Topology-reducing surface simplification using a discrete solid representation

Abstract

This paper presents a new approach for generating coarse-level approximations of topologically complex models. Dramatic\ud topology reduction is achieved by converting a 3D model to and from a volumetric representation. Our approach produces valid,\ud error-bounded models and supports the creation of approximations that do not interpenetrate the original model, either being completely contained in the input solid or bounding it. Several simple to implement versions of our approach are presented and discussed. We show that these methods perform significantly better than other surface-based approaches when simplifying topologically-rich models such as scene parts and complex mechanical assemblies.Postprint (published version

A survey of CAD model simplification techniques for physics-based simulation applications

“…In case of volumetric entity based techniques, the features are simplified by operating on volumetric entities from the model. The major techniques reported under this category are effective volume [Lee05a,Choi02], cellular representation [Lee04,Lim04], and voxel [He95,Andu02] based approaches. In the explicit feature representation based techniques, the feature information and semantics is explicitly extracted from CAD model or is present in the model in addition to geometric and topological data.…”

“…Andújar et al proposed Trihederal Discretized Polyhedra Simplification (TDPS) based topology reducing surface simplification technique [Andu02]. The aim of this work is finding a reduced valid polyhedral approximation of a solid model such that the maximum solid Hausdorff distance is below an error value.…”

Relief Mapping on Cubic Cell Complexes

“…This can be done either in the CPU, following the discretization algorithm described in (Andujar et al, 2002), or in the GPU, using a voxelization algorithm (Eisemann and Décoret, 2008). Our current implementation uses the CPU-based approach because it also provides, for each G cell, the list of faces intersecting it, which greatly accelerates the sampling of surface attributes discussed below.…”

Surface remeshing in arbitrary codimensions

“…Other methods exist that reconstruct or repair a surface by finding its intersection with a grid or an octree [16,4,22,20]. They are typically separated in two stages: a scanconversion stage, and a contouring stage that may be based on a primal [4,22,20] or a dual grid [16].…”