Efficient Collision Detection for Animation and Robotics Part 1 doc

[...]... obstacles before an actual collision occurs Similarly, in computer animation, interactions among objects are simulated by modeling the contact constraints and impact dynamics Since prompt recognition of possible impacts is a key to successful response to collisions in a timely fashion, a simple yet e cient algorithm for collision detection is important for fast and realistic animation and simulation... : : : 10 3 6.4 An example of the algorithm in the 2-d workspace : : : : : : : : : : : 10 5 1 1 2 3 0 3 1 Chapter 1 Introduction The problem of collision detection or contact determination between two or more objects is fundamental to computer animation, physical based modeling, molecular modeling, computer simulated environments e.g virtual environments and robot motion planning as well 3, 7, 12 , 20,... Hierarchical representation of a torus composed of B zier surfaces : : e 1 1 1 2 2 2 15 24 26 27 28 30 31 35 43 44 44 45 53 55 59 63 67 71 75 ix 6 .1 A schematized 2-d con guration space and the partition of free space into x -channels : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 94 6.2 Two channels C and C joining the channel C , and a bridge curve in C : : : : : : : : : : : : : : : : : : : :... interference detection, clash detection, intersection tests, etc. In robotics, an essential component of robot motion planning and collision avoidance is a geometric reasoning system which can detect potential contacts and determine the exact collision points between the robot manipulator and the obstacles in the workspace Although it doesn't provide a complete solution to the path planning and obstacle... of the edge's left and right faces : : : : : : : : : : : : : : : : : : : : : : : : 3.8 A Side View for Point-Vertex Applicability Criterion Proof : : : : : : 3.9 An Overhead View for Point-Edge Applicability Criterion Proof : : : 3 .10 A Side View for Point-Edge Applicability Criterion Proof : : : : : : : 3 .11 A Side View for Point-Face Applicability Criterion Proof : : : : : : : 3 .12 Computation time... even thousands of objects in the virtual world, a naive algorithm would probably take hours just to check for possible interference whenever a human participant moves This is not acceptable for an interactive virtual environment Therefore, a simple yet e cient collision detection algorithm is almost indispensable to an interactive, realistic virtual environment The objective of collision detection. .. information which is needed in path planning for robots The static collision detection problem is often studied and then later extended to a dynamic environment However, the choice of step size can easily a ect the outcome of the dynamic algorithms If the position and orientation of the objects is known in advance, the collision detection can be solved as a function of time A related problem to collision. .. The interference detection problem has been considered one of the major bottlenecks in acheiving real-time dynamic simulation Collision detection is also an integral part of many new, exciting technolog- 2 ical developments Virtual prototyping systems create electronic representations of mechanical parts, tools, and machines, which need to be tested for interconnectivity, functionality, and reliability... of these systems is to save processing and manufacturing costs by avoiding the actual physical manufacture of prototypes This is similar to the goal of CAD tools for VLSI, except that virtual prototyping is more demanding It requires a complete test environment containing hundreds of parts, whose complex interactions are based on physics and geometry Collision detection is vital component of such environments... term promoting much hypes and hopes In a synthetic environment, virtual objects most of them stationary are created and placed in the world A human participant may wish to move the virtual objects or alter the scene Such a simple action as touching and grasping involves geometric contacts A collision detection algorithm must be implemented to achieve any degree of realism for such a basic motion However, .