Direct extraction of surface meshes from implicitly represented heterogeneous volumes

This paper describes a novel algorithm to extract surface meshes directly from implicitly represented heterogeneous models made of different constituent materials. Our approach can directly convert implicitly represented heterogeneous objects into a surface model separating homogeneous material regions, where every homogeneous region in a heterogeneous structure is enclosed by a set of two-manifold surface meshes. Unlike other discretization techniques of implicitly represented heterogeneous objects, the intermediate surfaces between two constituent materials can be directly extracted by our algorithm. Therefore, it is more convenient to adopt the surface meshes from our approach in the boundary element method (BEM) or as a starting model to generate volumetric meshes preserving intermediate surfaces for the finite element method (FEM). The algorithm consists of three major steps: firstly, a set of assembled two-manifold surface patches coarsely approximating the interfaces between homogeneous regions are extracted and segmented; secondly, signed distance fields are constructed such that each field expresses the Euclidean distance from points to the surface of one homogeneous material region; and finally, coarse patches generated in the first step are dynamically optimized to give adaptive and high-quality surface meshes. The manifold topology is preserved on each surface patch. (C) 2006 Elsevier Ltd. All rights reserved.