CN116680933B - Cone surface modeling method based on conformal grid generation - Google Patents
Cone surface modeling method based on conformal grid generation Download PDFInfo
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Abstract
The invention discloses a conical surface modeling method based on conformal grid generation, which comprises the following steps: s1, establishing a sector model to be conformal to the side surface of a cone, performing quadrilateral mesh subdivision of the sector model, and deriving a mesh file generated by subdivision; s2, establishing a mapping relation between each quadrilateral unit and materials in the sector model; s3, acquiring coordinates of three vertexes from the fan-shaped model, and converting the fan-shaped model into a conical surface; s4, generating a conical surface conformal grid; s5, constructing an electromagnetic model of the conical surface. The invention can complete electromagnetic modeling of the conical surface by constructing the sector model, corresponding the units of the sector model to the materials, and then converting the sector model to the conical surface.
Description
Technical Field
The invention relates to electromagnetic modeling, in particular to a conical surface modeling method based on conformal grid generation.
Background
In the fields of computer graphics, computer aided design, computer aided engineering, etc., mesh generation of conical surfaces is an important issue. The traditional conical surface grid generation method generally adopts a parameterization method or directly carries out grid division on the conical surface, but the methods have complex processing and high difficulty in grid generation, so that the problem of difficult modeling can occur when the conical surface needs to be modeled.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a conical surface modeling method based on conformal grid generation, which can complete the generation of the conformal grid of the conical surface by constructing a fan-shaped model, corresponding units of the fan-shaped model to materials, converting the fan-shaped model to the conical surface, and completing the electromagnetic modeling of the conical surface based on the material numbers corresponding to the units.
The aim of the invention is realized by the following technical scheme: a conical surface modeling method based on conformal mesh generation, comprising the steps of:
s1, establishing a sector model to be conformal to the side surface of a cone, performing quadrilateral mesh subdivision of the sector model, and deriving a mesh file generated by subdivision;
the grid file comprises a point coordinate list { Pts } of a fan-shaped model and a quadrilateral unit list { Elm };
the point coordinate listThe number of midpoints is +.>Point coordinate list->Each point having a sequence number, wherein the ith point coordinate is expressed as +.>，
The number of quadrangular units in the quadrangular unit list { Elm } isThe point numbers of the respective vertices in the jth quadrilateral unit are expressed as: />；
S2, establishing a mapping relation between each quadrilateral unit and materials in the sector model;
s3, acquiring coordinates of three vertexes from the fan-shaped model, and converting the fan-shaped model into a conical surface;
s4, generating a conical surface conformal grid: sector mouldEach point in the point coordinate list { Pts } is converted to the conical surface to obtain a new point coordinate listAnd acquires a new quadrangular unit list +.>And the material of each quadrilateral element;
s5, according to the point coordinate listList of quadrilateral elements->And a quadrangular unit listAnd constructing an electromagnetic model of the conical surface by using the materials corresponding to each quadrilateral unit list.
The beneficial effects of the invention are as follows: the method can complete the generation of the conformal grid of the conical surface by constructing a fan-shaped model, corresponding the units of the fan-shaped model to materials, then converting the fan-shaped model to the conical surface, and completing the electromagnetic modeling of the conical surface based on the material numbers corresponding to the units.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of a sector model transition to a conical surface;
FIG. 3 shows an arbitrary point inside a sectorCalculating the point on the side of the cylindrical model +.>Schematic of (2);
fig. 4 is a schematic diagram of the relationship of two coordinate systems.
Detailed Description
The technical solution of the present invention will be described in further detail with reference to the accompanying drawings, but the scope of the present invention is not limited to the following description.
As shown in fig. 1, a conical surface modeling method based on conformal mesh generation includes the following steps:
s1, establishing a sector model to be conformal to the side surface of a cone, performing quadrilateral mesh subdivision of the sector model, and deriving a mesh file generated by subdivision;
the grid file comprises a point coordinate list { Pts } of a fan-shaped model and a quadrilateral unit list { Elm };
the point coordinate listThe number of midpoints is +.>Point coordinate list->Each point has a sequence number, wherein the ith point coordinate (the point coordinate of the point with the sequence number i) is expressed as follows:
the number of quadrangular units in the quadrangular unit list { Elm } isThe point numbers of the respective vertices in the jth quadrilateral unit are expressed as: />；
S2, establishing a mapping relation between each quadrilateral unit and materials in the sector model;
the step S2 includes:
s201, setting materials for different quadrilateral units of the sector model, wherein a material list is { icoat }, and each material in the list is provided with a number;
s202, list quadrilateral unitsOne-to-one correspondence with the material list { icoat }, i.e. each quadrilateral element has a corresponding number in the material list, the material number of the jth quadrilateral element being expressed asThe material numbers are integers.
S3, acquiring coordinates of three vertexes from the fan-shaped model, and converting the fan-shaped model into a conical surface:
as shown in fig. 2, in the step S3,is fan-shaped with three vertexes +.>, and />Two sides forming a sector, then:
sector radius，/>Fan arc length；
In order to consider the situation that the fan surface does not cover the conical surface completely, a coefficient is setSo that the arc length is +.>The sector of (2) can just cover the whole conical surface to obtain the diameter of the conical bottom surface +.>Thereby obtaining the included angle of the conical surfaceThe height of the cone is +.>。
S4, generating and calculating the conformal grid of the conical surface to obtain a new point coordinate list；
As shown in fig. 3, the point coordinate list is performed in the step S4In the acquisition, the points inside the sector are converted to the side of the conical model, and any point inside the sector is utilized>Calculating the point on the side of the conical model +.>The way of (2) is as follows:
establishing a local coordinate system and />，/>Is the center of the bottom surface of the cone, and is>Point P1, < >>The vertex is a fan-shaped vertex, P1 is a conformal edge vertex of the fan shape, and P3 is another edge vertex of the fan shape;
as shown in fig. 4, the relationship of two local coordinate systems is expressed as:
wherein ,,/>is vector cross multiplication;
then there are:
；
sector radius in position ∈>Arc angle isThere is arc length +>Mapping to +.>In the position of the device, the device is provided with a plurality of grooves,radius of circular arc at position +.>，/>，
Is->And->Connecting the extension line with the conical bottom surface->Included angle->Is->In the x-axis direction component, +.>Is thatIn the y-axis direction component, +.>Is->In the z-axis direction, there are:
namely:
。
in the step S4, each point in the point coordinate list { Pts } of the fan-shaped model is converted to the conical surface to obtain a new point coordinate listThe process of (1) comprises:
s401 initializing a Point listIs->A two-dimensional array of (a) is provided; the three columns store the dot list respectivelyXYZ coordinate floating point data of (a); walk->List of individual points->Obtain the i-th point->The coordinates of this point are expressed as: />And is marked as +.>；
S402.Sector radius in position ∈>Arc angle isThere is arc length +>Mapping to +.>In position, a->Radius of circular arc at position +.>The method comprises the following steps of:
，
calculating and obtaining new coordinates of the mapping points as：
；
S403, ith will beCoordinates of->Assigning new coordinates->：
；
S404, circulating the steps S401 to S403 until the completionAnd (5) finishing the calculation flow of generating the conformal grid of the conical surface until the points are traversed.
The new quadrilateral unit list of the conical surface is obtainedAnd the process of the material of each quadrilateral element includes:
a1, for quadrilateral Unit listFirst according to the numbers of the four vertexesIn the dot coordinate list->Searching corresponding four vertex coordinates, searching four vertex coordinates obtained after the fourth vertex is converted to the conical surface, and obtaining a jth quadrilateral unit +_ in the sector model>Corresponding +.>And will->Material number>Marked as->；
A2 for quadrilateral Unit ListRepeating step A1 to obtain a quadrangular unit list of conical surfaces ++>And a material number of each quadrangular unit.
S5, according to the point coordinate listList of quadrilateral elements->And a quadrangular unit listAnd constructing an electromagnetic model of the conical surface by using the materials corresponding to each quadrilateral unit list.
The foregoing is a preferred embodiment of the invention, and it is to be understood that the invention is not limited to the form disclosed herein, but is not to be construed as limited to other embodiments, but is capable of other combinations, modifications and environments and is capable of changes or modifications within the scope of the inventive concept, either as a result of the foregoing teachings or as a result of the knowledge or knowledge of the relevant art. And that modifications and variations which do not depart from the spirit and scope of the invention are intended to be within the scope of the appended claims.
Claims (4)
1. A conical surface modeling method based on conformal grid generation is characterized by comprising the following steps of: the method comprises the following steps:
s1, establishing a sector model to be conformal to the side surface of a cone, performing quadrilateral mesh subdivision of the sector model, and deriving a mesh file generated by subdivision;
the grid file comprises a point coordinate list { Pts } of a fan-shaped model and a quadrilateral unit list { Elm };
the point coordinate listThe number of midpoints is +.>Point coordinate list->Each point has a sequence number, wherein the ith point coordinate is expressed as: />，
The number of quadrangular units in the quadrangular unit list { Elm } isThe point numbers of the respective vertices in the jth quadrilateral unit are expressed as: />；
S2, establishing a mapping relation between each quadrilateral unit and materials in the sector model;
s3, acquiring coordinates of three vertexes from the fan-shaped model, and converting the fan-shaped model into a conical surface;
s4, generating a conical surface conformal grid: converting each point in the point coordinate list { Pts } of the fan-shaped model into a conical surface to obtain a new point coordinate listAnd acquires a new quadrangular unit list { about the conical surface>-and the material of each quadrilateral element;
the point coordinate list is performed in the step S4In the acquisition, the points inside the sector are converted to the side of the conical model, and any point inside the sector is utilized>Calculating the point on the side of the conical model +.>The way of (2) is as follows:
establishing a local coordinate system and />，/>Is the center of the bottom surface of the cone, and is>The point is defined as the P1 point,the vertex is a fan-shaped vertex, P1 is a conformal edge vertex of the fan shape, and P3 is another edge vertex of the fan shape;
the relationship of the two local coordinate systems is expressed as:
wherein ,,/>is vector cross multiplication;
then there are:
；
sector radius in position ∈>Arc angle +.>There is arc length +>Mapping to +.>In position, a->Radius of circular arc at position +.>，，
Is->And->Connecting the extension line with the conical bottom surface->Is included in the plane of the first part; />Is->In the x-axis direction component, +.>Is->In the y-axis direction component, +.>Is->In the z-axis direction, there are:
namely:
in the step S4, each point in the point coordinate list { Pts } of the fan-shaped model is converted to the conical surface to obtain a new point coordinate listThe process of (1) comprises:
s401 initializing a Point listIs->A two-dimensional array of (a) is provided; the three columns store the dot list +.>XYZ coordinate floating point data of (a); walk->List of individual points->Obtain the i-th point->The coordinates of this point are expressed as:and is marked as +.>；
S402.Sector radius in position ∈>Arc angle +.>There is arc length +>Mapping to +.>In position, a->Radius of circular arc at position +.>The method comprises the following steps of:
，
calculating and obtaining new coordinates of the mapping points as,/>)：
；
S403, ith will beCoordinates of->Assigning new coordinates->：
；
S404, circulating the steps S401 to S403 until the completionFinishing the calculation flow of generating the conformal grid of the conical surface until the points are traversed;
s5, according to sittingLabel listList of quadrilateral elements->And quadrangular unit list ++>And constructing an electromagnetic model of the conical surface by using the materials corresponding to each quadrilateral unit list.
2. A method of modeling a conical surface based on conformal mesh generation according to claim 1, wherein: the step S2 includes:
s201, setting materials for different quadrilateral units of the sector model, wherein a material list is { icoat }, and each material in the list is provided with a number;
s202, list quadrilateral unitsOne-to-one correspondence with the material list { icoat }, i.e. each quadrilateral unit has a corresponding number in the material list, the material number of the jth quadrilateral unit is denoted +.>The material numbers are integers.
3. A method of modeling a conical surface based on conformal mesh generation according to claim 1, wherein: in the step S3 of the above-mentioned process,is fan-shaped with three vertexes +.> and />Two sides forming a sector, then:
sector radius，/>Sector arc length +.>；
In order to consider the situation that the fan surface does not cover the conical surface completely, a coefficient is setSo that the arc length is +.>The sector of (2) can just cover the whole conical surface to obtain the diameter of the conical bottom surface +.>Thereby obtaining the cone angle +.>The height of the cone is +.>。
4. A method of modeling a conical surface based on conformal mesh generation according to claim 1, wherein: in the step S4, a new quadrilateral unit list { of the conical surface is obtainedThe process of the material of each quadrilateral element includes:
a1 { for quadrilateral element listThe j-th quadrilateral unit of the first four vertices are numbered according to the numbers of the four verticesIn the dot coordinate list->Searching corresponding four vertex coordinates, searching four vertex coordinates obtained after the fourth vertex is converted to the conical surface, and obtaining a jth quadrilateral unit +_ in the sector model>Corresponding +.>And will->Material numbering in (a)Marked as->;
A2 { for quadrilateral element listEach quadrangular unit of }, repeating the step A1 to obtain a quadrangular unit list of conical surfaces { }>And the material number of each quadrangular unit.
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| CN113221370A (en) * | 2021-05-25 | 2021-08-06 | 西安电子科技大学 | FSS antenna housing modeling method based on conical surface projection |
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| KR100695019B1 (en) * | 2005-10-28 | 2007-03-14 | 삼성중공업 주식회사 | Window sampling method using digital image |
| CN113221370A (en) * | 2021-05-25 | 2021-08-06 | 西安电子科技大学 | FSS antenna housing modeling method based on conical surface projection |
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