U-SPLINES: SPLINES OVER UNSTRUCTURED MESHES

摘要

U-splines are an improved spline construction 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 elements 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 geometrically exact adaptivity in h (element size) t) (polynomial degree), and (smoothness) simultaneously over any mesh topology. U-splines have no restrictions on the placement of T-junctions in the mesh. Mixed element meshes (e.g., triangle and quadrilateral elements in the same surface mesh) are also supported. Additionally, the U-spline basis is positive, forms a partition of unity, is linearly independent, and provides optimal approximation when used in analysis.