Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
Computer-Aided Mechanical Design Using Configuration Spaces
Computing in Science and Engineering
Near Neighbor Search in Large Metric Spaces
VLDB '95 Proceedings of the 21th International Conference on Very Large Data Bases
Collision prediction for polyhedra under screw motions
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Geometrical analysis of compliant mechanisms in robotics (euclidean group, elastic systems, generalized springs
Energy-minimizing splines in manifolds
ACM SIGGRAPH 2004 Papers
Generalized penetration depth computation
Computer-Aided Design
Spatial Planning: A Configuration Space Approach
IEEE Transactions on Computers
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
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We address the problem of computing a measure of the distance between two configurations of a rigid or an articulated model. The underlying distance metric is defined as the maximum length of the displacement vectors over the vertices of the model between two configurations. Our algorithm is based on Chasles theorem from Screw theory, and we show that for a rigid model the maximum distance is realized by one of the vertices on the convex hull of the model. We use this formulation to compute the distance, and present two acceleration techniques: incremental walking on the dual space of the convex hull and culling vertices on the convex hull using a bounding volume hierarchy (BVH). Our algorithm can be easily extended to articulated models by maximizing the distance over its each link and we also present culling techniques to accelerate the computation. We highlight the performance of our algorithm on many complex models and demonstrate its applications to generalized penetration depth computation and motion planning.