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“Automatic Mesh to Spline Surface Conversion”
Wan-Chiu Li
Ph.D. thesis, 2006

Abstract: Aiming at converting a triangular mesh into a CAGD/CAM spline surface, this thesis focuses on one of the most crucial problems of the conversion process, i.e. extracting a ``good'' quadrilateral control mesh of the surface. What we mean by good is that the edges of the control mesh should be orthogonal and aligned with the principal directions of curvature of the surface. These two properties make the control mesh optimum in an approxmiation point of view, and greatly help to reduce unwanted oscillations on the final spline surface built from it. To solve this problem, we propose a new automatic algorithm, called \emphperiodic global parameterization. The basic idea is to find a ``geometry-meaningful'' parameterization guided by a pair of orthogonal anisotropic direction fields. Then, the iso-value lines of this parameterization will be extracted to define an initial control mesh, that satisfies the two criteria of a good control mesh.

BibTex reference

   AUTHOR     = "Li, Wan-Chiu",
   TITLE      = "Automatic Mesh to Spline Surface Conversion",
   YEAR       = "2006",
   MONTH      = "Nov",
   SCHOOL     = "INPL, France",