CN114429535A - Smooth cutting method and device for triangular mesh curved surface - Google Patents
Smooth cutting method and device for triangular mesh curved surface Download PDFInfo
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- CN114429535A CN114429535A CN202111676318.8A CN202111676318A CN114429535A CN 114429535 A CN114429535 A CN 114429535A CN 202111676318 A CN202111676318 A CN 202111676318A CN 114429535 A CN114429535 A CN 114429535A
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- 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
Abstract
The invention discloses a smooth cutting method and device for a triangular mesh curved surface. The system obtains the intersection points of the first triangular mesh curved surface and the second triangular mesh curved surface on the triangular patch by traversing all triangular patches of a plurality of intersected triangular mesh curved surfaces, connects the intersection points on the same triangular patch to obtain a series of intersected line segments, and sequentially connects the intersected line segments to obtain the intersected curve of the first triangular mesh curved surface and the second triangular mesh curved surface; and cutting the plurality of intersected triangular mesh curved surfaces according to the intersected curves, and performing first re-subdivision processing on each first patch of the plurality of triangular mesh curved surfaces obtained after cutting according to a Jordan broken line method, wherein the first patch is a non-triangular patch. The technical scheme of the invention improves the smoothness of the cutting boundary when the intersected triangular mesh curved surface is cut.
Description
Technical Field
The invention relates to the technical field of curved surface cutting, in particular to a smooth cutting method and device for a triangular mesh curved surface.
Background
The method is applied to the fields of virtual reality, digital twinning, Computer Aided Design (CAD) and the like, and is particularly applied to the operations of intersection, cutting, editing and the like of the curved surface of the digital model. The triangular mesh has the advantages of simplicity, strong operability, wide support by graphic hardware and the like, and is one of the mainstream methods for representing complex three-dimensional digital models and three-dimensional curved surfaces. Mathematically, a triangle mesh surface (shortly called triangle mesh) is defined as a form of a single connectivity graph:
S＝S(X,G), (1)
wherein X ═ { X ═ Xi＝(xi,yi,zi) I ═ 1,2, …, N } is the geometric position of the triangle mesh vertex, G ═ G (V, E, F) is a simply connected triangle plane graph, and a triangle mesh model is formed by three parts of mesh points (vertices), mesh edges (edges), and triangle patches (faces) in sequence according to a prescribed connection mode, as shown in fig. 3.
With the wide application of triangular mesh surfaces in the fields of geometric modeling, three-dimensional reconstruction, digital twinning, virtual reality and the like, geometric processing for triangular mesh surfaces, such as surface intersection, cutting and the like, becomes one of the most basic and important problems, and is widely concerned in the industry as a basic technical means for completing three-dimensional modeling of complex products and three-dimensional virtual simulation of complex scenes and a main performance index for measuring system design and interaction capacity. The surfaces of a plurality of complex products and complex scenes cannot be represented by using a complete curved surface, and the requirement of modeling and three-dimensional reconstruction can be met only by performing curved surface intersection and cutting during splicing of a plurality of curved surfaces.
In the process of intersection and clipping of the triangular mesh curved surface, the vertex of the intersection line of the mesh curved surface is caused to fall inside the mesh patch instead of on the boundary mesh line by the error generated by floating point operation, which destroys the topological structure of the original mesh. Even if the intersection line L is found that does not change the original topology of the two triangular mesh curved surfaces M1 and M2, the intersection line L usually falls inside the mesh curved surface M1 to be cut, i.e., the intersection line L divides the mesh curved surface M1 into two regions, as shown in fig. 4. The traditional surface clipping method adopts a method of deleting vertexes and edges, which causes unsmooth boundary of the clipped mesh surface and generates stronger saw-tooth noise. Smooth clipping of the mesh surface requires re-meshing (remesh) of the mesh surface M1 with the intersection line L, which is a technical difficulty to be solved.
Disclosure of Invention
The invention provides a smooth cutting method and a smooth cutting device for a triangular mesh curved surface, which improve the smoothness of a cutting boundary when cutting an intersected triangular mesh curved surface.
An embodiment of the present invention provides a smooth clipping method for a triangular mesh curved surface, including the following steps:
the method comprises the steps that all triangular surface patches of a plurality of intersected triangular mesh surface surfaces are traversed to obtain intersection points of a first triangular mesh surface and a second triangular mesh surface on the triangular surface patches, the intersection points on the same triangular surface patch are connected to obtain a series of intersected line segments, and the intersected line segments are sequentially connected to obtain an intersected curve of the first triangular mesh surface and the second triangular mesh surface;
and cutting the plurality of intersected triangular mesh curved surfaces according to the intersected curves, and performing first re-subdivision processing on each first patch of the plurality of triangular mesh curved surfaces obtained after cutting according to a Jordan broken line method, wherein the first patch is a non-triangular patch.
Further, the cutting of the plurality of intersecting triangular mesh curved surfaces according to the intersecting curves specifically comprises:
determining each triangular patch where the intersection curve is located, obtaining an intersection line on the triangular patches, and cutting the triangular patches according to the intersection line to obtain a plurality of second patches;
judging whether an intersection line exists on the second panel, if not, stopping cutting, if so, acquiring the intersection line on the second panel, cutting the second panel according to the acquired intersection line, marking the cut panel as the second panel, and continuing to judge the second panel until the intersection line does not exist on the second panel.
Further, according to a Jordan broken line method, performing first re-subdivision processing on each first surface piece of the plurality of triangular mesh curved surfaces obtained after cutting, specifically:
forming a point set by the vertexes of the first patches according to a clockwise or anticlockwise sequence, and calculating the direction vector of the plane where the polygonal patch is located according to the point set and a tangent rotation theorem;
selecting a vertex meeting a first preset condition from the point set according to the direction vector, wherein the first preset condition comprises that an angle where the vertex is located is an internal angle and a connecting line of two adjacent vertexes of the vertex in the point set does not intersect with a boundary line of the first patch;
and establishing a first triangular patch and a second patch according to the selected vertex, judging whether the second patch is the triangular patch, if so, stopping subdivision, otherwise, recording the second patch as the first patch, and continuing the first subdivision processing until the second patch is triangular, and stopping subdivision.
Further, selecting a vertex meeting a first preset condition from the point set according to the direction vector, specifically:
determining the direction vector and the vector (p)i-pi-1)∧(pi+1-pi) Whether or not in the same direction, wherein piRepresenting a certain vertex, p, of said set of pointsi+1Representing a vertex piAt the latter vertex in the set of points, pi-1A previous vertex in the set of points; if yes, judging the vertex piThe angle is an internal angle; if not, judging the vertex piThe angle is not an internal angle;
judging whether the vertex q is positioned at the vertex pi+1、piAnd pi-1Within the enclosed triangle, the vertex q is the point set divided by pi+1、piAnd pi-1One vertex outside; if the vertex q is in the triangle, judging the vertex piA connecting line of two adjacent vertexes in the point set is intersected with a boundary line of the first patch; if the vertex q is not in the triangle, judging the vertex piA connecting line of two adjacent vertexes in the point set does not intersect with the boundary line of the first patch;
selecting a vertex p meeting a first predetermined conditioniThe vertex piThe angle is an internal angleAnd said vertex piA line connecting two adjacent vertices in the set of points does not intersect a boundary line of the first patch.
The invention also provides a smooth cutting device for the triangular mesh curved surface, which is characterized by comprising a module for calculating an intersecting curve and a cutting module;
the intersection curve calculating module is used for obtaining intersection points of the first triangular mesh curved surface and the second triangular mesh curved surface on the triangular surface patch by traversing all triangular surface patches of a plurality of intersecting triangular mesh curved surfaces, connecting the intersection points on the same triangular surface patch to obtain a series of intersection line segments, and sequentially connecting the intersection line segments to obtain an intersection curve of the first triangular mesh curved surface and the second triangular mesh curved surface;
the cutting module is used for cutting the plurality of intersected triangular mesh curved surfaces according to the intersected curves, and carrying out first re-subdivision processing on each first surface piece of the plurality of triangular mesh curved surfaces obtained after cutting according to a Jordan broken line method, wherein the first surface piece is a non-triangular surface piece.
The embodiment of the invention has the following beneficial effects:
the invention provides a smooth cutting method and a device for a triangular mesh curved surface, which solve the problem of intersection of the mesh curved surface by subdividing a polygonal patch by adopting a Jordan broken line method, namely solve the problem that the intersection point of the mesh curved surface is positioned inside the triangular patch to destroy the topological structure of a mesh model. The smoothness of the cutting boundary is improved when the given triangular mesh curved surface is cut, and the boundary sawtooth phenomenon generated when the curved surface is cut by the traditional method is avoided. The embodiment of the invention can give consideration to the dual targets of triangular mesh surface intersection and clipping, realizes automatic intersection operation and clipping operation of a large-scale virtual scene model, can provide important technical support for the fields of virtual reality, digital twins and the like, and has great significance for realizing fully-adaptive interactive virtual scene construction and editing technology.
Drawings
FIG. 1 is a flowchart of a smooth clipping method for triangular mesh surfaces according to an embodiment of the present invention;
FIG. 2 is a block diagram of a smooth clipping apparatus for triangular mesh surfaces according to an embodiment of the present invention;
FIG. 3 is a comparison of a triangular mesh surface and a triangular plane provided by the present invention;
FIG. 4 is a schematic diagram of an intersection L between a triangle mesh surface M1 and a triangle mesh surface M2 according to an embodiment of the present invention;
FIG. 5 is a schematic diagram illustrating a patch clipping of a triangular mesh surface according to an embodiment of the present invention;
FIG. 6 is a schematic diagram illustrating a further patch clipping of a triangular mesh surface according to an embodiment of the present invention;
fig. 7 is a schematic diagram of establishing a first triangular patch according to an embodiment of the present invention.
Detailed Description
The technical solutions in the present invention will be described clearly and completely with reference to the accompanying drawings, and it is obvious that the described embodiments are only some embodiments of the present invention, not all embodiments. 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.
As shown in fig. 1, a smooth clipping method for a triangular mesh curved surface according to an embodiment of the present invention includes the following steps:
step S101: the method comprises the steps that all triangular surface patches of a plurality of intersected triangular mesh surface surfaces are traversed to obtain intersection points of a first triangular mesh surface and a second triangular mesh surface on the triangular surface patches, the intersection points on the same triangular surface patch are connected to obtain a series of intersected line segments, and the intersected line segments are sequentially connected to obtain an intersected curve of the first triangular mesh surface and the second triangular mesh surface;
step S102: and cutting the plurality of intersected triangular mesh curved surfaces according to the intersected curves, and performing first re-subdivision processing on each first patch of the plurality of triangular mesh curved surfaces obtained after cutting according to a Jordan broken line method, wherein the first patch is a non-triangular patch.
And (4) after the subdivision processing is carried out on the surface patches of the intersected triangular mesh curved surfaces, a plurality of subdivided triangular mesh curved surfaces are obtained. And the intersection lines among the subdivided triangular mesh curved surfaces are just the boundary line segments of the triangular mesh curved surfaces. Therefore, the clipping is only required to be performed along the boundary of the subdivided triangular mesh surface. Specifically, when the triangular mesh curved surface is cut along the boundary, the cutting operation is carried out according to the storage structure of the triangular mesh curved surface, and the storage structure information of the cut mesh curved surface is stored, including the storage structure information of the cut non-triangular surface patch.
As an embodiment, the cutting the plurality of intersecting triangular mesh curved surfaces according to the intersecting curves specifically includes:
as shown in fig. 5, determining each triangular patch where the intersection curve is located, obtaining an intersection line on the triangular patch, and cutting the triangular patch according to the intersection line to obtain a plurality of second patches;
judging whether an intersection line exists on the second panel, and if not, stopping cutting; as shown in fig. 6, if yes, an intersection line on the second patch is obtained, the second patch is cut according to the obtained intersection line, the cut patch is marked as a second patch, and the cutting of the second patch is continued until no intersection line exists on the second patch.
As one embodiment, the first re-subdivision processing is performed on each first surface piece of the plurality of triangular mesh curved surfaces obtained after cutting according to a Jordan broken line method, specifically:
forming a point set by the vertexes of each first patch according to a clockwise or anticlockwise sequence, and calculating a direction vector of a plane where the polygonal patch is located according to the point set and a tangent gyration theorem; the set of points is denoted p0,p1,…,pn-1。
Selecting a vertex meeting a first preset condition from the point set according to the direction vector, wherein the first preset condition comprises that an angle where the vertex is located is an internal angle and a connecting line of two adjacent vertexes of the vertex in the point set does not intersect with a boundary line of the first patch;
as shown in fig. 7, a first triangular patch and a third patch are established according to the selected vertex, whether the third patch is a triangular patch is judged, if so, the subdivision is stopped, otherwise, the third patch is marked as the first patch, and the first subdivision processing is continued until the third patch is a triangle, and the subdivision is stopped.
Due to the rounding and error precision problems of the floating point number of the computer, the intersection points on each patch cannot be guaranteed to be correctly corresponding and connected. When the intersection points fall in the triangular mesh surface, but not on the edge of the mesh, the topology structure of the original mesh surface is damaged by directly connecting the intersection points, so that the first subdivision processing needs to be performed on each first surface sheet of the plurality of triangular mesh surface aiming at the problem. And when judging whether the intersection point falls on the boundary of the triangular surface patch, calculating the distance from the intersection point to the boundary, if the distance is smaller than a preset threshold value, judging that the intersection point falls on the corresponding edge, otherwise, judging that the intersection point falls inside the surface patch.
As an embodiment, selecting a vertex meeting a first preset condition from the point set according to the direction vector includes:
determining the direction vector and the vector (p)i-pi-1)∧(pi+1-pi) Whether or not in the same direction, wherein piRepresenting a certain vertex, p, of said set of pointsi+1Representing a vertex piAt the latter vertex in the set of points, pi-1A previous vertex in the set of points; if yes, judging the vertex piThe angle is an internal angle; if not, judging the vertex piThe included angle is not an interior angle.
Judging whether the vertex q is positioned at the vertex pi+1、piAnd pi-1Within the enclosed triangle, the vertex q is the point set divided by pi+1、piAnd pi-1One vertex outside; if the vertex q is in the triangle, judging the vertex piA line connecting two adjacent vertices in the set of points with the patch of the first patchThe boundary lines are crossed; if the vertex q is not in the triangle, judging the vertex piA connecting line of two adjacent vertexes in the point set does not intersect with the boundary line of the first patch; wherein
Selecting a vertex p meeting a first predetermined conditioniThe vertex piThe angle is an internal angle, and the vertex piA line connecting two adjacent vertices in the set of points does not intersect a boundary line of the first patch. That is, it is necessary to determine whether the first triangular patch created by splitting is combined with the original area boundary and intersected with the original area boundary (i.e., whether the first triangular patch is combined with the first patch before this splitting and intersected).
As an embodiment, calculating the direction vector of the plane specifically includes: for the point set p0,p1,…,pn-1Each vertex p in (1)iComputing
Due to each vertex
Direction of (a) and (p)i-pi-1)∧(pi+1-pi) In the same direction, the two ends of the steel wire are connected with the same wire,
has a mode length of theta equal to theta, theta being pi-pi-1And pi+1-piIs then
According to the method and the device, the problem of intersection of the mesh curved surface is solved by adopting a Jordan broken line method to subdivide the polygonal patch, namely the problem that the topological structure of the mesh model is damaged when the intersection point of the mesh curved surface is positioned inside the triangular patch is solved. The method has the advantages that when the given triangular mesh curved surface is cut, the smoothness of the cutting boundary is kept, and the boundary sawtooth phenomenon caused by the traditional method when the curved surface is cut is avoided. The embodiment of the invention can give consideration to the dual targets of triangular mesh surface intersection and clipping, realizes automatic intersection operation and clipping operation of a large-scale virtual scene model, can provide important technical support for the fields of virtual reality, digital twins and the like, and has great significance for realizing fully-adaptive interactive virtual scene construction and editing technology.
As shown in fig. 2, on the basis of the above method embodiment, the present invention correspondingly provides an apparatus embodiment;
the invention provides a smooth cutting device for a triangular mesh curved surface, which comprises a module for calculating an intersecting curve and a cutting module;
the intersection curve calculating module is used for obtaining intersection points of the first triangular mesh curved surface and the second triangular mesh curved surface on the triangular surface patch by traversing all triangular surface patches of a plurality of intersecting triangular mesh curved surfaces, connecting the intersection points on the same triangular surface patch to obtain a series of intersection line segments, and sequentially connecting the intersection line segments to obtain an intersection curve of the first triangular mesh curved surface and the second triangular mesh curved surface;
the cutting module is used for cutting the plurality of intersected triangular mesh curved surfaces according to the intersected curves, and carrying out first re-subdivision processing on each first surface piece of the plurality of triangular mesh curved surfaces obtained after cutting according to a Jordan broken line method, wherein the first surface piece is a non-triangular surface piece
As an embodiment, the cutting the plurality of intersecting triangular mesh curved surfaces according to the intersecting curves specifically includes:
determining each triangular patch where the intersection curve is located, obtaining an intersection line on the triangular patches, and cutting the triangular patches according to the intersection line to obtain a plurality of second patches;
judging whether an intersection line exists on the second panel, if not, stopping cutting, if so, acquiring the intersection line on the second panel, cutting the second panel according to the acquired intersection line, marking the cut panel as the second panel, and continuing to judge the second panel until the intersection line does not exist on the second panel.
As one embodiment, the first re-subdivision processing is performed on each first surface piece of the plurality of triangular mesh curved surfaces obtained after cutting according to a Jordan broken line method, specifically:
forming a point set by the vertexes of each first patch according to a clockwise or anticlockwise sequence, and calculating a direction vector of a plane where the polygonal patch is located according to the point set and a tangent gyration theorem;
selecting a vertex meeting a first preset condition from the point set according to the direction vector, wherein the first preset condition comprises that an angle where the vertex is located is an internal angle and a connecting line of two adjacent vertexes of the vertex in the point set does not intersect with a boundary line of the first patch;
and establishing a first triangular patch and a second patch according to the selected vertex, judging whether the second patch is the triangular patch, if so, stopping subdivision, otherwise, recording the second patch as the first patch, and continuing the first subdivision processing until the second patch is triangular, and stopping subdivision.
As an embodiment, selecting a vertex meeting a first preset condition from the point set according to the direction vector includes:
determining the direction vector and the vector (p)i-pi-1)∧(pi+1-pi) Whether or not in the same direction, wherein piRepresenting a certain vertex, p, of said set of pointsi+1Representing a vertex piAt the latter vertex in the set of points, pi-1A previous vertex in the set of points; if yes, judging the vertex piThe angle is an internal angle; if not, judging the vertex piThe angle is not an internal angle;
judging whether the vertex q is positioned at the vertex pi+1、piAnd pi-1Within the enclosed triangle, the vertex q is the point set divided by pi+1、piAnd pi-1One vertex outside; if the vertex q is in the triangle, judging the vertex piTwo neighbors in said set of pointsThe connecting line of the top points is intersected with the boundary line of the first patch; if the peak q is not in the triangle, judging the peak piA connecting line of two adjacent vertexes in the point set does not intersect with the boundary line of the first patch;
selecting a vertex p meeting a first predetermined conditioniThe vertex piThe angle is an internal angle, and the vertex piA line connecting two adjacent vertices in the set of points does not intersect a boundary line of the first patch.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.
It will be understood by those skilled in the art that all or part of the processes of the above embodiments may be implemented by hardware related to instructions of a computer program, and the computer program may be stored in a computer readable storage medium, and when executed, may include the processes of the above embodiments. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like.
Claims (5)
1. A smooth cutting method for a triangular mesh curved surface is characterized by comprising the following steps:
the method comprises the steps that all triangular surface patches of a plurality of intersected triangular mesh surface surfaces are traversed to obtain intersection points of a first triangular mesh surface and a second triangular mesh surface on the triangular surface patches, the intersection points on the same triangular surface patch are connected to obtain a series of intersected line segments, and the intersected line segments are sequentially connected to obtain an intersected curve of the first triangular mesh surface and the second triangular mesh surface;
and cutting the plurality of intersected triangular mesh curved surfaces according to the intersected curves, and performing first re-subdivision processing on each first patch of the plurality of triangular mesh curved surfaces obtained after cutting according to a Jordan broken line method, wherein the first patch is a non-triangular patch.
2. The smooth clipping method for triangular mesh curved surfaces according to claim 1, wherein clipping the plurality of intersecting triangular mesh curved surfaces according to the intersecting curves is specifically:
determining each triangular patch where the intersection curve is located, obtaining an intersection line on the triangular patches, and cutting the triangular patches according to the intersection line to obtain a plurality of second patches;
judging whether an intersection line exists on the second panel, if not, stopping cutting, if so, acquiring the intersection line on the second panel, cutting the second panel according to the acquired intersection line, marking the cut panel as the second panel, and continuing to judge the second panel until the intersection line does not exist on the second panel.
3. The smooth clipping method for triangular mesh curved surfaces according to claim 2, wherein the first re-subdivision process is performed on each first surface slice of the plurality of triangular mesh curved surfaces obtained after clipping according to a Jordan broken line method, specifically:
forming a point set by the vertexes of each first patch according to a clockwise or anticlockwise sequence, and calculating a direction vector of a plane where the polygonal patch is located according to the point set and a tangent gyration theorem;
selecting a vertex meeting a first preset condition from the point set according to the direction vector, wherein the first preset condition comprises that an angle where the vertex is located is an internal angle and a connecting line of two adjacent vertexes of the vertex in the point set is not intersected with a boundary line of the first patch;
and establishing a first triangular patch and a second patch according to the selected vertex, judging whether the second patch is the triangular patch, if so, stopping subdivision, otherwise, recording the second patch as the first patch, and continuing the first subdivision processing until the second patch is triangular, and stopping subdivision.
4. The method for smooth clipping of a triangular mesh curved surface according to any one of claims 1 to 3, wherein a vertex meeting a first preset condition is selected from the point set according to the direction vector, specifically:
determining the direction vector and the vector (p)i-pi-1)∧(pi+1-pi) Whether or not in the same direction, wherein piRepresenting a certain vertex, p, of said set of pointsi+1Representing a vertex piAt the latter vertex in the set of points, pi-1A previous vertex in the set of points; if yes, judging the vertex piThe angle is an internal angle; if not, judging the vertex piThe angle is not an internal angle;
judging whether the vertex q is positioned at the vertex pi+1、piAnd pi-1Within the enclosed triangle, the vertex q is the point set divided by pi+1、piAnd pi-1One vertex outside; if the vertex q is in the triangle, judging the vertex piA connecting line of two adjacent vertexes in the point set is intersected with a boundary line of the first patch; if the vertex q is not in the triangle, judging the vertex piA connecting line of two adjacent vertexes in the point set does not intersect with the boundary line of the first patch;
selecting a vertex p meeting a first predetermined conditioniThe vertex piThe angle is an internal angle, and the vertex piA line connecting two adjacent vertices in the set of points does not intersect a boundary line of the first patch.
5. A smooth cutting device for a triangular mesh curved surface is characterized by comprising a module for calculating an intersecting curve and a cutting module;
the intersection curve calculating module is used for obtaining intersection points of the first triangular mesh curved surface and the second triangular mesh curved surface on the triangular surface patch by traversing all triangular surface patches of a plurality of intersecting triangular mesh curved surfaces, connecting the intersection points on the same triangular surface patch to obtain a series of intersection line segments, and sequentially connecting the intersection line segments to obtain an intersection curve of the first triangular mesh curved surface and the second triangular mesh curved surface;
the cutting module is used for cutting the plurality of intersected triangular mesh curved surfaces according to the intersected curves, and carrying out first re-subdivision processing on each first surface piece of the plurality of triangular mesh curved surfaces obtained after cutting according to a Jordan broken line method, wherein the first surface piece is a non-triangular surface piece.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116720234A (en) * | 2023-08-11 | 2023-09-08 | 中国空气动力研究与发展中心计算空气动力研究所 | Curved surface grid generation method, device, equipment and storage medium |
| CN116977598A (en) * | 2023-09-22 | 2023-10-31 | 芯瑞微(上海)电子科技有限公司 | Triangular mesh numerical simulation smoothing method |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116720234A (en) * | 2023-08-11 | 2023-09-08 | 中国空气动力研究与发展中心计算空气动力研究所 | Curved surface grid generation method, device, equipment and storage medium |
| CN116720234B (en) * | 2023-08-11 | 2023-10-20 | 中国空气动力研究与发展中心计算空气动力研究所 | Curved surface grid generation method, device, equipment and storage medium |
| CN116977598A (en) * | 2023-09-22 | 2023-10-31 | 芯瑞微(上海)电子科技有限公司 | Triangular mesh numerical simulation smoothing method |
| CN116977598B (en) * | 2023-09-22 | 2023-12-15 | 芯瑞微(上海)电子科技有限公司 | Triangular mesh numerical simulation smoothing method |
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