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Linear Angle Based Parameterization

Rhaleb Zayer 1 Bruno Lévy 2 Hans-Peter Seidel 3
2 ALICE - Geometry and Lighting
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : In the field of mesh parameterization, the impact of angular and boundary distortion on parameterization quality have brought forward the need for robust and efficient free boundary angle preserving methods. One of the most prominent approaches in this direction is the Angle Based Flattening (ABF) which directly formulates the problem as a constrained nonlinear optimization in terms of angles. Since the original formulation of the ABF, a steady research effort has been dedicated to improving its efficiency. As for any well posed numerical problem, the solution is generally an approximation of the underlying mathematical equations. The economy and accuracy of the solution are to a great extent affected by the kind of approximation used. In this work we reformulate the problem based on the notion of error of estimation. A careful manipulation of the resulting equations yields for the first time a linear version of angle based parameterization. The error induced by this linearization is quadratic in terms of the error in angles and the validity of the approximation is further supported by numerical results. Besides performance speedup, the simplicity of the current setup makes re-implementation and reproduction of our results straightforward.
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Submitted on : Monday, November 12, 2007 - 4:14:45 PM
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Rhaleb Zayer, Bruno Lévy, Hans-Peter Seidel. Linear Angle Based Parameterization. Fifth Eurographics Symposium on Geometry Processing - SGP 2007, Jul 2007, Barcelone, Spain. pp.135-141. ⟨inria-00186848⟩

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