Solid T-spline Construction from Boundary Triangulations with Arbitrary Genus Topology

Abstract

A comprehensive scheme is described to construct rational 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 solid 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 obtained T-spline 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.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 2012
Accession Number
ADA561514

Entities

People

  • Lei Liu
  • Thomas J.R. Hughes
  • Wenyan Wang
  • Yongjie Zhang

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Cartography
  • Construction
  • Continuity
  • Demographic Cohorts
  • Engineering
  • Flow
  • Geometric Processing
  • Geometry
  • Linear Systems
  • Maps
  • Mechanical Engineering
  • Template Patterns
  • Topology
  • Triangles
  • Triangulation

Readers

  • Calculus or Mathematical Analysis
  • Computational Fluid Dynamics (CFD)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)