Contouring 1- and 2-Manifolds in Arbitrary Dimensions

We propose an algorithm for contouring k-manifolds (k = 1, 2) embedded in an arbitrary n-dimensional space. We assume (n−k) geometric constraints are represented as polynomial equations in n variables. The common zero-set of these (n−k) equations is computed as a 1- or 2-manifold, respectively, for k = 1 or k = 2. In the case of 1-manifolds, this framework is a generalization of techniques for contouring regular intersection curves between two implicitlydefined surfaces of the form F(x, y, z) = G(x, y, z) = 0. Moreover, in the case of 2-manifolds, the algorithm is similar to techniques for contouring iso-surfaces of the form F(x, y, z) = 0, where n = 3 and only one (= 3 − 2) constraint is provided. By extending the Dual Contouring technique to higher dimensions, we approximate the simultaneous zero-set as a piecewise linear 1- or 2-manifold. There are numerous applications for this technique in data visualization and modeling, including the processing of various geometric const...

• Type: Conference
• Year: 2005
• Where: SMI
• Authors: Joon-Kyung Seong, Gershon Elber, Myung-Soo Kim
• Keywords: Arbitrary N-dimensional Space, Dual Contouring Technique, Geometric Constraints, SMI 2005