阅读说明：本技术 一种适用于矩量法的参数化曲线建模、网格生成系统和方法 (Parameterized curve modeling and grid generating system and method suitable for moment method ) 是由 曹成 李尧尧 蔡少雄 苏东林 于 2021-09-23 设计创作，主要内容包括：本发明公开了一种适用于矩量法的参数化曲线建模、网格生成系统和方法,系统包括：曲线建模模块：用于根据曲线自身属性进行建模；所述曲线自身属性包括有公式表征的和无公式表征的；线模型保存模块：用于将建模过程中的包括曲线阶数、参数范围、参数样本点、控制坐标点在内的曲线模型数据按照几何模型格式进行保存；线模型剖分模块：用于将参数空间按照线性等分成K+1份,得到包括生成曲线网络模型顶点的坐标和生成曲线连接单元的用于构成线模型的剖分网络模型；矩量法电磁计算模块。本发明可以有效克服以下几种情况：(1)细线结构网格的连续性问题；(2)细线结构网格的剖分密度控制问题；(3)细线结构模型的阶数控制问题。(The invention discloses a parameterized curve modeling and grid generating system and method suitable for a moment method, wherein the system comprises the following steps: a curve modeling module: the modeling is carried out according to the attribute of the curve; the attributes of the curve comprise those represented by a formula and those represented by no formula; the line model storage module: the system is used for storing curve model data including curve orders, parameter ranges, parameter sample points and control coordinate points in the modeling process according to a geometric model format; a line model subdivision module: the subdivision network model is used for dividing the parameter space into K +1 parts according to linear equal division to obtain a subdivision network model which comprises coordinates of the vertex of the generated curve network model and a generated curve connecting unit and is used for forming a line model; and a moment method electromagnetic calculation module. The invention can effectively overcome the following conditions: (1) continuity problems of fine line structured grids; (2) the subdivision density of the fine line structure grid is controlled; (3) order control of the thin line structure model.)

1. A parameterized curve modeling and grid generation system suitable for a moment method is characterized in that: the method comprises the following steps:

a curve modeling module: the modeling is carried out according to the attribute of the curve; the attributes of the curve comprise those represented by a formula and those represented by no formula; modeling a space three-dimensional curve with formula representation by adopting a curve structure modeling mode with formula representation; for a space three-dimensional curve without formula representation, a fitting function of the space three-dimensional curve is established by utilizing coordinate points, and the fitting function is brought into a curve structure modeling mode with formula representation for modeling;

the line model storage module: the system is used for storing curve model data including curve orders, parameter ranges, parameter sample points and control coordinate points in the modeling process according to a geometric model format;

a line model subdivision module: the subdivision network model is used for dividing the parameter space into K +1 parts according to linear equal division to obtain a subdivision network model which comprises coordinates of the vertex of the generated curve network model and a generated curve connecting unit and is used for forming a line model;

moment method electromagnetism calculation module: for converting the line model into a system matrix by a moment method.

2. The system of claim 1, wherein the system is adapted to model a parametric curve using a moment method and generate a mesh, and comprises: the modeling is carried out on the space three-dimensional curve with the formula representation by adopting a curve structure modeling mode with the formula representation, and comprises the following steps:

the formula of the known spatial three-dimensional stereocurve is characterized as follows:

wherein the integer N is the control order of the curve obtained by curve order control, and the parameter space [ t₀，t_N+1]Equally dividing into N +1 parts according to linearity to obtain a parameter sample point of [ t₀，t₁，...，t_N，t_N+1]And the control coordinate point of the curve model is [ (x)₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_N+1，y_N+1，z_N+1)]

Wherein the content of the first and second substances,

the curve model can be generated through the parameter range, the parameter sample points and the control point coordinates, and the modeling of the parameter curve with formula representation is completed.

3. The system of claim 2, wherein the system is adapted to model a parametric curve using a moment method and generate a mesh, and comprises: for the space three-dimensional curve without formula representation, the fitting function of the space three-dimensional curve is established by using the coordinate points, and the fitting function comprises the following steps:

first, coordinate points of a spatial three-dimensional stereo curve are obtained, which can be obtained from a known gridPicking up in model to form point coordinate list [ P₁，P₂，...，P_M]；

Let i point P therein_iHas the coordinates of (x)_i，y_i，z_i) Cumulative calculation from the starting point P₁To P_iCumulative approximate arc length ofSetting s₁0, wherein_j-P_j-1I denotes the slave point P_jTo P_j-1Is a linear distance in space, i.e.Respectively fitting(s) by using a third-order spline fitting algorithm_i，x_i)、(s_i，y_i) And(s)_i，z_i) Three functions are formed: x ═ x(s); y(s); z ═ z(s); the fitting function of the obtained spatial three-dimensional stereo curve is as follows:

4. the system of claim 3, wherein the system is adapted to model a parametric curve using a moment method and generate a mesh, and comprises: the curve order is N, the parameter range is t₀And t_N+1The parameter sample point is t₀，t₁，...，t_N，t_N+1The control coordinate point is (x)₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_N+1，y_N+1，，z_N+1)；

The method for equally dividing the parameter space into K +1 parts according to linearity to obtain a subdivision network model which forms a line model and comprises a coordinate of a vertex of a generated curve network model and a connecting part of a generated curve unit comprises the following steps:

will parameter space t₀，t_N+1]Equally dividing into K +1 parts according to linearity, the obtained sample point of the parameter is [ t₀，t₁，...，t_K，t_K+1]Then there is t_N+1＝t_K+1And generating coordinates [ (x) of vertices of the curved mesh model₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_K+1，y_K+1，z_K+1)]；

Wherein the content of the first and second substances,

curve generating unit connecting part C₀，C₁，...，C_i，...，C_KIn which C is_iThat is, (i, i +1) indicates that the ith vertex and the (i +1) th vertex constitute the ith curve connecting unit.

5. The system of claim 4, wherein the system is adapted to model a parametric curve using a moment method and generate a mesh, and comprises: the converting the line model into the system matrix by the moment method includes:

loading the generated line grid model into a memory, extracting all adjacent line segment units with common points from all line element grids, and forming a list [ f ] containing nbase line element basis functions₁，f₂，...，f_nbase]According to the following filling formula:

for the basis function f_mAnd a basis function f_mThe inner field value is integrated to obtain an element a_mnFrom a to a_mnForm a system matrix [ A ]]_nbasexnbaseCompleting the line element grid model to the system matrix [ A ]]_nbasexnbaseThe transformation of (3); wherein f is_mAnd f_nIs the m-th and n-th line element basis functions, G is the three-dimensional green's function, ω is the angular frequency,μ_lis relative permeability,. epsilon_lIn order to have a dielectric constant,for the differential operator, r and r' respectively represent f_nCoordinate vector sum f in the basis function domain_mA coordinate vector within the basis function domain;

for the basis function f according to the following filling formula_mThe inner field value is integrated to obtain an element b_mFrom b_mConstitute the right vector rhs, rhs ═ b_m]_nbaseWherein, in the step (A),for field distribution in the mth basis function domain:

solving and calculating Ax (rhs) through matrix solution to obtain the current amount x [ ibase ] on the unknown quantity of each base function ibase of x, wherein the ibase is an integer subscript from 1 to nbase; and completing electromagnetic calculation of a moment method, thereby obtaining a system matrix A.

6. A parameterized curve modeling and grid generating method suitable for a moment method is characterized in that: the method comprises the following steps:

modeling according to the attributes of the curve; the attributes of the curve comprise those represented by a formula and those represented by no formula; modeling a space three-dimensional curve with formula representation by adopting a curve structure modeling mode with formula representation; for a space three-dimensional curve without formula representation, a fitting function of the space three-dimensional curve is established by utilizing coordinate points, and the fitting function is brought into a curve structure modeling mode with formula representation for modeling;

storing curve model data including curve orders, parameter ranges, parameter sample points and control coordinate points in a modeling process according to a geometric model format;

equally dividing the parameter space into K +1 parts according to linearity to obtain a subdivision network model which comprises coordinates of the vertex of the generated curve network model and a generated curve connecting unit and is used for forming a line model;

the line model is converted into a system matrix by a moment method.

7. The method of claim 6, wherein the method comprises the steps of: the modeling is carried out on the space three-dimensional curve with the formula representation by adopting a curve structure modeling mode with the formula representation, and comprises the following steps:

the formula of the known spatial three-dimensional stereocurve is characterized as follows:

wherein the integer N is the control order of the curve obtained by curve order control, and the parameter space [ t₀，t_N+1]Equally dividing into N +1 parts according to linearity to obtain a parameter sample point of [ t₀，t₁，...，t_N，t_N+1]And the control coordinate point of the curve model is [ (x)₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_N+1，y_N+1，z_N+1)]

Wherein the content of the first and second substances,

the curve model can be generated through the parameter range, the parameter sample points and the control point coordinates, and the modeling of the parameter curve with formula representation is completed.

8. The method of claim 7, wherein the method comprises the steps of: for the space three-dimensional curve without formula representation, the fitting function of the space three-dimensional curve is established by using the coordinate points, and the fitting function comprises the following steps:

coordinate points of a spatial three-dimensional stereo curve are first obtained, which can be picked from a known mesh model to form a point coordinate list [ P [ ]₁，P₂，...，P_M]；

Let i point P therein_iHas the coordinates of (x)_i，y_i，z_i) Cumulative calculation from the starting point P₁To P_iCumulative approximate arc length ofSetting s₁0, wherein_j-P_j-1I denotes the slave point P_jTo P_j-1Is a linear distance in space, i.e.Respectively fitting(s) by using a third-order spline fitting algorithm_i，x_i)、(s_i，y_i) And(s)_i，z_i) Three functions are formed: x ═ x(s); y(s); z ═ z(s); the fitting function of the obtained spatial three-dimensional stereo curve is as follows:

9. the method of claim 8, wherein the method comprises the steps of: the curve order is N, the parameter range is t₀And t_N+1The parameter sample point is t₀，t₁，...，t_N，t_N+1The control coordinate point is (x)₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_N+1，y_N+1，z_N+1)；

The method for equally dividing the parameter space into K +1 parts according to linearity to obtain a subdivision network model which forms a line model and comprises a coordinate of a vertex of a generated curve network model and a connecting part of a generated curve unit comprises the following steps:

will parameter space t₀，t_N+1]Equally dividing into K +1 parts according to linearity, the obtained sample point of the parameter is [ t₀，t₁，...，t_K，t_K+1]Then there is t_N+1＝t_K+1And generating coordinates [ (x) of vertices of the curved mesh model₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_K+1，y_K+1，z_K+1)]；

Wherein the content of the first and second substances,

curve generating unit connecting part C₀，C₁，...，C_i，...，C_KIn which C is_iThat is, (i, i +1) indicates that the ith vertex and the (i +1) th vertex constitute the ith curve connecting unit.

10. The method of claim 6, wherein the method comprises the steps of: the converting the line model into the system matrix by the moment method includes:

loading the generated line grid model into a memory, extracting all adjacent line segment units with common points from all line element grids, and forming a list [ f ] containing nbase line element basis functions₁，f₂，...，f_nbase]According to the following filling formula:

for the basis function f_mAnd a basis function f_mThe inner field value is integrated to obtain an element a_mnFrom a to a_mnComposition systemMatrix [ A ]]_nbase×nbaseCompleting the line element grid model to the system matrix [ A ]]_nbase×nbaseThe transformation of (3); wherein f is_mAnd f_nIs the m-th and n-th line element basis functions, G is the three-dimensional green's function, ω is the angular frequency,μ_lis relative permeability,. epsilon_lIn order to have a dielectric constant,for the differential operator, r and r' respectively represent f_nCoordinate vector sum f in the basis function domain_mA coordinate vector within the basis function domain;

for the basis function f according to the following filling formula_mThe inner field value is integrated to obtain an element b_mFrom b_mConstitute the right vector rhs, rhs ═ b_m]_nbaseWherein, in the step (A),for field distribution in the mth basis function domain:

solving and calculating Ax (rhs) through matrix solution to obtain the current amount x [ ibase ] on the unknown quantity of each base function ibase of x, wherein the ibase is an integer subscript from 1 to nbase; and completing electromagnetic calculation of a moment method, thereby obtaining a system matrix A.

Technical Field

The invention relates to the field of electromagnetic field analysis, in particular to a parameterized curve modeling and grid generating system and method suitable for a moment method.

Background

The parameterized curve structure has very wide application in electromagnetic field analysis, such as the fields of thin-line antenna structures, the construction of complex curved surfaces in electromagnetic field analysis and the like. However, the following problems exist in the prior art: (1) continuity problems of fine line structured grids; (2) the subdivision density of the fine line structure grid is controlled; (3) order control of the fine line structure model; (4) the wire mesh is more uniform and is suitable for moment method calculation; (5) the method solves the problems of model generation and mesh generation of a thin line structure which cannot be expressed by a formula.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides a system and a method for parametric curve modeling and grid generation suitable for a moment method.

The purpose of the invention is realized by the following technical scheme:

in a first aspect of the present invention, a parameterized curve modeling and grid generating system suitable for a moment method is provided, which includes:

a curve modeling module: the modeling is carried out according to the attribute of the curve; the attributes of the curve comprise those represented by a formula and those represented by no formula; modeling a space three-dimensional curve with formula representation by adopting a curve structure modeling mode with formula representation; for a space three-dimensional curve without formula representation, a fitting function of the space three-dimensional curve is established by utilizing coordinate points, and the fitting function is brought into a curve structure modeling mode with formula representation for modeling;

the line model storage module: the system is used for storing curve model data including curve orders, parameter ranges, parameter sample points and control coordinate points in the modeling process according to a geometric model format;

a line model subdivision module: the subdivision network model is used for dividing the parameter space into K +1 parts according to linear equal division to obtain a subdivision network model which comprises coordinates of the vertex of the generated curve network model and a generated curve connecting unit and is used for forming a line model;

moment method electromagnetism calculation module: for converting the line model into a system matrix by a moment method.

Further, the modeling of the spatial three-dimensional stereo curve with the formula representation by adopting a curve structure modeling manner with the formula representation includes:

the formula of the known spatial three-dimensional stereocurve is characterized as follows:

wherein the integer N is the control order of the curve obtained by curve order control, and the parameter space [ t₀，t_N+1]Equally dividing into N +1 parts according to linearity to obtain a parameter sample point of [ t₀，t₁，...，t_N，t_N+1]And the control coordinate point of the curve model is [ (x)₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_N+1，y_N+1，z_N+1)]

Wherein the content of the first and second substances,i＝0，1，2，…，N+1

the curve model can be generated through the parameter range, the parameter sample points and the control point coordinates, and the modeling of the parameter curve with formula representation is completed.

Further, for a formulaically characterizable spatial three-dimensional solid curve, establishing a fitting function of the spatial three-dimensional solid curve by using the coordinate points includes:

coordinate points of a spatial three-dimensional stereo curve are first obtained, which can be picked from a known mesh model to form a point coordinate list [ P [ ]₁，P₂，...，P_M]；

Let i point P therein_iHas the coordinates of (x)_i，y_i，z_i) Cumulative calculation from the starting point P₁To P_iCumulative approximate arc length ofSetting s₁0, wherein_j-P_j-1I denotes the slave point P_jTo P_j-1Is a linear distance in space, i.e.Respectively fitting(s) by using a third-order spline fitting algorithm_i，x_i)、(s_i，y_i) And(s)_i，z_i) Three functions are formed: x ═ x(s); y(s); z ═ z(s); the fitting function of the obtained spatial three-dimensional stereo curve is as follows:

further, the curve order is N, and the parameter range is t₀And t_N+1The parameter sample point is t₀，t₁，...，t_N，t_N+1The control coordinate point is (x)₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_N+1，y_N+1，z_N+1)；

The method for equally dividing the parameter space into K +1 parts according to linearity to obtain a subdivision network model which forms a line model and comprises a coordinate of a vertex of a generated curve network model and a connecting part of a generated curve unit comprises the following steps:

will parameter space t₀，t_N+1]Equally dividing into K +1 parts according to linearity, the obtained sample point of the parameter is [ t₀，t₁，...，t_K，t_K+1]Then there is t_N+1＝t_K+1And generating coordinates [ (x) of vertices of the curved mesh model₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_K+1，y_K+1，z_K+1)]；

Wherein the content of the first and second substances,i＝0，1，2，…，K+1

curve generating unit connecting part C₀，C₁，...，C_i，...，C_KIn which C is_i＝(i，i+1) indicates that the ith vertex and the (i +1) th vertex constitute the ith curve connecting unit.

Further, the converting the line model into the system matrix by a moment method includes:

loading the generated line grid model into a memory, extracting all adjacent line segment units with common points from all line element grids, and forming a list [ f ] containing nbase line element basis functions₁，f₂，...，f_nease]According to the following filling formula:

for the basis function f_mAnd a basis function f_mThe inner field value is integrated to obtain an element a_mnFrom a to a_mnForm a system matrix [ A ]]_nbase×nbaseCompleting the line element grid model to the system matrix [ A ]]_nbase×nbaseThe transformation of (3); wherein f is_mAnd f_mIs the m-th and n-th line element basis functions, G is the three-dimensional green's function, ω is the angular frequency,μ_lis relative permeability,. epsilon_lIn order to have a dielectric constant,for the differential operator, r and r' respectively represent f_nCoordinate vector sum f in the basis function domain_mA coordinate vector within the basis function domain;

for the basis function f according to the following filling formula_mThe inner field value is integrated to obtain an element b_mFrom b_mConstitute the right vector rhs, rhs ═ b_m]_nbaseWherein, in the step (A),for field distribution in the mth basis function domain:

solving and calculating Ax (rhs) through matrix solution to obtain the current amount x [ ibase ] on the unknown quantity of each base function ibase of x, wherein the ibase is an integer subscript from 1 to nbase; and completing electromagnetic calculation of a moment method, thereby obtaining a system matrix A.

The second aspect of the present invention provides a parameterized curve modeling and grid generating method suitable for a moment method, comprising the following steps:

modeling according to the attributes of the curve; the attributes of the curve comprise those represented by a formula and those represented by no formula; modeling a space three-dimensional curve with formula representation by adopting a curve structure modeling mode with formula representation; for a space three-dimensional curve without formula representation, a fitting function of the space three-dimensional curve is established by utilizing coordinate points, and the fitting function is brought into a curve structure modeling mode with formula representation for modeling;

storing curve model data including curve orders, parameter ranges, parameter sample points and control coordinate points in a modeling process according to a geometric model format;

equally dividing the parameter space into K +1 parts according to linearity to obtain a subdivision network model which comprises coordinates of the vertex of the generated curve network model and a generated curve connecting unit and is used for forming a line model;

the line model is converted into a system matrix by a moment method.

Further, the modeling of the spatial three-dimensional stereo curve with the formula representation by adopting a curve structure modeling manner with the formula representation includes:

the formula of the known spatial three-dimensional stereocurve is characterized as follows:

wherein the integer N is the control order of the curve obtained by curve order control, and the parameter space [ t₀，t_N+1]According to the lineEqually dividing the sex into N +1 parts, and obtaining a parameter sample point of [ t₀，t₁，...，t_N，t_N+1]And the control coordinate point of the curve model is [ (x)₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_N+1，y_N+1，z_N+1)]

Wherein the content of the first and second substances,i＝0，1，2，…，N+1

the curve model can be generated through the parameter range, the parameter sample points and the control point coordinates, and the modeling of the parameter curve with formula representation is completed.

Further, for a formulaically characterizable spatial three-dimensional solid curve, establishing a fitting function of the spatial three-dimensional solid curve by using the coordinate points includes:

coordinate points of a spatial three-dimensional stereo curve are first obtained, which can be picked from a known mesh model to form a point coordinate list [ P [ ]₁，P₂，...，P_M]；

Let i point P therein_iHas the coordinates of (x)_i，y_i，z_i) Cumulative calculation from the starting point P₁To P_iCumulative approximate arc length ofSetting s₁0, wherein_j-P_j-1I denotes the slave point P_jTo P_j-1Is a linear distance in space, i.e.Respectively fitting(s) by using a third-order spline fitting algorithm_i，x_i)、(s_i，y_i) And(s)_i，z_i) Three functions are formed: x ═ x(s); y(s); z ═ z(s); the fitting function of the obtained spatial three-dimensional stereo curve is as follows:

further, the curve order is N, and the parameter range is t₀And t_N+1The parameter sample point is t₀，t₁，...，t_N，t_N+1The control coordinate point is (x)₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_N+1，y_N+1，z_N+1)；

The method for equally dividing the parameter space into K +1 parts according to linearity to obtain a subdivision network model which forms a line model and comprises a coordinate of a vertex of a generated curve network model and a connecting part of a generated curve unit comprises the following steps:

will parameter space t₀，t_N+1]Equally dividing into K +1 parts according to linearity, the obtained sample point of the parameter is [ t₀，t₁，...，t_K，t_K+1]Then there is t_N+1＝t_K+1And generating coordinates [ (x) of vertices of the curved mesh model₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_K+1，y_K+1，z_K+1)]；

Wherein the content of the first and second substances,i＝0，1，2，…，K+1

curve generating unit connecting part C₀，C₁，...，C_i，...，C_KIn which C is_iThat is, (i, i +1) indicates that the ith vertex and the (i +1) th vertex constitute the ith curve connecting unit.

Further, the converting the line model into the system matrix by a moment method includes:

loading the generated line grid model into a memory, extracting all adjacent line segment units with common points from all line element grids, and forming a list [ f ] containing nbase line element basis functions₁，f₂，...，f_nbase]Push-buttonFill formula as follows:

for the basis function f_mAnd a basis function f_mThe inner field value is integrated to obtain an element a_mnFrom a to a_mnForm a system matrix [ A ]]_nbase×nbaseCompleting the line element grid model to the system matrix [ A ]]_nbase×nbaseThe transformation of (3); wherein f is_mAnd f_nIs the m-th and n-th line element basis functions, G is the three-dimensional green's function, ω is the angular frequency,μ_lis relative permeability,. epsilon_lIn order to have a dielectric constant,for the differential operator, r and r' respectively represent f_nCoordinate vector sum f in the basis function domain_mA coordinate vector within the basis function domain;

for the basis function f according to the following filling formula_mThe inner field value is integrated to obtain an element b_mFrom b_mConstitute the right vector rhs, rhs ═ b_m]_nbaseWherein, in the step (A),for field distribution in the mth basis function domain:

solving and calculating Ax (rhs) through matrix solution to obtain the current amount x [ ibase ] on the unknown quantity of each base function ibase of x, wherein the ibase is an integer subscript from 1 to nbase; and completing electromagnetic calculation of a moment method, thereby obtaining a system matrix A.

The invention has the beneficial effects that:

(1) in an exemplary embodiment of the present invention, the following conditions can be effectively overcome: (1) continuity problems of fine line structured grids; (2) the subdivision density of the fine line structure grid is controlled; 3) order control of the fine line structure model; 4) the problems of model generation and mesh generation of a fine line structure which cannot be expressed by a formula are solved, so that a parameterized curve modeling and mesh generation system which has a good effect and is suitable for a moment method is realized.

(2) In an exemplary embodiment of the invention, specific implementations of the steps are disclosed.

Drawings

FIG. 1 is a block diagram of a parameterized curve modeling and grid generation system suitable for a moment method according to an exemplary embodiment of the present invention;

FIG. 2 is a schematic diagram of a coordinate point pick-up of a curve during modeling of a formulaically characterizable three-dimensional spatial solid curve according to an exemplary embodiment of the present disclosure;

FIG. 3 is a schematic diagram of modeling by substituting a fitting function into a curve structure modeling manner with formula representation in a process of modeling a three-dimensional space curve without formula representation according to an exemplary embodiment of the present invention;

FIG. 4 is a schematic modeling diagram of a helical antenna as disclosed in an exemplary embodiment of the present invention;

fig. 5 is a schematic split view of a helical antenna disclosed in an exemplary embodiment of the present invention;

fig. 6 is a schematic diagram illustrating calculation of a helical antenna according to an exemplary embodiment of the present invention.

Detailed Description

The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

In the description of the present invention, it should be noted that directions or positional relationships indicated by "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", and the like are directions or positional relationships described based on the drawings, and are only for convenience of description and simplification of description, and do not indicate or imply that the device or element referred to must have a specific orientation, be configured and operated in a specific orientation, and thus, should not be construed as limiting the present invention.

In the description of the present invention, it should be noted that, unless otherwise explicitly stated or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. As used in this application and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.

It is to be understood that although the terms first, second, third, etc. may be used herein to describe various information, such information should not be limited to these terms. These terms are only used to distinguish one type of information from another. For example, first information may also be referred to as second information, and similarly, second information may also be referred to as first information, without departing from the scope of the present application. The word "if" as used herein may be interpreted as "at … …" or "when … …" or "in response to a determination", depending on the context. Furthermore, the terms "first" and "second" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.

In addition, the technical features involved in the different embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

Referring to fig. 1, fig. 1 is a block diagram illustrating a parameterized curve modeling and grid generation system suitable for a moment method according to an exemplary embodiment of the present invention, including:

a curve modeling module: the modeling is carried out according to the attribute of the curve; the attributes of the curve comprise those represented by a formula and those represented by no formula; modeling a space three-dimensional curve with formula representation by adopting a curve structure modeling mode with formula representation; for a space three-dimensional curve without formula representation, a fitting function of the space three-dimensional curve is established by utilizing coordinate points, and the fitting function is brought into a curve structure modeling mode with formula representation for modeling;

the line model storage module: the system is used for storing curve model data including curve orders, parameter ranges, parameter sample points and control coordinate points in the modeling process according to a geometric model format;

a line model subdivision module: the subdivision network model is used for dividing the parameter space into K +1 parts according to linear equal division to obtain a subdivision network model which comprises coordinates of the vertex of the generated curve network model and a generated curve connecting unit and is used for forming a line model;

moment method electromagnetism calculation module: for converting the line model into a system matrix by a moment method.

In particular, the method of the present exemplary embodiment may effectively overcome the following situations: (1) continuity problems of fine line structured grids; (2) the subdivision density of the fine line structure grid is controlled; 3) order control of the fine line structure model; 4) the problems of model generation and mesh generation of a fine line structure which cannot be expressed by a formula are solved, so that a parameterized curve modeling and mesh generation system which has a good effect and is suitable for a moment method is realized.

Preferably, in an exemplary embodiment, the modeling the formulaic spatial three-dimensional volume curve by using a formulaic curve structure modeling method includes:

the formula of the known spatial three-dimensional stereocurve is characterized as follows:

wherein the integer N is the control order of the curve obtained by curve order control, and the parameter space [ t₀，t_N+1]Equally dividing into N +1 parts according to linearity to obtain a parameter sample point of [ t₀，t₁，...，t_N，t_N+1]And the control coordinate point of the curve model is [ (x)₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_N+1，y_N+1，z_N+1)]

Wherein the content of the first and second substances,i＝0，1，2，…，N+1

the curve model can be generated through the parameter range, the parameter sample points and the control point coordinates, and the modeling of the parameter curve with formula representation is completed.

Preferably, in an exemplary embodiment, the establishing a fitting function of the spatial three-dimensional stereo curve using the coordinate points for the spatial three-dimensional stereo curve without formula representation includes:

coordinate points of a spatial three-dimensional stereo curve are first obtained, which can be picked from a known mesh model (e.g., the metachromatic points in FIG. 2), forming a point coordinate list [ P [ -P ]₁，P₂，...，P_M]；

Let i point P therein_iHas the coordinates of (x)_i，y_i，z_i) Cumulative calculation from the starting point P₁To P_iCumulative approximate arc length ofSetting s₁0, wherein_j-P_j-1Represents a slave point P_jTo P_j-1Is a linear distance in space, i.e.Respectively fitting(s) by using a third-order spline fitting algorithm_i，x_i)、(s_i，y_i) And(s)_i，z_i) Three functions are formed: x ═ x(s); y(s); z ═ z(s); the fitting function of the obtained spatial three-dimensional stereo curve is as follows:

and then, the fitting function is brought into a curve structure modeling mode with formula representation for modeling, as shown in FIG. 3.

Preferably, in an exemplary embodiment, during the storage process, a common geometric model format such as brep, step, or iges may be adopted for storage, and the storage format of the model is described below by taking iges as an example (other formats are different only in data definition, but the contained data is substantially similar).

The curve order is N, the parameter range is t₀And t_N+1The parameter sample point is t₀，t₁，...，t_N，t_N+1The control coordinate point is (x)₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_N+1，y_N+1，，z_N+1)；

The method for equally dividing the parameter space into K +1 parts according to linearity to obtain a subdivision network model which forms a line model and comprises a coordinate of a vertex of a generated curve network model and a connecting part of a generated curve unit comprises the following steps:

will parameter space t₀，t_N+1]Equally dividing into K +1 parts according to linearity, the obtained sample point of the parameter is [ t₀，t₁，...，t_K，t_K+1]Then there is t_N+1＝t_K+1And generating coordinates [ (x) of vertices of the curved mesh model₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_K+1，y_K+1，z_K+1)]；

Wherein the content of the first and second substances,i＝0，1，2，…，K+1

curve generating unit connecting part C₀，C₁，...，C₁，...，C_KIn which C is_iThat is, (i, i +1) indicates that the ith vertex and the (i +1) th vertex constitute the ith curve connecting unit.

Preferably, in an exemplary embodiment, the converting the line model into the system matrix by a moment method includes:

loading the generated line grid model into a memory, extracting all adjacent line segment units with common points from all line element grids, and forming a list [ f ] containing nbase line element basis functions₁，f₂，...，f_nease]According to the following filling formula:

for the basis function f_mAnd a basis function f_mThe inner field value is integrated to obtain an element a_mnFrom a to a_mnForm a system matrix [ A ]]_nbase×nbaseCompleting the line element grid model to the system matrix [ A ]]_nbase×nbaseThe transformation of (3); wherein f is_mAnd f_nIs the m-th and n-th line element basis functions, G is the three-dimensional green's function, ω is the angular frequency,μ_lis relative permeability,. epsilon_lIn order to have a dielectric constant,for the differential operator, r and r' respectively represent f_nCoordinate vector sum f in the basis function domain_mA coordinate vector within the basis function domain;

for the basis function f according to the following filling formula_mThe inner field value is integrated to obtain an element b_mFrom b_mConstitute the right vector rhs, rhs ═ b_m]_nbaseWherein, in the step (A),for field distribution in the mth basis function domain:

solving and calculating Ax (rhs) through matrix solution to obtain the current amount x [ ibase ] on the unknown quantity of each base function ibase of x, wherein the ibase is an integer subscript from 1 to nbase; and completing electromagnetic calculation of a moment method, thereby obtaining a system matrix A.

The following will illustrate a specific case, modeling, subdivision and calculation of the helical antenna:

the formula for a certain helical antenna operating at 1.645GHz is known as: x is 0.0286cos (2 pi t); y ═ 0.0286sin (2 π t); 0.0387 t; the parameter t range is: t is more than or equal to 0 and less than or equal to 10; and (3) matching with the upper base, wherein the circle with (0, 0, 0) as the center and 0.135 as the radius is obtained, obtaining a spiral antenna model with the base as shown in figure 4, and meshing the spiral antenna model to obtain a divided antenna model as shown in figure 5. The model was analyzed using the method of the exemplary embodiment described above to obtain a 3D far field pattern of the antenna at 1.645GHz, as shown in fig. 6.

The same inventive concept as the above exemplary embodiment, still another exemplary embodiment of the present invention provides a parameterized curve modeling and grid generation method suitable for a moment method, including the steps of:

modeling according to the attributes of the curve; the attributes of the curve comprise those represented by a formula and those represented by no formula; modeling a space three-dimensional curve with formula representation by adopting a curve structure modeling mode with formula representation; for a space three-dimensional curve without formula representation, a fitting function of the space three-dimensional curve is established by utilizing coordinate points, and the fitting function is brought into a curve structure modeling mode with formula representation for modeling;

storing curve model data including curve orders, parameter ranges, parameter sample points and control coordinate points in a modeling process according to a geometric model format;

equally dividing the parameter space into K +1 parts according to linearity to obtain a subdivision network model which comprises coordinates of the vertex of the generated curve network model and a generated curve connecting unit and is used for forming a line model;

the line model is converted into a system matrix by a moment method.

Correspondingly, in an exemplary embodiment, the modeling the formulaically characterized spatial three-dimensional stereo curve by using a formulaically characterized curve structure modeling manner includes:

the formula of the known spatial three-dimensional stereocurve is characterized as follows:

wherein the integer N is the control order of the curve obtained by curve order control, and the parameter space [ t₀，t_N+1]Equally dividing into N +1 parts according to linearity to obtain a parameter sample point of [ t₀，t₁，...，t_N，t_N+1]And the control coordinate point of the curve model is [ (x)₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_N+1，y_N+1，z_N+1)]

Wherein the content of the first and second substances,i＝0，1，2，…，N+1

the curve model can be generated through the parameter range, the parameter sample points and the control point coordinates, and the modeling of the parameter curve with formula representation is completed.

Correspondingly, in an exemplary embodiment, for a formulaless spatial three-dimensional stereo curve, establishing a fitting function of the spatial three-dimensional stereo curve using coordinate points includes:

coordinate points of a spatial three-dimensional stereo curve are first obtained, which can be picked from a known mesh model to form a point coordinate list [ P [ ]₁，P₂，...，P_M]；

Let i point P therein_iHas the coordinates of (x)_i，y_i，z_i) Cumulative calculation from the starting point P₁To P_iCumulative approximate arc length ofSetting s₁0, wherein_j-P_j-1Represents a slave point P_jTo P_j-1Is a linear distance in space, i.e.Respectively fitting(s) by using a third-order spline fitting algorithm_i，x_i)、(s_i，y_i) And(s)_i，z_i) Three functions are formed: x ═ x(s); y(s); z ═ z(s); the fitting function of the obtained spatial three-dimensional stereo curve is as follows:

correspondingly, in an exemplary embodiment, the curve order is N, and the parameter range is t₀And t_N+1The parameter sample point is t₀，t₁，...，t_N，t_N+1The control coordinate point is (x)₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_N+1，y_N+1，z_N+1)；

The method for equally dividing the parameter space into K +1 parts according to linearity to obtain a subdivision network model which forms a line model and comprises a coordinate of a vertex of a generated curve network model and a connecting part of a generated curve unit comprises the following steps:

will be parameterSpace [ t ]₀，t_N+1]Equally dividing into K +1 parts according to linearity, the obtained sample point of the parameter is [ t₀，t₁，...，t_K，t_K+1]Then there is t_N+1＝t_K+1And generating coordinates [ (x) of vertices of the curved mesh model₀，y₀，z₀)，...，(x_i，y_i，z_i)，...，(x_K+1，y_K+1，z_K+1)]；

Wherein the content of the first and second substances,i＝0，1，2，…，K+1

curve generating unit connecting part C₀，C₁，...，C_i，...，C_KIn which C is_iThat is, (i, i +1) indicates that the ith vertex and the (i +1) th vertex constitute the ith curve connecting unit.

Correspondingly, in an exemplary embodiment, the converting the line model into the system matrix by the moment method includes:

loading the generated line grid model into a memory, extracting all adjacent line segment units with common points from all line element grids, and forming a list [ f ] containing nbase line element basis functions₁，f₂，...，f_nbase]According to the following filling formula:

for the basis function f_mAnd a basis function f_mThe inner field value is integrated to obtain an element a_mnFrom a to a_mnForm a system matrix [ A ]]_nbase×nbaseCompleting the line element grid model to the system matrix [ A ]]_nbase×nbaseThe transformation of (3); wherein f is_mAnd f_nIs the m-th and n-th line element basis functions, G is the three-dimensional green's function, ω is the angular frequency,μ_lis relative permeability,. epsilon_lIn order to have a dielectric constant,for the differential operator, r and r' respectively represent f_nCoordinate vector sum f in the basis function domain_mA coordinate vector within the basis function domain;

for the basis function f according to the following filling formula_mThe inner field value is integrated to obtain an element b_mFrom b_mConstitute the right vector rhs, rhs ═ bm]_nbaseWherein, in the step (A),for field distribution in the mth basis function domain:

solving and calculating Ax (rhs) through matrix solution to obtain the current amount x [ ibase ] on the unknown quantity of each base function ibase of x, wherein the ibase is an integer subscript from 1 to nbase; and completing electromagnetic calculation of a moment method, thereby obtaining a system matrix A.

Having the same inventive concept as the above-described exemplary embodiments, an exemplary embodiment of the present invention provides a storage medium having stored thereon computer instructions that, when executed, perform the steps of the method for parameterized curve modeling and grid generation suitable for the moment method.

Having the same inventive concept as the above-described exemplary embodiments, an exemplary embodiment of the present invention provides a terminal, including a memory and a processor, where the memory stores computer instructions executable on the processor, and the processor executes the computer instructions to perform the steps of the parameterized curve modeling and grid generating method suitable for the moment method.

Based on such understanding, the technical solution of the present embodiment or parts of the technical solution may be essentially implemented in the form of a software product stored in a storage medium and including instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-only memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.

It is to be understood that the above-described embodiments are illustrative only and not restrictive of the broad invention, and that various other modifications and changes in light thereof will be suggested to persons skilled in the art based upon the above teachings. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications of the invention may be made without departing from the spirit or scope of the invention.