U-splines: splines over unstructured meshes

A method for constructing a U-spline basis over a mesh, the method comprising:

• accessing data representing a mesh, the mesh comprising a plurality of cuboidal or simplicial elements, connectivity between adjacent elements, parametric data assigned to each edge of every element including parametric length and direction within a local coordinate system of the every element, specification of a desired level of continuity on each interface between adjacent elements, and data that defines a Bernstein-like basis on each element;
• determining a set of basis functions for the mesh by, for each seed Bernstein index of the mesh:
• a) constructing a function index support that has the each seed as a corner;
• b) determining whether a function with a same function index support has already been created;
• and
• c) when a function with the same index support has not already been created, determining coefficient values for the function;
• normalizing the determined set of functions such that for each index in the mesh, a sum of all nonzero coefficients sharing the each index for any functions in the mesh is equal to one;
• and
• outputting the determined set of basis functions for subsequent further use in design or analysis.

A computer program product for constructing a U-spline basis over a mesh, the computer program product comprising one or more computer-readable storage devices having stored therein computer-executable instructions which, when executed within a computing system, configure the system to perform a method comprising:

• accessing data representing a mesh, the mesh comprising a plurality of cuboidal or simplicial elements, connectivity between adjacent elements, parametric data assigned to each edge of every element including parametric length and direction within a local coordinate system of the every element, specification of a desired level of continuity on each interface between adjacent elements, and data that defines a Bernstein-like basis on each element;
• determining a set of basis functions for the mesh by, for each seed Bernstein index of the mesh:
• a) constructing a function index support that has the each seed as a corner;
• b) determining whether a function with a same function index support has already been created;
• and
• c) when a function with the same index support has not already been created, determining coefficient values for the function;
• normalizing the determined set of functions such that for each index in the mesh, a sum of all nonzero coefficients sharing the each index for any functions in the mesh is equal to one;
• and
• outputting the determined set of basis functions for subsequent further use in design or analysis.