Parameterizing a 3D modeled object for tessellation

Patent metadata

Field	Value
Publication number	US-9836884-B2
Application number	US-201314139539-A
Country	US
Kind code	B2
Filing date	Dec 23, 2013
Priority date	Dec 28, 2012
Publication date	Dec 5, 2017
Grant date	Dec 5, 2017

Abstract

It is proposed a computer-implemented method for parameterizing a three-dimensional modeled object for tessellation. The method comprising the steps of providing a boundary representation of the modeled object, the boundary representation comprising geometrical data including parametric surfaces and topological data including a set of faces each defined as a portion of the 2D domain of a respective parametric surface; determining 2D meshes each fitting a respective face; and associating the 2D meshes to the geometrical data of the boundary representation. Such a solution improves the tessellation of a 3D modeled object.

First claim

What is claimed is:

1. A method, implemented by a computer system, for parameterizing a three-dimensional modeled object for tessellation, comprising the steps of:
providing a boundary representation of the modeled object, the boundary representation comprising geometrical data including parametric surfaces and topological data including a set of faces each defined as a portion of a 2D domain of a respective parametric surface;
determining, for each respective face, a respective 2D mesh fitting said respective face, comprising the steps of:
subdividing boundary edges of the respective face into parametric arcs, wherein each parametric arc is 2D and defined as a function of one parameter, the function of one parameter outputting values in the 2D domain of the respective parametric surface defining the respective face,
defining a set of vertices within the respective face, the vertices being points defined on the portion of the 2D domain of the respective parametric surface defining the respective face, and
determining a partition of the respective face with parametric patches bounded by the parametric arcs and the vertices of the set of vertices, wherein each parametric patch is 2D and defined as a function of two parameters, the function of two parameters outputting values in the 2D domain of the respective parametric surface defining the respective face;

associating the 2D meshes to the geometrical data of the boundary representation, the 2D meshes comprising the parametric patches, wherein at least one of the parametric patches includes a curved side; and
storing the 2D meshes associated to the geometrical data on non-volatile memory of the computer system or sending the 2D meshes associated to the geometrical data to another computer system, wherein the stored 2D meshes associated to the geometrical data or the sent 2D meshes associated to the geometrical data represent the modeled object parameterized for tessellation.

2. The method of claim 1 , wherein the parametric patches of the partition each have boundary arcs that do not cross each other and/or oneself, and/or the parametric patches of the partition avoid inner inversion.

3. The method of claim 1 , wherein determining the 2D meshes further comprises, for each respective face, subdividing the partition according to criteria including at least a maximal deviation between the 3D meshes and the respective parametric surfaces.

4. The method of claim 3 , wherein the criteria according to which subdividing the partition is performed further include a maximal number of times for further subdividing the 2D meshes before a step of determining 3D meshes by evaluating the position of vertices of the 2D meshes on the respective parametric surfaces.

5. The method of claim 1 , wherein the subdividing of boundary edges of the respective face into parametric arcs is performed until none of the arcs cross each other.

6. The method of claim 1 , wherein at least one of: (i) the parametric arcs are 2D Bézier arcs outputting values in the 2D domain of the respective parametric surface defining the respective face and (ii) the parametric patches are 2D Bézier patches outputting values in the 2D domain of the respective parametric surface defining the respective face.

7. The method of claim 1 , wherein for each pair of faces having a common boundary edge, the 2D meshes are determined to share the same vertices fitting the common boundary edge.

8. A method, implemented by a computer system, for tessellating a three-dimensional modeled object parameterized for tessellation, comprising the steps of:
providing, by retrieval from non-volatile memory of the computer system or by reception from another computer system, 2D meshes associated, according to the method of claim 1 , to geometrical data of a boundary representation of the modeled object, the boundary representation comprising the geometrical data including parametric surfaces and topological data including a set of faces each defined as a portion of the 2D domain of a respective parametric surface, the 2D meshes each forming a partition of a respective face with parametric patches bounded by vertices within the respective face and by parametric arcs that correspond to a subdivision of boundary edges of the respective face; and
determining 3D meshes by evaluating the position of vertices of the 2D meshes on the respective parametric surfaces.

9. The method of claim 8 , wherein the method further comprises subdividing the 2D meshes before determining the 3D meshes.

10. The method of claim 9 , wherein the 2D meshes are associated to the geometrical data of the boundary representation of the modeled object according to claim 4 , and the subdividing the 2D meshes before determining the 3D meshes is performed said maximal number of times.

11. The method of claim 8 , wherein the geometrical data include parametric curves representing intersections between the parametric surfaces and the faces of the boundary representation each have boundary edges each defined as a portion of the domain of a respective parametric curve, and determining the 3D meshes further comprises evaluating the position of vertices of the 2D meshes fitting the boundary edges on the respective parametric curves.

12. The method of claim 8 , wherein the method further comprises associating to the 3D meshes normal vectors computed based on their respective parametric surfaces.

13. A computer program product, comprising:
a non-transitory computer readable storage medium coupleable to a computer system, the computer readable storage medium having instructions for parameterizing a three-dimensional modeled object for tessellation by:
providing a boundary representation of the modeled object, the boundary representation comprising geometrical data including parametric surfaces and topological data including a set of faces each defined as a portion of a 2D domain of a respective parametric surface;
determining, for each respective face, a respective 2D mesh fitting said respective face by:
subdividing boundary edges of the respective face into parametric arcs, wherein each parametric arc is 2D and defined as a function of one parameter, the function of one parameter outputting values in the 2D domain of the respective parametric surface defining the respective face,
defining a set of vertices within the respective face, the vertices being points defined on the portion of the 2D domain of the respective parametric surface defining the respective face, and
determining a partition of the respective face with parametric patches bounded by the parametric arcs and the vertices of the set of vertices, wherein each parametric patch is 2D and defined as a function of two parameters, the function of two parameters outputting values in the 2D domain of the respective parametric surface defining the respective face;

associating the 2D meshes to the geometrical data of the boundary representation, the 2D meshes comprising the parametric patches, wherein at least one of the parametric patches includes a curved side; and
storing the 2D meshes associated to the geometrical data on non-volatile memory of the computer system or sending the 2D meshes associated to the geometrical data to another computer system, wherein the stored 2D meshes associated to the geometrical data or the sent 2D meshes associated to the geometrical data represent the modeled object parameterized for tessellation.

14. A CAD system comprising a processor coupled to a memory and a graphical user interface, the memory having recorded thereon a computer program comprising instructions for performing a computer-implemented method f

Assignees

• Dassault Systemes

Inventors

• Quilot Laurent
• Feki Abdelmonem
• Phung Tuan Anh
• Roudil Daniel

Classifications

• G06T17/30

  Polynomial surface description · CPC title

• G06T17/20 Primary

  Finite element generation, e.g. wire-frame surface description, {tesselation} · CPC title

• G06T17/10

  Constructive solid geometry [CSG] using solid primitives, e.g. cylinders, cubes · CPC title