Efficient Collision Detection for Animation and Robotics Part 9 pdf

[...]... system for collision detection, we still have to face the problem when we are given only the face information without any special format to extract the geometry information to construct the sub -part hierarchical tree This is an interesting and challenging geometry and modeling problem      7.2.3 Collision Detection for Deformable objects One of most challenging problems is collision detection for. .. which has been studied in robotics, computational geometry and computer graphics for several years The treatment of these topics was far from exhaustive There is no shortage of open problems awaiting for new ideas and innovative solutions 120 7.2.1 Overlap Detection for Convex Polyhedra The core of the collision detection algorithm is built upon the concepts of Voronoi regions for convex polyhedra As... queue and sweeping and sorting techniques described in Chapter 5 with the basic algorithm for nonconvex objects to further reduce the number of intersection tests needed inside of the concavities 1 1 2i 2 2i 2 Automated Generation of the Sub -Part Hierarchical Representation To support the simulation, geometric modeling to represent three-dimensional objects is necessary for collision detection and dynamics... extremely useful in handling complex, non-convex objects in a computer generated simulation Our collision detection algorithm for non-convex objects uses the sub -part hierarchical tree representation to model each non-convex object If the objects are generated by hand, this representation is easy to use However, if we are given a set of faces describing the non-convex object without any special format, we can... objects of deformable materials or with time varying surfaces In terms of complexity, deformable objects o er us the greatest challenge for the problem of contact determination Our algorithms presented in this thesis work extremely well with rigid bodies Whereas using deformable models, it is very di cult to predict where concavity and degeneracy may be introduced due to external forces, and the shape... external forces, and the shape of objects can be changed in all possible ways Therefore, the problem of collision detection becomes rather complex and almost impossible to solve interactively Some work has been done for time-dependent parametric surfaces 45 Herzen and etc use a hierarchical algorithm which rst nds the potential collision over large ... we have to build the sub -part hierarchical tree by both visual inspection of the data and extracting the information by hand, in order to take advantage of the geometry of the original object This is a rather painful and time consuming process One proposed solution would be to generate all models by a Computer Aided Geometric Design tool which has only union as a primitive and all primitive volumes... problem itself is NP-complete 52, 67, 22, 76 Therefore, applying our sub -part hierarchical tree representation directly to the output of a non-optimal convex decomposition routine may not yield satisfactory results for the purpose of collision detection, especially if we have numerous number of convex pieces One possibility is to establish a criterion for grouping volume A B nodes, e.g maximize volume... the weighted average, and then construct the constraint planes of each face to the centroid of the polyhedron These interior constraint planes of a face F are the hyperplanes passing through the centroid and each edge in F 's boundary and the hyperplane containing the face F If all the faces are equi-distant from the centroid, these hyperplanes form the exact Voronoi diagrams for the interior of the... the overlap detection module described here, whenever a feature lies beneath another face However, to ensure convergence, we will need to construct the exact Voronoi regions of the interior space or use special cases analysis to guarantee that each switch of feature necessarily decreases the distance between two objects 7.2.2 Intersection Test for Concave Objects New Approaches for Collision Detection .