Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
View-dependent simplification of arbitrary polygonal environments
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Progressive simplicial complexes
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
A topology modifying progressive decimation algorithm
VIS '97 Proceedings of the 8th conference on Visualization '97
Surface reconstruction by Voronoi filtering
Proceedings of the fourteenth annual symposium on Computational geometry
A condition guaranteeing the existence of higher-dimensional constrained Delaunay triangulations
Proceedings of the fourteenth annual symposium on Computational geometry
Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations
Proceedings of the sixteenth annual symposium on Computational geometry
Topology preserving and controlled topology simplifying multiresolution isosurface extraction
Proceedings of the conference on Visualization '00
Controlled Topology Simplification
IEEE Transactions on Visualization and Computer Graphics
Topology Simplification for Polygonal Virtual Environments
IEEE Transactions on Visualization and Computer Graphics
Isosurface Reconstruction with Topology Control
PG '02 Proceedings of the 10th Pacific Conference on Computer Graphics and Applications
Weighted alpha shapes
Removing excess topology from isosurfaces
ACM Transactions on Graphics (TOG)
Topology Repair of Solid Models Using Skeletons
IEEE Transactions on Visualization and Computer Graphics
Editing the topology of 3D models by sketching
ACM SIGGRAPH 2007 papers
Delaunay refinement algorithms for triangular mesh generation
Computational Geometry: Theory and Applications
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The topology of polygonal meshes has a large impact on the performance of various geometric processing algorithms, such as rendering and collision detection algorithms. Several approaches for simplifying topology have been discussed in the literature. These methods operate locally on models, which makes their effect on topology hard to predict and analyze. Most existing methods also tend to exhibit various disturbing artifacts, such as shrinking of the input and splitting of its components. We propose a novel top-down method for topology simplification that avoids the problems common in existing methods. The method starts with a simple, genus-zero mesh that bounds the input and gradually introduces topological features by a series of carving operations. Through this process a multiresolution stream of meshes is created with increasing topologic level of detail. Following the proposed approach, we present a practical carving algorithm that is based on the Constrained Delaunay Tetrahedralization (CDT). The algorithm pretetrahedralizes the complement of the input with respect to its convex hull and then eliminates tetrahedra in a prioritized manner. We present quality results for two families of meshes that are difficult to simplify by all existing methods known to us - topologically complex and highly clustered meshes.