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Research Papers

Continuous Collision and Interference Detection for 3D Geometric Models

[+] Author and Article Information
Horea T. Ilieş

Department of Mechanical Engineering, Computational Design Laboratory, University of Connecticut, Storrs, CT 06269-3139ilies@engr.uconn.edu

Rational motions discussed, for example, in Refs. 29-32, have the property that the trajectory of any moving point is a NURBS curve, which can be obtained, in principle, directly from the motion formulation.

Observe that many applications requiring interactive collision detection have only “local” information about the motion of each object in the environment, usually obtained by integrating the equations of motion. In principle, the trajectories of the moving points can be obtained through this integration.

J. Comput. Inf. Sci. Eng 9(2), 021007 (Jun 04, 2009) (7 pages) doi:10.1115/1.3130142 History: Received December 29, 2006; Revised January 23, 2009; Published June 04, 2009

This paper describes a new approach to perform continuous collision and interference detection between a pair of arbitrarily complex objects moving according to general three-dimensional affine motions. Our approach, which does not require any envelope computations, recasts the problem of detecting collisions and computing the interfering subsets in terms of inherently parallel set membership classification tests of specific curves against the original (static) geometric representations. We show that our approach can compute the subsets of the moving objects that collide and interfere, as well as the times of collision, which has important applications in mechanical design and manufacturing. Our approach can be implemented for any geometric representation that supports curve-solid intersections, such as implicit and parametric representations. We describe an implementation of the proposed technique for solids given as a boundary representation (B-rep), and illustrate its effectiveness for several rigid and deformable moving objects bounded by tesselated and freeform surfaces of various complexities. Furthermore, we show that our approach can be extended to also identify the local and global self-intersections of the envelopes of the moving objects without requiring to compute these envelopes explicitly. The paper concludes by summarizing the proposed approach as well as reviewing relevant computational improvements that can decrease the computational cost of the prototype implementation by orders of magnitude.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 2

Collision and interference detection based on SMCs of the inverted trajectory against the original static object representation

Grahic Jump Location
Figure 3

Sampling only boundary points of B does not provide the interior points of B that will interfere with A. Using only these boundary points to estimate the interfering subsets can lead to either an underestimated (in case of B) or an overestimated (in case of A) set of points of interference as shown in (b).

Grahic Jump Location
Figure 4

Continuous collision and interference detection between rigid and deformable shapes

Grahic Jump Location
Figure 1

Trajectory of point y∊T̂x will pass through x at some parameter value during the relative motion

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