CN112348963A - Efficient FDTD grid subdivision method for unstructured complex target - Google Patents

Efficient FDTD grid subdivision method for unstructured complex target Download PDF

Info

Publication number
CN112348963A
CN112348963A CN202011382727.2A CN202011382727A CN112348963A CN 112348963 A CN112348963 A CN 112348963A CN 202011382727 A CN202011382727 A CN 202011382727A CN 112348963 A CN112348963 A CN 112348963A
Authority
CN
China
Prior art keywords
ray
intersection
equal
equation
triangular
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202011382727.2A
Other languages
Chinese (zh)
Inventor
刘虎锋
黄正宇
尹翼
姜书瑞
田越
孔怡
赵嘉晨
陈子安
侯亚彤
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Nanjing Beiye Electromechanical Equipment Co ltd
Original Assignee
Nanjing Beiye Electromechanical Equipment Co ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Nanjing Beiye Electromechanical Equipment Co ltd filed Critical Nanjing Beiye Electromechanical Equipment Co ltd
Priority to CN202011382727.2A priority Critical patent/CN112348963A/en
Publication of CN112348963A publication Critical patent/CN112348963A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/20—Finite element generation, e.g. wire-frame surface description, tesselation
    • G06T17/205—Re-meshing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2200/00—Indexing scheme for image data processing or generation, in general
    • G06T2200/04—Indexing scheme for image data processing or generation, in general involving 3D image data

Landscapes

  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Computer Graphics (AREA)
  • Geometry (AREA)
  • Software Systems (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Analysing Materials By The Use Of Radiation (AREA)
  • Image Generation (AREA)

Abstract

The invention discloses a high-efficiency FDTD mesh generation method aiming at an unstructured complex target, which comprises the following steps of firstly determining rays and the direction thereof; through simultaneous rays and a triangular surface element equation, the rays and the vector coordinates of each vertex are substituted into the simultaneous equation to obtain the coordinate system; judging the solved plane parameters u and v, and judging whether the intersection point is positioned in the triangular surface element according to whether u and v meet the condition that u is more than or equal to 0, v is more than or equal to 0 and u + v is less than or equal to 1; if the condition is satisfied, substituting u, v into the obtained t, and substituting the obtained t into (x)0，y0，z0+ t) to the intersection point where the ray intersects the triangular bin. The method simplifies the conventional method of directly solving all parameters of the ray intersection equation by using the Cramer rule and the mixed product, simplifies the solution of the original ternary linear equation set into a binary linear equation set by determining the direction of the ray, solves the condition parameter for judging intersection by simplifying complex calculation, judges and solves another parameter according to whether the two parameters are intersected or not, and greatly reduces the time complexity of program operation.

Description

Efficient FDTD grid subdivision method for unstructured complex target
Technical Field
The invention relates to a high-efficiency FDTD mesh generation method aiming at an unstructured complex target, and belongs to the technical field of mesh generation.
Background
The Finite Difference Time Domain (FDTD) method is a numerical algorithm directly based on time domain electromagnetic field differential equations, is one of effective methods for solving the electromagnetic problem of complex engineering model calculation, and disperses time and space in Maxwell equations, and obtains the rule of distribution and change of electromagnetic fields in space by replacing the differential equations with the differential equations. When the FDTD method is applied to research the electromagnetic scattering characteristics of the target, the key is to carry out grid discretization on the target.
With the rapid development of commercial modeling software, the modeling of a complex model is more convenient, and a fitting target model such as a triangular surface element is often adopted for the modeling of a three-dimensional object. Therefore, when a complex model mesh is divided, a key step is to convert triangular surface element model data extracted by commercial modeling software into a Yee cell model, and a dividing method based on a ray intersection principle is a more common method at present, and the method is to emit rays from the center of a bottom mesh, determine the range of the model by judging whether the rays intersect with a triangular surface element and the number of times of intersection, as shown in fig. 1, the key of the ray intersection method is to determine whether the intersection point of the rays and a plane is inside the triangular surface element, express the triangular surface element by barycentric coordinates, and judge whether the rays intersect with the triangular surface element by parameter sizes.
The ray is expressed as a parametric equation:
P(t)＝P0+t·al(A)
Wherein, P0Represents a ray origin; a islIs a unit vector, representing the ray direction; t is a variable ranging from (0, ∞);
points lying on the same plane as the triangular bin can be represented as:
Q(u，v)＝(1-u-v)V1+uV2+vV3(II)
Wherein, V1，V2，V3Three vertexes of the triangular surface element; u and v are variables in the range (-infinity, ∞). When the point is in the interior of the triangular surface element, u and v satisfy the condition: u is more than or equal to 0, v is more than or equal to 0, and u + v is less than or equal to 1;
setting the ray direction a for judging whether the ray intersects with the triangular surface elementl(x ', y ', z ') where three vertices of the triangular bin are (x)1，y1，z1)，(x2，y2，z2)，(x3，y3，z3) Substituting the equation into the simultaneous equation set of the equations (one) and (two) and expanding to obtain:
Figure BDA0002809981050000021
after finishing, the following can be obtained:
Figure BDA0002809981050000022
let H equal to x2-x1，I＝x3-x1，J＝-x'，K＝y2-y1，L＝y3-y1，M＝-y'，N＝z2-z1，O＝z3-z1，P＝-z'，Q＝x0-x1，R＝y0-y1，S＝z0-z1The result of solving using the claime rule is:
Figure BDA0002809981050000023
wherein T, U, V and W are respectively matrixes
Figure BDA0002809981050000024
According to the calculation, in the process of solving the intersection point of the ray and the triangular surface element by using the ray intersection method, if all parameters of the ray intersection method are solved by directly adopting the Cramer's law and the vector cross product, the general formula calculation is relatively complex because the particularity of the ray direction is not considered, and 48 times of value multiplication is required for solving a ternary equation set. However, when a complex model is used, the operation efficiency is also a very important index in addition to the accuracy, and under the condition that the number of triangular surface elements is very large and the model is relatively complex, the algorithm is simplified, the time required by calculation is reduced, and the importance of improving the calculation efficiency is particularly obvious.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a high-efficiency FDTD mesh generation method for an unstructured complex target, which can have higher operation efficiency and precision when an unstructured complex target mesh (such as a warship aircraft and the like) is generated.
In order to achieve the purpose, the invention adopts the following technical scheme: an efficient FDTD mesh generation method aiming at an unstructured complex target comprises the following steps:
step one, determining rays and directions thereof, wherein the known ray starting point O is (x)0，y0，z0) Let the ray direction D be (0, 0, 1), then the intersection of the ray and the triangular bin be (x)0，y0，z0+t)；
Step two, solving the intersection point of the triangular surface element and the ray by using a ray intersection method, and obtaining an equation of the simultaneous ray and the triangular surface:
O+tD＝(1-u-v)V1+uV2+vV3 (1)，
wherein, V1，V2，V3Three vertexes of the triangular surface element are respectively (x)1，y1，z1)，(x2，y2，z2)，(x3，y3，z3)；
And step three, substituting the ray and the vector coordinates of each vertex into a formula (1) to obtain:
Figure BDA0002809981050000031
step four, obtaining a solving formula of u and v by the first two equations in the simultaneous formula (2):
Figure BDA0002809981050000032
wherein A ═ x2-x1，B＝x3-x1，C＝y2-y1，D＝y3-y1，E＝x0-x1，F＝y0-y1；
Judging u and v solved in the fourth step, and judging whether the intersection point is positioned in the triangular surface element or not by determining whether u and v meet the condition that u is more than or equal to 0, v is more than or equal to 0 and u + v is less than or equal to 1; if the condition is satisfied, substituting u, v into the third equation in formula (2) to obtain t, and substituting u, v, t into (x)0，y0，z0+ t) to obtain the intersection point of the ray and the triangular bin.
Compared with the prior art, the method comprises the steps of converting a triangular surface element model into a Yee cell model, solving the intersection point coordinates and intersection times of a triangular surface element and rays by adopting a ray intersection method to determine the model range, and firstly determining the rays and the direction thereof; through simultaneous rays and a triangular surface element equation, the rays and the vector coordinates of each vertex are substituted into the simultaneous equation to obtain the coordinate system; judging the solved plane parameters u and v, and judging whether the intersection point is positioned in the triangular surface element according to whether u and v meet the condition that u is more than or equal to 0, v is more than or equal to 0 and u + v is less than or equal to 1; if the condition is satisfied, substituting u, v into the obtained t, and substituting the obtained t into (x)0，y0，z0+ t) to the intersection point where the ray intersects the triangular bin. Finally, by applying the conventional method directly to CramerThe method for solving all parameters of the ray intersection equation by the rule and the mixed product is simplified, the original ternary linear equation set is simplified into a binary linear equation set by determining the direction of the ray, the condition parameter for judging intersection is solved by simplifying complex calculation, and then the other parameter is judged and solved according to whether the intersection exists, so that the time complexity of program operation is greatly reduced.
Drawings
FIG. 1 is a model of a triangular bin intersecting a ray;
FIG. 2 is a triangular bin model of a warship;
FIG. 3 is a Yee network model of the warship of FIG. 2;
FIG. 4 is a triangular bin model of an aircraft f 22;
FIG. 5 is a Yee network model of the airplane f22 of FIG. 4.
Detailed Description
The technical solutions in the implementation of the present invention will be made clear and fully described below with reference to the accompanying drawings, and the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention provides a high-efficiency FDTD grid division method aiming at an unstructured complex target, which comprises the following steps:
step one, determining rays and directions thereof, wherein the known ray starting point O is (x)0，y0，z0) Let the ray direction D be (0, 0, 1), then the intersection of the ray and the triangular bin be (x)0，y0，z0+t)；
Step two, solving the intersection point of the triangular surface element and the ray by using a ray intersection method, and obtaining an equation of the simultaneous ray and the triangular surface:
O+tD＝(1-u-v)V1+uV2+vV3 (1)，
wherein, V1，V2，V3Three vertexes of the triangular surface element are respectively (x)1，y1，z1)，(x2，y2，z2)，(x3，y3，z3)；
And step three, substituting the ray and the vector coordinates of each vertex into a formula (1) to obtain:
Figure BDA0002809981050000051
step four, obtaining a solving formula of u and v by the first two equations in the simultaneous formula (2):
Figure BDA0002809981050000052
wherein A ═ x2-x1，B＝x3-x1，C＝y2-y1，D＝y3-y1，E＝x0-x1，F＝y0-y1；
Judging u and v solved in the fourth step, and judging whether the intersection point is positioned in the triangular surface element or not by determining whether u and v meet the condition that u is more than or equal to 0, v is more than or equal to 0 and u + v is less than or equal to 1; if the condition is satisfied, substituting u, v into the third equation in formula (2) to obtain t, and substituting u, v, t into (x)0，y0，z0+ t) to obtain the intersection point of the ray and the triangular bin.
The original method and the method of the invention are utilized to respectively carry out mesh subdivision on the warship in fig. 2 and the aircraft f22 complex model in fig. 4, and the results are shown in table 1 through the optimization of simplified front and back comparison verification efficiency:
TABLE 1 comparison of efficiencies before and after simplification
Figure BDA0002809981050000053
The warship model in fig. 2 is composed of 14320 triangular surface elements, and is divided into 20 × 132 × 31 meshes as shown in fig. 3, under the condition that other programs are not changed, the division needs 182s by using an unreduced method, the program running time is reduced from 182s to 46s after simplification, and is 25.27% of the original time, and the effect is remarkably improved.
Fig. 4 shows an airplane f22 model, which is composed of 22472 triangular bins, and is divided into 80 × 105 × 28 grids as shown in fig. 5, and the simplified program running time is reduced from 652s to 188s, which is 28.83% of the original time.
From the subdivision result, the efficiency after optimization is obviously improved by a lot compared with that of the original method, and when the two examples are processed, the efficiency improvement is kept between 70% and 75%, and the method is very considerable. From the appearance of the subdivision results, the subdivision results of the two methods are basically consistent. The method has the advantages that when the subdivision result has high precision requirement, namely the number of surface elements needing to be distinguished is large, the efficiency is obviously improved, and the precision of the subdivision model can be correspondingly guaranteed.
In conclusion, the invention aims at an unstructured target complex model, improves a ray intersection grid division algorithm, simplifies the conventional method of directly applying the Kramer rule and the mixed product to solve all parameters of a ray intersection method equation, firstly solves a condition parameter for judging intersection through the special simple and complex calculation of a ray parallel to a Z axis, then judges whether to solve another parameter according to intersection, if the special calculation of the method is not considered, the direct solution of a ternary equation set is designed, 48 times of value multiplication is required, compared with the improved algorithm, the ternary equation is converted into a binary equation set, only 8 times of value multiplication is required, and 11 times of multiplication operation is required to obtain the same result as the previous result by adding t solution, therefore, under the condition that the ray direction is determined, a matrix operation of 3 x 3 is calculated into a matrix operation of 2, the running time of the program can be greatly reduced, and when the number of the triangular surface elements is more, the efficiency is improved more obviously.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should make the description as a whole, and the embodiments may be appropriately combined to form other embodiments understood by those skilled in the art.

Claims (1)

1. An efficient FDTD mesh generation method aiming at an unstructured complex target is characterized by comprising the following steps:
step one, determining rays and directions thereof, wherein the known ray starting point O is (x)0，y0，z0) Let the ray direction D be (0, 0, 1), then the intersection of the ray and the triangular bin be (x)0，y0，z0+t)；
Step two, solving the intersection point of the triangular surface element and the ray by using a ray intersection method, and obtaining an equation of the simultaneous ray and the triangular surface:
O+tD＝(1-u-v)V1+uV2+vV3 (1)，
wherein, V1，V2，V3Three vertexes of the triangular surface element are respectively (x)1，y1，z1)，(x2，y2，z2)，(x3，y3，z3)；
And step three, substituting the ray and the vector coordinates of each vertex into a formula (1) to obtain:
Figure FDA0002809981040000011
step four, obtaining a solving formula of u and v by the first two equations in the simultaneous formula (2):
Figure FDA0002809981040000012
wherein A ═ x2-x1，B＝x3-x1，C＝y2-y1，D＝y3-y1，E＝x0-x1，F＝y0-y1；
Judging u and v solved in the fourth step, and judging whether the intersection point is positioned in the triangular surface element or not by determining whether u and v meet the condition that u is more than or equal to 0, v is more than or equal to 0 and u + v is less than or equal to 1; if the condition is satisfied, substituting u, v into the third equation in formula (2) to obtain t, and substituting u, v, t into (x)0，y0，z0+ t) to obtain the intersection point of the ray and the triangular bin.
CN202011382727.2A 2020-12-01 2020-12-01 Efficient FDTD grid subdivision method for unstructured complex target Pending CN112348963A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011382727.2A CN112348963A (en) 2020-12-01 2020-12-01 Efficient FDTD grid subdivision method for unstructured complex target

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011382727.2A CN112348963A (en) 2020-12-01 2020-12-01 Efficient FDTD grid subdivision method for unstructured complex target

Publications (1)

Publication Number Publication Date
CN112348963A true CN112348963A (en) 2021-02-09

Family

ID=74427152

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011382727.2A Pending CN112348963A (en) 2020-12-01 2020-12-01 Efficient FDTD grid subdivision method for unstructured complex target

Country Status (1)

Country Link
CN (1) CN112348963A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117315194A (en) * 2023-09-27 2023-12-29 南京航空航天大学 Triangular mesh representation learning method for large aircraft appearance

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117315194A (en) * 2023-09-27 2023-12-29 南京航空航天大学 Triangular mesh representation learning method for large aircraft appearance
CN117315194B (en) * 2023-09-27 2024-05-28 南京航空航天大学 Triangular mesh representation learning method for large aircraft appearance

Similar Documents

Publication Publication Date Title
Ronfard et al. Full‐range approximation of triangulated polyhedra.
CN103985155B (en) Scattered point cloud Delaunay triangulation curved surface reconstruction method based on mapping method
CN113096234B (en) Method and device for generating three-dimensional grid model by using multiple color pictures
CN107993279B (en) Scene accurate expression method
Hel-Or et al. Relaxed parametric design with probabilistic constraints
CN106981097A (en) A kind of T spline surface approximating methods based on subregion Local Fairing weight factor
CN115758938B (en) Adhesive boundary flow field numerical simulation-oriented boundary layer grid generation method
CN112348963A (en) Efficient FDTD grid subdivision method for unstructured complex target
CN110826122B (en) Voxel method and system for nuclear power three-dimensional layout design model
KR101032397B1 (en) Apparatus and method for representing 3d shape using spherical coordinate system
CN101877145A (en) Quality factor based method for pre-dividing complicated plane surface meshes
CN107767458B (en) Irregular triangulation network curved surface geometric topology consistency analysis method and system
Pang et al. Interactive evolutionary 3d fractal modeling
CN115935673A (en) FDTD mesh generation method and system based on ray tracing
CN113076571B (en) Real-time simulation editing method and system for three-dimensional clothes
CN115512075A (en) Quadrilateral mesh feature preserving re-partition method based on topological directed graph
CN114841079A (en) Continuous collision detection method based on deep neural network optimization
CN110111407B (en) Scheduling rendering method and system for massive three-dimensional grid data
CN113127967A (en) 3D model object of a physical prototype of a product
Docampo-Sánchez et al. A regularization approach for automatic quad mesh generation
Kholodilov et al. Analysis of the Technology of Transfering a Three-Dimensional Model from Cad Format to the Control Code For 3D Printing
CN111400969A (en) Method for accelerating generation of unstructured right-angle grid
US6903740B1 (en) Volumetric-based method and system for visualizing datasets
CN116416409B (en) Fluid simulation particle self-adaptive resolution surface reconstruction method and system
Zhao et al. Using interactive particle-based rendering to visualize a large-scale time-varying unstructured volume with mixed cell types

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination