US 2023/0120926 A1 · U-SPLINES: SPLINES OVER UNSTRUCTURED MESHES

Abstract

U-splines are a novel approach to the construction of a spline basis for representing smooth objects in Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE). A spline is a piecewise-defined function that satisfies continuity constraints between adjacent cells in a mesh. U-splines differ from existing spline constructions, such as Non-Uniform Rational B-splines (NURBS), subdivision surfaces, T-splines, and hierarchical B-splines, in that they can accommodate local variation in cell size, polynomial degree, and smoothness simultaneously over more varied mesh configurations. Mixed cell types (e.g., triangle and tetrahedron and quadrilateral and hexahedral cells in the same mesh) and T-junctions are also supported. The U-spline construction is presented for curves, surfaces, and volumes with higher dimensional generalizations possible. A set of requirements are given to ensure that the U-spline basis is positive, forms a partition of unity, is complete, and is locally linearly independent.

Claims24

Dependent claims

A system for constructing a U-spline mesh in computer aided design (CAD) or computer aided engineering (CAE), the system comprising:

one or more computer processors;
and
computer readable memory having stored therein computer-executable instructions which, when executed by the one or more computer processors, configures the system to:
construct a mesh which comprises a plurality of cells;
assign a coordinate system to each cell in the mesh, wherein each coordinate system is barycentric or formed from tensor products of barycentric coordinate systems;
assign a parametric length to each edge of each cell in the mesh, wherein the parametric lengths satisfy the conditions for seamless similarity maps;
assign a basis to each cell in the mesh, wherein each basis of each cell is a Bernstein or Bernstein-like basis;
assign a minimum desired continuity to each interface between adjacent cells in the mesh;
construct a system of continuity constraints, termed the global system of constraints, from each interface in the mesh, wherein the global system of constraints is derived from a coordinate system, parametric lengths, and basis for each cell and the continuity associated with each interface;
and
store the U-spline mesh in durable data storage such that the U-spline mesh is accessible to or is transmittable to CAD or CAE processes for display or further analysis.

8 more elements

A method for constructing a U-spline mesh in computer aided design (CAD) or computer aided engineering (CAE), the method performed within a computing system, the method comprising:

construct a plurality of cells;
assign a coordinate system to each cell in the mesh, wherein each coordinate system is barycentric or formed from tensor products of barycentric coordinate systems;
assign a parametric length to each edge of each cell in the mesh, wherein the parametric lengths satisfy the conditions for seamless similarity maps;
assign a basis to each cell in the mesh, wherein each basis of each cell is a Bernstein or Bernstein-like basis;
assign a minimum desired continuity to each interface between adjacent cells in the mesh;
construct a system of continuity constraints, termed the global system of constraints, from each interface in the mesh, wherein the global system of constraints is derived from a coordinate system, parametric lengths, and basis for each cell and the continuity associated with each interface;
and
storing the U-spline mesh in durable data storage such that the U-spline mesh is accessible to or is transmittable to CAD or CAE processes for display or further analysis.

5 more elements

A computer program product for constructing a U-spline mesh in computer aided design (CAD) or computer aided engineering (CAE), the system comprising:

computer readable data storage having stored therein computer-executable instructions which, when executed by one or more computer processors within a computing system, configures the computing system to:
construct a plurality of cells;
assign a coordinate system to each cell in the mesh, wherein each coordinate system is barycentric or formed from tensor products of barycentric coordinate systems;
assign a parametric length to each edge of each cell in the mesh, wherein the parametric lengths satisfy the conditions for seamless similarity maps;
assign a basis to each cell in the mesh, wherein each basis of each cell is a Bernstein or Bernstein-like basis;
assign a minimum desired continuity to each interface between adjacent cells in the mesh;
construct a system of continuity constraints, termed the global system of constraints, from each interface in the mesh, wherein the global system of constraints is derived from a coordinate system, parametric lengths, and basis for each cell and the continuity associated with each interface;
and
store the U-spline mesh in durable data storage such that the U-spline mesh is accessible to or is transmittable to CAD or CAE processes for display or further analysis.

6 more elements

Dependencies are inferred from the claim text.

U-splines: splines over unstructured meshes

Life of this patent

U-splines: splines over unstructured meshes

Life of this patent

Abstract

Claims24