Abstract
This chapter focuses on the problem of computing a hierarchical representation of the geometric description of each simulated object, as well as the simulated world. This representation is used to speed collision-detection checks by taking advantage of the geometric arrangement of the objects in the simulated world, such that collision tests are only carried out on objects that are “close enough” to collide. The hierarchical decomposition of the colliding objects is used to prune unnecessary intersection tests and quickly specify the collision points, or discard the collision if no intersections are found. The types of hierarchical representations discussed in this book include axis-aligned bounding boxes, oriented bounding boxes, bounding spheres, convex hulls and spatial grids, both static and continuous (i.e., taking time into account when checking for collisions).
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Notes
- 1.
This is discussed in detail in Appendix B (Chap. 7).
- 2.
The computation of the convex hull of a vertex set is described in Sect. 2.2.4.
- 3.
Recall that we are using the right-hand coordinate system.
- 4.
The size of particles in a particle system is not taken into account during this computation because particles are usually considered as point mass, as explained in detail in Chap. 3.
- 5.
In this book we assume objects are represented by closed meshes.
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Coutinho, M.G. (2013). Hierarchical Representation of 3D Polyhedra. In: Guide to Dynamic Simulations of Rigid Bodies and Particle Systems. Simulation Foundations, Methods and Applications. Springer, London. https://doi.org/10.1007/978-1-4471-4417-5_2
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