Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Approximating polyhedra with spheres for time-critical collision detection
ACM Transactions on Graphics (TOG)
On the definition and the construction of pockets in macromolecules
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations
Proceedings of the sixteenth annual symposium on Computational geometry
A point-placement strategy for conforming Delaunay tetrahedralization
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Conforming Delaunay triangulations in 3D
Proceedings of the eighteenth annual symposium on Computational geometry
Graded conforming Delaunay tetrahedralization with bounded radius-edge ratio
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Updating and constructing constrained delaunay and constrained regular triangulations by flips
Proceedings of the nineteenth annual symposium on Computational geometry
Approximation by skin surfaces
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Weighted alpha shapes
Quality meshing for polyhedra with small angles
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Feature-Sensitive 3D Shape Matching
CGI '04 Proceedings of the Computer Graphics International
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
Approximating polyhedral objects with deformable smooth surfaces
Computational Geometry: Theory and Applications
Approximating polygonal objects by deformable smooth surfaces
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
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Given two simplicial complexes ${\mathcal C}_{\rm 1}$ and ${\mathcal C}_{\rm 2}$ embedded in Euclidean space ${\mathbb R}^{d}$, ${\mathcal C}_{\rm 1}$subdivides${\mathcal C}_{\rm 2}$ if (i) ${\mathcal C}_{\rm 1}$ and ${\mathcal C}_{\rm 2}$ have the same underlying space, and (ii) every simplex in ${\mathcal C}_{\rm 1}$ is contained in a simplex in ${\mathcal C}_{\rm 2}$. In this paper we present a method to compute a set of weighted points whose alpha complex subdivides a given simplicial complex. Following this, we also show a simple method to approximate a given polygonal object with a set of balls via computing the subdividing alpha complex of the boundary of the object. The approximation is robust and is able to achieve a union of balls whose Hausdorff distance to the object is less than a given positive real number ε.