
z=30
Sin(
π x/ 50)+30
Cos(
π y/ 50), 0≤
x≤200,0≤
y≤200 curved surface explanation is decided the node discharge curve and is approached and the process of surface mesh generation optimisation technique and the effect of each step thereof.
At first according to instance
z=30
Sin(
π x/ 50)+30
Cos(
π y/ 50), 0≤
x≤200,0≤
y≤200 confirm the border of curved surface, suppose that it is 25 * 25 that the user imports the number of grid that will disperse, maximum step-length coefficient
a Max Be 1.4, the minimum step coefficient
a Min Be 0.7.
Step (1.2) is curved surface projection to a plane, and the body fitted grids of regeneration view field projects to this body fitted grids on the curved surface at last, accomplishes the initial mesh of curved surface.Practical implementation is following: with the instance curved surface projection in cartesian coordinate system
XyOn the coordinate system face, then this curved surface be mapped as 0≤
x≤200,0≤
y≤200 square-shaped planar, the flat shape that mapping forms is relevant with actual curved surface; According to the body fitted grids of number of grid generation view field, method mainly contains algebraic approach, method of interpolation, and differential equation method etc., the two-dimentional body fitted grids of generation is as shown in Figure 2; Next on the former curved surface with the body fitted grids mapping, accomplish the initial mesh of curved surface; The initial mesh of curved surface is as shown in Figure 3.
Optimize the border of surface mesh in the step (1.3) according to the length maximal criterion.The length maximal criterion is defined as: under the condition of given curve shape and node amount, make the broken line length that node is in turn connected on the curve maximum.The design sketch of optimizing net boundary according to the length maximal criterion is as shown in Figure 4, and the false code of its length maximal criterion optimized Algorithm is following:
Initialization
s1=0,
s2=1,
D=2,
E=1.5,
e=
s2/10000
Do?While?Fabs(
s1-
s2)<
e
s1=
s2
For
i=1?To?
N
k=0
M=0
Do?While?
k<3
Calculate random number
R
Z=?
R+E*M
If Z<0 Then
At line segment
P I-1
P i On ask a bit
P 1, make
P 1With
P i Air line distance do
Z
Else
At line segment
P i P I+1
On ask a bit
P 1, make
P 1With
P i Air line distance do
Z
End?If
Ask on the curve from point
P 1Nearest point
P 2
s3=
P i With
P I-1
Air line distance+
P i With
P I+1
Air line distance
s4=
P 2With
P I-1
Air line distance+
P 2With
P I+1
Air line distance
If
s4>
s3?Then
P i =
?P 2
M=Z
?k=0
Else
M=Z/D
k++
End?If
End?While
End?For
s2=0
For
?i=1?To?N
s2=
s2+
P i With
P I-1
Air line distance
End?For
e=?
s2/10000
End?While?。
Step (1.4) is to optimize the inner node of surface mesh according to the area maximal criterion.Being defined as of area maximal criterion: under the condition of given curve form and grid node amount, make the quadrilateral mesh area maximum through the mode that changes node location.In this algorithm implementation process, be converted into optimization surface mesh line length sum greatest problem, the problem that occurs dispersing when preventing directly to optimize grid with the mode of quadrilateral mesh area optimizing surface mesh area greatest problem.The lopsided grid of zigzag shown in Figure 5 can occur when solving through mesh lines length and largest optimization surface mesh, the minor increment revised law that proposes among the present invention is used for the fairing grid.The minor increment revised law is defined as: node and adjacent conllinear node minimum apart from sum, and as shown in Figure 6 according to the effect behind the minor increment revised law correction zigzag deformity grid.In sum, the optimized Algorithm of area maximal criterion is through combining length maximal criterion optimized Algorithm and minor increment revised law to implement.The design sketch of optimizing grid according to the area maximal criterion is as shown in Figure 7, and the false code of its area maximal criterion optimized Algorithm is following:
Initialization
s1=0,
s2=1
Do?While?Fabs(
s1-
s2)<
s2/10000
s1=
s2;
For
i=1 To
N i -1 '
N i For
XDirection node number
Optimize according to length maximal criterion optimized Algorithm
YOn the direction
iBar grid curve
End?For
For
j=1 To
N j -1 '
N j For
YDirection node number
Optimize according to length maximal criterion optimized Algorithm
XOn the direction
jBar grid curve
End?For
For
i=1?To?
N i ?-1
For
j=1?To?
N j -1
According to minor increment revised law correction node
Q (
i,
j)
Coordinate
End?For
End?For
Calculate the surface mesh area
s2
End?While?。
Optimize grid according to the optimized Algorithm that limits mesh spacing in the step (1.5), the optimized Algorithm that limits mesh spacing is through the step-length adjustment to every mesh lines, to realize the optimization of mesh spacing.Grid according to after the optimized Algorithm optimization that limits mesh spacing is as shown in Figure 8.
In the present invention; Step-length method such as use that the length maximal criterion can be accomplished can't be accomplished makes the maximum requirement of broken line length; The broken line of optimizing according to the length maximal criterion can be more true to nature the description space curve, this criterion is all significant to machining, numerical simulation, curve display; The area maximal criterion optimization that proposes among the present invention is to be implemented in the description curve form that makes under the condition that does not change mesh topology and number of nodes that grid can be maximum.This criterion is all significant in numerical simulation and visualization technique.The minor increment revised law that proposes among the present invention except the grid to the optimization of area maximal criterion carries out the fairing smoothing processing, also can be used for the quadrilateral surface mesh that the fairing additive method generates for optimizing the fairing of net surfaces ruling; The optimized Algorithm of the qualification mesh spacing that proposes among the present invention except that being used to optimize the surface mesh of optimizing through maximal criterion, also can be used to optimize additive method discrete curve or grid, as is used to optimize the grid of local refinement or alligatoring.In sum, four kinds of optimization methods all can be used separately according to actual needs among the present invention.
What should explain at last is; Above embodiment is only unrestricted in order to technical scheme of the present invention to be described; Although with reference to preferred embodiment the present invention is specified, those of ordinary skill in the art should be appreciated that technical method of the present invention is made amendment or is equal to replacement; And not breaking away from the spirit and the scope of technical scheme of the present invention, it all should be encompassed in power of the present invention and want in the middle of the point range.
Claims (6)
1. decide that the node discharge curve approaches and surface mesh generates optimisation technique for one kind, it is characterized in that may further comprise the steps:
(1.1) utilize computing machine to set up surface model; Confirm the quantity and the mesh spacing of curve form, border, generating mesh;
(1.2),, generate two-dimentional body fitted grids according to the curved surface projection zone with curved surface projection to a plane according to curve form and border; This body fitted grids is mapped on the former curved surface, forms the initial mesh of curved surface;
(1.3) optimize the surface mesh boundary node according to the length maximal criterion;
(1.4) optimize the surface mesh internal node according to the area maximal criterion;
(1.5) optimize mesh spacing according to the optimized Algorithm that limits mesh spacing.
2. according to claim 1ly decide that the node discharge curve approaches and surface mesh generates optimisation technique, it is characterized in that, in the said step (1.3), it is maximum that the length maximal criterion is meant on the optimal curve that the position of node makes node form broken line length, and its process is:
(2.1) the node on the curve be created as a set that order point arranged
P i |
I=0,1,
N;
(2.2) from
iNode is sought in=1 beginning
P I-1
With node
P I+1
Between point in the curve regions
P, make a little
PFrom node
P I-1
And node
P I+1
Maximum apart from sum, use a little
PCoordinate replace node
P i Coordinate, up to
I=N-1 finishes;
(2.3) repeat (2.2), finish when the broken line length that node is formed on curve no longer changes to optimize, accomplish of the optimization of length maximal criterion curve.
3. according to claim 2ly decide that the node discharge curve approaches and surface mesh generates optimisation technique, it is characterized in that, comprised in the said step (2.2) and sought node
P I-1
With node
P I+1
Between point in the curve regions
P, make a little
PFrom node
P I-1
And node
P I+1
The algorithm maximum apart from sum, its algorithm is:
(3.1) initialization data memory
M, the memory decay factor
D, the memory enhancer
E, be provided with and judge to revise finish the factor
K=0;
(3.2) point
P i The coordinate assignment give point
P
(3.3) ask for random number with computing machine
R, the scope of random number be [
-b,
b], (
bFor the point
P i From adjacent node
P I-1
With node
P I+1
Apart from sum 1/10th), calculate a little
PMovable length
Z i , its computing formula is:
Z i ?=?
R+E*M （1）
(3.4) basis
Z i Value calculates a little
PThe position, the direction that sign representative is different;
(3.5) calculate
PPosition change before and after point
PFrom node
P I-1
And node
P I+1
Apart from sum;
(3.6) if point
PPosition change after become big apart from sum, then use
PThe coordinate of point upgrades
P i Coordinate is used
Z i Upgrade
MValue, be provided with
k=0, and forward (3.3) step to;
(3.7) if point
PPosition change after diminish apart from sum, then be provided with
M=M/D,
k++;
(3.8) if
kLess than 3, then forward (3.3) step to.
4. according to claim 1ly decide that the node discharge curve approaches and surface mesh generates optimisation technique; It is characterized in that; In the said step (1.4), the area maximal criterion is to make its surface mesh area maximum through optimizing surface mesh internal node position, and its process is:
(4.1) characteristic according to surface mesh is divided into two families with the grid curve, mutually disjoints with the curve of gang, is defined as respectively
XThe curve of direction with
YThe curve of direction;
(4.2) optimize according to the length maximal criterion
YThe curve of direction;
(4.3) optimize according to the length maximal criterion
XThe curve of direction;
(4.4) according to minor increment revised law correction surface mesh;
(4.5) repeat (4.2) to (4.4) step, up to satisfying convergent requirement.
5. according to claim 4ly decide that the node discharge curve approaches and surface mesh generates optimisation technique; It is characterized in that; The algorithm that has comprised the minor increment revised law in the said step (4.4); Its algorithm purpose is to make to revise the minimum apart from sum of node and adjacent conllinear node, and its algorithm steps comprises:
(5.1) initialization surface mesh node subscript
i=1
(5.2) initialization surface mesh node subscript
j=1;
(5.3) calculate with node on the surface mesh
Q (
i,
j)
Be the summit, with line segment
Q (
i,
j)
Q (
i-1,
j)
With
Q (
i,
j)
Q (
i+ 1,
j)
Angle for the limit
α 1Value;
(5.4) calculate with node on the surface mesh
Q (
i,
j)
Be the summit, with line segment
Q (
i,
j)
Q (
i,
j-1)
With
Q (
i,
j)
Q (
i,
j+ 1)
Angle for the limit
α 2Value;
(5.5) if
α 1Less than
α 2, then at segment of curve
Q (
i,
j-1)
Q (
i,
j+ 1)
On ask a little
Q,Make straight-line segment
QQ (
i-1,
j)
,
QQ (
i+ 1,
j)
,
QQ (
i,
j-1)
With
QQ (
i,
j+ 1)
Length and minimum, otherwise at curve
Q (
i-1,
j)
Q (
i+ 1,
j)
On ask a little
Q, make straight-line segment
QQ (
i-1,
j)
,
QQ (
i+ 1,
j)
,
QQ (
i,
j-1)
With
QQ (
i,
j+ 1)
Length and minimum;
(5.6) with point
QThe coordinate assignment give
Q (
i,
j)
(5.7) if
jLess than maximum dimension
j Max , then
j++, and forward (5.2) to;
(5.8) if
iLess than maximum dimension
i Max , then
i++, and forward (5.1) to.
6. according to claim 1ly decide that the node discharge curve approaches and surface mesh generates optimisation technique; It is characterized in that; The optimized Algorithm of the qualification mesh spacing in the said step (1.5); This algorithm is to accomplish mesh spacing optimization through the step-length of optimizing every mesh lines, and the step of its every mesh lines step-length optimized Algorithm comprises:
(6.1) the maximum step-length coefficient of initialization grid length of curve
α Max With the minimum step coefficient
α Min
(6.2) initialization node subscript
I=1, and the judgement correction end factor is set
K=0;
(6.3) computing grid length of a curve, and computing grid average step length
L Ave
(6.4) the maximum step-length of computing grid qualification
L Max =
α Max* L Ave And minimum step
L Min =
α Min* L Ave
(6.5) computing node
I-1 and node
iAir line distance
L i-1
, i
(6.6) if
iGreater than 1 and less than
N-1, then jump to (6.8) step, otherwise continue down to carry out;
(6.7) if
iEqual
N, then be designated as under the node of optimal curve section:
j 1=
N-2,
j 2=
N-1,
j 3=
N, otherwise
j 1=0,
j 2=1,
j 3=2, and jump to (6.12) step;
(6.8) calculated line distance
L i-2,
i-1
With
L i,
i+ 1
(6.9) if
L i-2,
i-1
Greater than
L i,
i+ 1
Then continue down to carry out, otherwise jump to (6.11) step;
(6.10) if
L i-1
, i Less than
L Min , then
j 1=
i-2,
j 2=
i-1,
j 3=
i, otherwise
j 1=
i-1,
j 2=
i,
j 3=
i+ 1, and jump to (6.12) step;
(6.11) if
L i-1
, i Greater than
L Max , then
j 1=
i-2,
j 2=
i-1,
j 3=
i, otherwise
j 1=
i-1,
j 2=
i,
j 3=
i+ 1;
(6.12) if
L i-1
, i Less than
L Min , then at segment of curve
j 1 j 3Last searching node
j 2Coordinate, make
L i-1
, i Equal
L Min , and be provided with
k=1;
(6.13) if
L i-1
, i Greater than
L Max , then at segment of curve
j 1 j 3Last searching node
j 2Coordinate, make
L i-1
, i Equal
L Max , and be provided with
k=1;
(6.14) if
iLess than the node number
NValue, then
i++, and forward (6.3) to;
(6.15) if
kEqual 1, then be provided with
i=1 draw
k=0, and forward (6.3) to.
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