Approximate medial axis for CAD models
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Sampling and meshing a surface with guaranteed topology and geometry
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Delaunay triangulations approximate anchor hulls
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Graphical Models
AFRIGRAPH '06 Proceedings of the 4th international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
Identifying flat and tubular regions of a shape by unstable manifolds
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Medial axis approximation and unstable flow complex
Proceedings of the twenty-second annual symposium on Computational geometry
Stability and homotopy of a subset of the medial axis
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Delaunay triangulations approximate anchor hulls
Computational Geometry: Theory and Applications
Reconstruction with Voronoi centered radial basis functions
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Defining and computing curve-skeletons with medial geodesic function
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Computing handle and tunnel loops with knot linking
Computer-Aided Design
Automatic road extraction from satellite imagery using LEGION networks
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
3D block-based medial axis transform and chessboard distance transform based on dominance
Image and Vision Computing
Computing medial axes of generic 3D regions bounded by B-spline surfaces
Computer-Aided Design
Normal and feature approximations from noisy point clouds
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Stress relief: improving structural strength of 3D printable objects
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Exact medial axis computation for triangulated solids with respect to piecewise linear metrics
Proceedings of the 7th international conference on Curves and Surfaces
ACM SIGAPP Applied Computing Review
Computer Graphics Forum
A fast algorithm for constructing approximate medial axis of polygons, using Steiner points
Advances in Engineering Software
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The medial axis of a surface in 3D is the closure of all points that have two or more closest points on the surface. It is an essential geometric structure in a number of applications involving 3D geometric shapes. Since exact computation of the medial axis is difficult in general, efforts continue to improve their approximations. Voronoi diagrams turn out to be useful for this approximation. Although it is known that Voronoi vertices for a sample of points from a curve in 2D approximate its medial axis, a similar result does not hold in 3D. Recently, it has been discovered that only a subset of Voronoi vertices converge to the medial axis as sample density approaches infinity. However, most applications need a nondiscrete approximation as opposed to a discrete one. To date no known algorithm can compute this approximation straight from the Voronoi diagram with a guarantee of convergence. We present such an algorithm and its convergence analysis in this paper. One salient feature of the algorithm is that it is scale and density independent. Experimental results corroborate our theoretical claims.