Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Differential and topological properties of medial axis transforms
Graphical Models and Image Processing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Computing and simplifying 2D and 3D continuous skeletons
Computer Vision and Image Understanding
Structural operators for modeling 3-manifolds
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Surface reconstruction by Voronoi filtering
Proceedings of the fourteenth annual symposium on Computational geometry
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Proceedings of the fifth ACM symposium on Solid modeling and applications
Accurate computation of the medial axis of a polyhedron
Proceedings of the fifth ACM symposium on Solid modeling and applications
Proceedings of the sixth ACM symposium on Solid modeling and applications
Delaunay based shape reconstruction from large data
PVG '01 Proceedings of the IEEE 2001 symposium on parallel and large-data visualization and graphics
The Medial axis of a union of balls
Computational Geometry: Theory and Applications
Approximate medial axis as a voronoi subcomplex
Proceedings of the seventh ACM symposium on Solid modeling and applications
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Efficient computation of a simplified medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Tight cocone: a water-tight surface reconstructor
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Free-form skeleton-driven mesh deformations
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Weighted alpha shapes
Medial axis based solid representation
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
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The medial axis (MA) of an object is homotopy equivalent to the solid model. This makes the medial axis a natural candidate for a skeleton representation of a general solid object. In addition, the medial axis transform is useful for many applications in computer graphics and other areas. In many applications it is not only important to have a description of the skeleton, but also to have the relation that links parts of the skeleton and the related parts of the model, both on the boundary and inside the solid volume. In this paper, we suggest a tetrahedral complex representation of the solid that is based on its MA approximation skeleton which preserves the topological relation between them. This representation is called the pair-mesh since each tetrahedron in the complex connects a MA approximation element and a boundary approximation element and has sub-simplices on both of them. Using the pair-mesh, we also derive a parametric representation of the volume between the skeleton and the boundary as a set of parametric triangular meshes. In these meshes each triangle deforms between a pair of simplices, one on the MA approximation and one on the boundary. Such meshes realize the deformation retraction between the skeleton and solid. The basis for the construction of the pair-mesh is the duality properties of Voronoi related structures and Delaunay triangulations.