Voronoi diagram for multiply-connected polygonal domains 1: algorithm
IBM Journal of Research and Development
Theory and application of the skeleton representation of continuous shapes
Theory and application of the skeleton representation of continuous shapes
The Euclidean distance transform
The Euclidean distance transform
Computation of the Medial Axis Transform of 3-D polyhedra
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Medial surface generation and refinement
GMCAD '96 Proceedings of the fifth IFIP TC5/WG5.2 international workshop on geometric modeling in computer aided design on Product modeling for computer integrated design and manufacture
Computer Aided Geometric Design
Accurate computation of the medial axis of a polyhedron
Proceedings of the fifth ACM symposium on Solid modeling and applications
Continuous Skeletons from Digitized Images
Journal of the ACM (JACM)
On the medial surface approximations of extrusions
Engineering with Computers
Boundary Representation Modelling Techniques
Boundary Representation Modelling Techniques
Interior Medial Axis Transform computation of 3D objects bound by free-form surfaces
Computer-Aided Design
Research on 3D medial axis transform via the saddle point programming method
Computer-Aided Design
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The Medial Axis Transform surface, (or MAT or MS) is proving to be a useful tool for several applications and geometric reasoning tasks. However, calculation of the MAT is a time-consuming task and the benefits of the mathematical-based tool are offset by the cost of the calculation. This paper presents a method for medial surface calculation which uses subdivision to simplify the problem and hence speed up the calculation, a so-called 'divide-and-conquer' approach. The basis for this is a modification of the dual structure of the original object. As the calculation proceeds this structure is broken up into sub-pieces each representing a simpler sub-part of the MAT. Perhaps more importantly, this method creates a correct node decomposition of the dual structure. The paper goes on to demonstrate some applications of the results for geometric tasks, specifically offsetting and model subdivision, which are normally expensive but are simpler based on the MAT calculation results.