Parameterization of Faceted Surfaces for Meshing using Angle-Based Flattening

By Alla Sheffer, Eric de Sturler. Engineering computations, 2001

340 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/9af8e536ebbe71228995134b16361eb890ddaac7

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Surface Parameterization: a Tutorial and Survey (2005, methodology): “The angle-based method of Sheffer and de Sturler [69] has been generalized in a straightforward manner to the spherical case by Sheffer, Gotsman, and Dyn [71] using a combination of angle and area distortion.”
Global conformal surface parameterization (2003, background): “Hq = ZqK=BqK: ( 31 ) Appendix B: Full rank of the linear system of closedness, harmonity and duality In order to prove the nondegeneracy of the linear system of closedness, harmonity and duality, it is sufficient and necessary to show its kernel space is zero only.”
Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm (2005, neutral): “A u t h o r ' s p e r s o n a l”
Fundamentals of spherical parameterization for 3D meshes (2003, methodology): “This is a highly non-linear optimization procedure, working with the angles of the spherical triangulation (as opposed to the vertex positions), inspired by the angle-based method of Sheffer and de Sturler [30] for planar parametrizations.”
Genus zero surface conformal mapping and its application to brain surface mapping (2004, methodology): “[18] introduce an angle-based flattening method to flatten a mesh to a two-dimensional plane so that it minimizes the relative distortion of the planar angles with respect to their counterparts in the three-dimensional (3-D) space.”