Differential and topological properties of medial axis transforms
Graphical Models and Image Processing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Surface reconstruction by Voronoi filtering
Proceedings of the fourteenth annual symposium on Computational geometry
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
Skeleton-based three-dimensional geometric morphing
Computational Geometry: Theory and Applications - special issue on virtual reality
Proceedings of the sixth ACM symposium on Solid modeling and applications
Approximate medial axis as a voronoi subcomplex
Proceedings of the seventh ACM symposium on Solid modeling and applications
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
Approximate medial axis for CAD models
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Shape Simplification Based on the Medial Axis Transform
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)
Homotopy-preserving medial axis simplification
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Skeleton based solid representation with topology preservation
Graphical Models - Special issue on SPM 05
Distance functions and skeletal representations of rigid and non-rigid planar shapes
Computer-Aided Design
A family of skeletons for motion planning and geometric reasoning applications
Artificial Intelligence for Engineering Design, Analysis and Manufacturing - Representing and Reasoning About Three-Dimensional Space
Medial zones: Formulation and applications
Computer-Aided Design
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The medial axis (MA) of an object and medial axis transform (MAT) have many applications in solid modeling, computer graphics and other areas. Exact computation of MA is complex and various medial axis approximation algorithms were studied. One of the most successful is based on the computation of the Voronoi diagram of a set of sample points on the boundary of the object. Based on this method we present a novel representation of solids, which we call a pair-mesh. The pair-mesh is a deformable manifold surface triangulation where each node deforms between a pair of vertices one on the MA approximation and one on the boundary. Consequently, it provides a continuous map between the inner Voronoi based structure and the boundary of the shape, encompassing the topological structures of them both. This representation can also be seen as a partitioning of the volume between the two, where each element in the partition is either a tetrahedron or a pyramid and includes vertices from both the MA approximation and the reconstructed boundary.