Surface Parameterization For Meshing by Triangulation Flattening

Proceedings, 9th International Meshing Roundtable, Sandia National Laboratories, pp.161-172, October 2000

MESHING
RESEARCH
CORNER

Alla Sheffer and E. de Struler
Computational Science and Engineering Program,
University of Illinois at Urbana Champaign,
Urbana, IL, 61801
Email: sheffa@uiuc.edu, sturler@uiuc.edu

Abstract
We propose a new method to compute planar triangulations of triangulated surfaces for surface paraxneterization. Our method computes a projection that minimizes the distortion of the surface metric structures (lengths, angles, etc.). It can handle any manifold surface for which a connected, valid, two-dimensional parameterization exists, including surfaces with large curvature gradients and non-convex domain boundaries. We use only the necessary and sufficient constraints for a valid two-dimensional triangulation. As a result, the existence of a theoretical solution to the minimization procedure is guaranteed.

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