Trivariate solid T-spline construction from boundary triangulations with arbitrary genus topology

Abstract

A comprehensive scheme is described to construct rational trivariate solid T-splines from boundary triangulations with arbitrary topology. To extract the topology of the input geometry, we first compute a smooth harmonic scalar field defined over the mesh, and saddle points are extracted to determine the topology. By dealing with the saddle points, a polycube whose topology is equivalent to the input geometry is built, and it serves as the parametric domain for the trivariate T-spline. A polycube mapping is then used to build a one-to-one correspondence between the input triangulation and the polycube boundary. After that, we choose the deformed octree subdivision of the polycube as the initial T-mesh, and make it valid through pillowing, quality improvement and applying templates to handle extraordinary nodes and partial extraordinary nodes. The T-spline that is obtained is C2-continuous everywhere over the boundary surface except for the local region surrounding polycube corner nodes. The efficiency and robustness of the presented technique are demonstrated with several applications in isogeometric analysis.