Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm
SIAM Journal on Computing
Convex decomposition of polyhedra and robustness
SIAM Journal on Computing
On the difficulty of triangulating three-dimensional nonconvex polyhedra.
Discrete & Computational Geometry
Strategies for polyhedral surface decomposition: an experimental study
Proceedings of the eleventh annual symposium on Computational geometry
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Bounded-distortion piecewise mesh parameterization
Proceedings of the conference on Visualization '02
Partitioning 3D Surface Meshes Using Watershed Segmentation
IEEE Transactions on Visualization and Computer Graphics
Variational sphere set approximation for solid objects
The Visual Computer: International Journal of Computer Graphics
Approximate convex decomposition of polyhedra
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Model Composition from Interchangeable Components
PG '07 Proceedings of the 15th Pacific Conference on Computer Graphics and Applications
Fast approximate convex decomposition using relative concavity
Computer-Aided Design
Real time dynamic fracture with volumetric approximate convex decompositions
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
gHull: A GPU algorithm for 3D convex hull
ACM Transactions on Mathematical Software (TOMS)
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Decomposing a complex object into simpler pieces, e.g., convex patches or convex polyhedra, is a well-studied geometry problem. A well constructed decomposition can greatly accelerate collision detection since intersections with and between convex objects are fast to compute. In this paper, we look at a particular instance of the convex decomposition problem which arises from real-world game development. Given a collection of polyhedral surfaces (possibly with boundaries, holes, and complex interior structures) that model the scene geometry in a game environment, we wish to find a small set of convex hulls such that colliding objects in the scene against such a set of convex hulls produces the same game behavior as colliding against the original surfaces. The vague formulation of the problem is due to the difficulty of defining the space accessible by the objects involved in the game play. Under reasonable assumptions, we arrive at a set of conditions for valid convex decomposition and develop a construction algorithm via greedy merging driven by patch compactness. We show that our validity conditions ensure valid collision-related game behavior. The effectiveness of our decomposition algorithm is demonstrated through real examples from game development. To the best of our knowledge, no previous convex hull decomposition or surface decomposition algorithms were designed to handle the type of models we consider or be able to compute a set of convex hulls that ensure accurate collision detection results.