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Best Quadratic Spline Approximation for Hierarchical Visualization

We present a method for hierarchical data approximation using quadratic simplicial elements for domain decomposition and field approximation. Higher-order simplicial elements can approximate data better than linear elements. Thus, fewer quadratic elements are required to achieve similar approximation quality. We use quadratic basis functions and compute best quadratic simplicial spline approximations that are C0-continuous everywhere. We adaptively refine a simplicial approximation by identifying and bisecting simplicial elements with largest errors. It is possible to store multiple approximation levels of increasing quality. We have tested the suitability and efficiency of our hierarchical data approximation scheme by applying it to several data sets.