A construction of injective parameterizations of domains for isogeometric applications

Authors:
Thien Nguyen;Bernard Mourrain;André Galligo;Gang Xu
Affiliations:
Inst. of Applied Geometry, JKU Linz, Austria;GALAAD, INRIA Sophia Antipolis, France;Nice University, Nice, France;Hangzhou Dianzi Univ., China
Venue:
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Year:
2012

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Abstract

We present a new method to construct a B-spline parameterization of a domain defined by its boundary curves or surfaces. The method is based on solving Laplace equations on the physical domain. The equations are then pulled back to the parameter domain to deduce an elliptic system of Partial Differential Equations with boundary conditions. This system, solved by relaxation techniques, yields the required parameterization.