Non-iterative Second-order Approximation of Signed Distance Functions for Any Isosurface Representation

Signed distance functions (SDF) to explicit or implicit surface representations are intensively used in various computer graphics and visualization algorithms. Among others, they are applied to optimize collision detection, are used to reconstruct data fields or surfaces, and, in particular, are an obligatory ingredient for most level set methods. Level set methods are common in scientific visualization to extract surfaces from scalar or vector fields. Usual approaches for the construction of an SDF to a surface are either based on iterative solutions of a special partial differential equation or on marching algorithms involving a polygonization of the surface. We propose a novel method for a non-iterative approximation of an SDF and its derivatives in a vicinity of a manifold. We use a second-order algebraic fitting scheme to ensure high accuracy of the approximation. The manifold is defined (explicitly or implicitly) as an isosurface of a given volumetric scalar field. The field may...

• Type: Journal
• Year: 2010
• Where: CGF
• Authors: Vladimir Molchanov, Paul Rosenthal, Lars Linsen
• Keywords: Algebraic Fitting Scheme, CGF 2010, Computational Geometry, Computer Graphics, Least Squares Approximation