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Accurate and efficient unions of balls
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A continuous skeletonization method based on level sets
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The Medial axis of a union of balls
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Reversible surface skeletons of 3D objects by iterative thinning of distance transforms
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Efficient computation of a simplified medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Approximate medial axis for CAD models
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Exact computation of the medial axis of a polyhedron
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Variational tetrahedral meshing
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Exact medial axis computation for triangulated solids with respect to piecewise linear metrics
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Scale filtered euclidean medial axis
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Skeletal representations of orthogonal shapes
Graphical Models
Sphere-Meshes: shape approximation using spherical quadric error metrics
ACM Transactions on Graphics (TOG)
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SIGGRAPH Asia 2013 Technical Briefs
Cross-sectional structural analysis for 3D printing optimization
SIGGRAPH Asia 2013 Technical Briefs
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This paper addresses the fundamental problem of computing stable medial representations of 3D shapes. We propose a spatially adaptive classification of geometric features that yields a robust algorithm for generating medial representations at different levels of abstraction. The recently introduced continuous scale axis transform serves as the mathematical foundation of our algorithm. We show how geometric and topological properties of the continuous setting carry over to discrete shape representations. Our method combines scaling operations of medial balls for geometric simplification with filtrations of the medial axis and provably good conversion steps to and from union of balls, to enable efficient processing of a wide variety shape representations including polygon meshes, 3D images, implicit surfaces, and point clouds. We demonstrate the robustness and versatility of our algorithm with an extensive validation on hundreds of shapes including complex geometries consisting of millions of triangles.