An efficient implementation of RBF-based progressive point-sampled geometry
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
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In this paper the applications of equilibrium equationto geometric modeling is exploited and efficientnumerical algorithms are proposed for solving theequilibrium equation. First we show that from diversegeometric modeling applications the equilibrium systemcan be extracted as the central framework. Second, byexploiting in-depth the special structures inherent in thegeometric applications, we present simplified analyticsolutions to the resulting geometric equilibrium equationsvia system decomposition. Finally, given the observationthat the geometric equilibrium systems are extremelysensitive to both perturbations in input data and round offerrors, efficient, stable and accurate numericalalgorithms are proposed.