An hp-Adaptive Discretization Algorithm for Signed Distance Field Generation

Dan Koschier, Crispin Deul, Magnus Brand, Jan Bender
IEEE Transactions on Visualization and Computer Graphics

In this paper we present an hp-adaptive algorithm to generate discrete higher-order polynomial Signed Distance Fields (SDFs) on axis-aligned hexahedral grids from manifold polygonal input meshes. Using an orthonormal polynomial basis, we efficiently fit the polynomials to the underlying signed distance function on each cell. The proposed error-driven construction algorithm is globally adaptive and iteratively refines the SDFs using either spatial subdivision (h-refinement) following an octree scheme or by cell-wise adaption of the polynomial approximation's degree (p-refinement). We further introduce a novel decision criterion based on an error-estimator in order to decide whether to apply p- or h-refinement. We demonstrate that our method is able to construct more accurate SDFs at significantly lower memory consumption compared to previous approaches. While the cell-wise polynomial approximation will result in highly accurate SDFs, it can not be guaranteed that the piecewise approximation is continuous over cell interfaces. Therefore, we propose an optimization-based post-processing step in order to weakly enforce continuity. Finally, we apply our generated SDFs as collision detector to the physically-based simulation of geometrically highly complex solid objects in order to demonstrate the practical relevance and applicability of our method.

» Show BibTeX

author = {Koschier, Dan and Deul, Crispin and Brand, Magnus and Bender, Jan},
title = {An hp-Adaptive Discretization Algorithm for Signed Distance Field Generation},
journal = {IEEE Transactions on Visualization and Computer Graphics},
year = {2017},
volume = {23},
number = {10},
pages = {1--14},
issn = {1077-2626},
doi = {10.1109/TVCG.2017.2730202}

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