http://digital.csic.es/bitstream/10261/30526/1/doc1.pdf

3D collision detection: a survey

A simple and efficient algorithm for finding the closest points between two convex polynomials is described. Data from numerous experiments tested on a broad set of convex polyhedra on R/sup 3/ show that the running time is roughly constant for finding closest points when nearest points are approximately known and is linear in total number of vertices if no special initialization is done. This algorithm can be used for collision detection, computation of the distance between two polyhedra in three-dimensional space, and other robotics problems. It forms the heart of the motion planning algorithm previously presented by the authors (Proc. IEEE ICRA, p.1554-9, 1990). >

/pdf/a-fast-algorithm-for-incremental-distance-calculation-303t7zu6co.pdf

A fast algorithm for incremental distance calculation

We present efficient algorithms for collision detection and contact determination between geometric models, described by linear or curved boundaries, undergoing rigid motion. The heart of our collision detection algorithm is a simple and fast incremental method to compute the distance between two convex polyhedra. It utilizes convexity to establish some local applicability criteria for verifying the closest features. A preprocessing procedure is used to subdivide each feature's neighboring features to a constant size and thus guarantee expected constant running time for each test.
The expected constant time performance is an attribute from exploiting the geometric coherence and locality. Let n be the total number of features, the expected run time is between $O(\sqrt{n})$ and O(n) depending on the shape, if no special initialization is done. This technique can be used for dynamic collision detection, planning in three-dimensional space, physical simulation, and other robotics problems.
The set of models we consider includes polyhedra and objects with surfaces described by rational spline patches or piecewise algebraic functions. We use the expected constant time distance computation algorithm for collision detection between convex polyhedral objects and extend it using a hierarchical representation to distance measurement between non-convex polytopes. Next, we use global algebraic methods for solving polynomial equations and the hierarchical description to devise efficient algorithms for arbitrary curved objects.
We also describe two different approaches to reduce the frequency of collision detection from$$N\choose2$$pairwise comparisons in an environment with n moving objects. One of them is to use a priority queue sorted by a lower bound on time to collision; the other uses an overlap test on bounding boxes.
Finally, we present an opportunistic global path planner algorithm which uses the incremental distance computation algorithm to trace out a one-dimensional skeleton for the purpose of robot motion planning.
The performance of the distance computation and collision detection algorithms attests their promise for real-time dynamic simulations as well as applications in a computer generated virtual environment.

Efficient collision detection for animation and robotics

This study of robot motion planning in dynamic domains presents algorithms for generating motion in an environment that changes over time. Their computational costs are also analyzed. The ability to plan motion in a dynamic domain is of critical importance to an autonomous robotic system that must operate in the presence of moving obstacles or other robots. The most important feature of the book is the presentation of algorithmic solutions to geometric aspects of dynamic motion planning problems which are of fundamental importance in robotics. Topics discussed include planning in time-dependent environments, generation of time-minimal paths in three dimensions, and the co-ordination of multiple mobile agents. The book can serve as a reference for those working on spatial reasoning and autonomous robotic systems.

Motion Planning in Dynamic Environments

Physically based modeling has become an important new approach to computer animation and computer graphics modeling. Although physically based modeling is inherently a mathematical subject, the math involved needn’t be any more difficult nor esoteric than the math that underlies many other areas of computer graphics, such as ray tracing or surface modeling. Many papers on the subject have presupposed a specialized mathematical background that many members of the computer graphics community lack. Consequently, many capable computer graphics practitioners, despite their interest in the subject, have simply been put off by the density of the math.

/pdf/physically-based-modeling-2th1gj5wsu.pdf

Physically Based Modeling

Iterative algorithms for detecting the collision of convex objects whose motion is characterized by a path in configuration space are described. They use as an essential substep the computation of the distance between the two objects. When the objects are polytopes in either two-dimensional or three-dimensional space, an algorithm is given which terminates in a finite number of iterations. It either determines that no collision occurs or locates the first collision point on the path. For practical problems it appears that the computational time is short and grows only linearly in the total number of vertices of the two polytopes. Numerical examples are presented. >

S.M. Hong

Papers

A new algorithm for detecting the collision of moving objects