Optimizing Triangulation of Implicit Surface Based on Quadric Error Metrics

Abstract

In this paper, based on quadric error metrics, we present an hybrid approach to optimize triangulation created from implicit surface with sharp features. The approach first uses a resampling process to update vertices positions of initial triangulation. A dual mesh of the triangulation is at the same time constructed to restrict the updated positions and to project the new positions onto the implicit surface. Each vertex position of the updated triangulation is then optimized by minimizing the squared distances from the vertex to tangent planes of the implicit surface at the corresponding vertex of the modified dual mesh. The optimization process combines with a curvature-dependent adaptive mesh subdivision. Our method uses an error metrics to measure deviation between the vertices in final triangulation and the implicit surface.