Empirical analysis of computational and accuracy tradeoffs using compactly supported radial basis functions for surface reconstruction

Implicit surfaces can be constructed from scattered surface points using radial basis functions (RBFs) to interpolate the surface's embedding function. Many researchers have used thin-plate spline RBFs for this because of their desirable smoothness properties. Others have used compactly supported RBFs, leading to a sparse matrix solution with lower computational complexity and better conditioning. However, the limited radius of support introduces a free parameter that leads to varying solutions as well as varying computational requirements: a larger radius of support leads to smoother and more accurate solutions but requires more computation. This work presents an empirical analysis of this radius of support. The results using compactly supported RBFs are compared for varying model sizes and radii of support, exploring the relationship between data density and the accuracy of the interpolated surface.