Decomposing a polygon into its convex parts
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Detection is easier than computation (Extended Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Computational geometry and convexity
Computational geometry and convexity
A Bibliography on Digital and Computational Convexity (1961-1988)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Accurate Minkowski sum approximation of polyhedral models
Graphical Models - Special issue on PG2004
Approximate convex decomposition of polyhedra
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Approximate convex decomposition of polyhedra and its applications
Computer Aided Geometric Design
Optimal Accurate Minkowski Sum Approximation of Polyhedral Models
ICIC '08 Proceedings of the 4th international conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications - with Aspects of Theoretical and Methodological Issues
Contributing vertices-based Minkowski sum computation of convex polyhedra
Computer-Aided Design
Contributing vertices-based Minkowski sum of a nonconvex--convex pair of polyhedra
ACM Transactions on Graphics (TOG)
Chopper: partitioning models into 3D-printable parts
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Fast approximate convex decomposition using relative concavity
Computer-Aided Design
A sweep and translate algorithm for computing voxelized 3D Minkowski sums on the GPU
Computer-Aided Design
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An important direction of research in computational geometry has been to find methods for decomposing complex structures into simpler components. In this paper, we examine the problem of decomposing a three-dimensional polyhedron P into a minimal number of convex pieces. Letting n be the number of vertices in P and N the number of edges which exhibit a reflex angle (i.e. the notches of P), our main result is an O(nN3) time algorithm for computing a convex decomposition of P. The algorithm produces O(N2) convex parts, which is optimal in the worst case. In most situations where the problem arises (e.g. graphics, tool design, pattern recognition), the number of notches N seems greatly dominated by the number of vertices n; the algorithm is therefore viable in practice.