Hierarchically partitioned implicit surfaces for interpolating large point set models
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
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Implicit surfaces can be constructed from scattered surfacepoints using radial basis functions (RBFs) to interpolatethe surfaceýs embedding function. Many researchershave used thin-plate spline RBFs for this because of theirdesirable smoothness properties. Others have used compactlysupported RBFs, leading to a sparse matrix solutionwith lower computational complexity and better conditioning.However, the limited radius of support introduces a freeparameter that leads to varying solutions as well as varyingcomputational requirements: a larger radius of supportleads to smoother and more accurate solutions but requiresmore computation. This paper presents an empirical analysisof this radius of support. The results using compactlysupported RBFs are compared for varying model sizes andradii of support, exploring the relationship between datadensity and the accuracy of the interpolated surface.