Voronoi diagram for multiply-connected polygonal domains 1: algorithm
IBM Journal of Research and Development
Thinning Methodologies-A Comprehensive Survey
IEEE Transactions on Pattern Analysis and Machine Intelligence
Differential and topological properties of medial axis transforms
Graphical Models and Image Processing
Handbook of mathematics (3rd ed.)
Handbook of mathematics (3rd ed.)
Proceedings of the sixth ACM symposium on Solid modeling and applications
Computing Voronoi skeletons of a 3-D polyhedron by space subdivision
Computational Geometry: Theory and Applications
An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids
IEEE Transactions on Visualization and Computer Graphics
Shape Description By Medial Surface Construction
IEEE Transactions on Visualization and Computer Graphics
Approximate medial axis for CAD models
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Exact computation of the medial axis of a polyhedron
Computer Aided Geometric Design
Efficient and robust computation of an approximated medial axis
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
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Numerous simplification methods have been proposed for speeding up engineering analysis/ simulation. A recently proposed medial axis reduction is one such method, that is particularly well suited for analyzing thin solids, wherein a governing equation is reduced to the medial axis, leading to significantly smaller stiffness matrices. However, this method involves the non-trivial computation of a piece-wise C1 continuous medial axis that must closely approximate the exact medial axis.In this paper, we propose a new medial mesh reduction that is computationally more efficient than medial axis reduction in that it only requires a C0 continuous tessellation of the medial axis. However, the proposed method retains all the advantages of the explicit medial axis reduction including automation and guaranteed numerical convergence. Furthermore, as the medial mesh converges to the exact medial axis, the computed solution also converges to the exact dimensionally reduced solution. These claims are substantiated through numerical experiments in 2-D and 3-D.