Solid T-spline Construction from Boundary Representations for Genus-Zero Geometry

This paper describes a novel method to construct solid rational T-splines for complex genus-zero geometry from boundary surface triangulations. We first build a parametric mapping between the triangulation and the boundary of the parametric domain, a unit cube. After that we adaptively subdivide the cube using an octree subdivision, project the boundary nodes onto the input triangle mesh, and at the same time relocate the interior nodes via mesh smoothing. This process continues until the surface approximation error is less than a pre-defined threshold. T-mesh is then obtained by pillowing the subdivision result one layer on the boundary and its quality is improved. Templates are implemented to handle extraordinary nodes and partial extraordinary nodes in order to get a gap-free T-mesh. The obtained solid T-spline is C2-continuous except for the local region around each extraordinary node and partial extraordinary node. The boundary surface of the solid T-spline is C2-continuous everywhere except for the local region around the eight nodes corresponding to the eight corners of the parametric cube. Finally, a Bézier extraction technique is used to facilitate T-spline based isogeometric analysis. The obtained Bézier mesh is analysis-suitable with no negative Jacobians. Several examples are presented in this paper to show the robustness of the algorithm.