Parts of Visual Form: Computational Aspects
IEEE Transactions on Pattern Analysis and Machine Intelligence
Folding flat silhouettes and wrapping polyhedral packages: new results in computational origami
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
The Power of Non-Rectilinear Holes
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Bounds on the Length of Convex Partitions of Polygons
Proceedings of the Fourth Conference on Foundations of Software Technology and Theoretical Computer Science
Polygon decomposition based on the straight line skeleton
Proceedings of the nineteenth annual symposium on Computational geometry
Approximate convex decomposition
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Shape partitioning by convexity
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Approximate convex decomposition
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Simultaneous shape decomposition and skeletonization
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Approximate convex decomposition of polyhedra
SIGGRAPH '04 ACM SIGGRAPH 2004 Posters
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
Efficient Interference Calculation by Tight Bounding Volumes
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part II
Greedy geographic routing in large-scale sensor networks: a minimum network decomposition approach
Proceedings of the eleventh ACM international symposium on Mobile ad hoc networking and computing
ACCORD: with approximate covering of convex orthogonal decomposition
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Decompositions, partitions, and coverings with convex polygons and pseudo-triangles
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Greedy geographic routing in large-scale sensor networks: a minimum network decomposition approach
IEEE/ACM Transactions on Networking (TON)
Approximate partitioning of 2D objects into orthogonally convex components
Computer Vision and Image Understanding
Technical note: Kinematic skeleton extraction from 3D articulated models
Computer-Aided Design
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We propose a strategy to decompose a polygon, containing zero or more holes, into ``approximately convex'' pieces. For many applications, the approximately convex components of this decomposition provide similar benefits as convex components, while the resulting decomposition is significantly smaller and can be computed more efficiently. Moreover, our approximate convex decomposition (ACD) provides a mechanism to focus on key structural features and ignoreless significant artifacts such as wrinkles and surface texture a user specified tolerance determines allowable concavity. We propose a simple algorithm that computes an ACD of a polygon by iteratively removing (resolving) the most significant non-convex feature (notch). As a by product, it produces an elegant hierarchical representation that provides a series of `increasingly convex' decompositions. Our algorithm computes an ACD of a simple polygon with n verticesand r notches in O(nr) time. In contrast, exact convex decomposition is NP-hard or,if the polygon has no holes, takes O(nr2) time.