Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Timewarp rigid body simulation
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Robot Motion Planning
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
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
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Interactive continuous collision detection for non-convex polyhedra
The Visual Computer: International Journal of Computer Graphics
Planning Algorithms
IEEE Transactions on Robotics
Generalized penetration depth computation
Computer-Aided Design
Deformable Proximity Queries and Their Application in Mobile Manipulation Planning
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Algorithms and theory of computation handbook
ACM Transactions on Graphics (TOG)
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The problem of distance computation arises in many applications including motion planning, CAD/CAM, dynamic simulation and virtual environments. Most prior work in this area has been restricted to separation or penetration distance computation between two objects. In this paper, we address the problem of computing a measure of distance between two configurations of a rigid or articulated model. The underlying distance metric is defined as the length of the longest displacement vector over the corresponding vertices of the model between two configurations. Our algorithm is based on Chasles theorem in Screw theory, and we show that the maximum distance can be realized only by a vertex of the convex hull of a rigid object. We use this formulation to compute the distance, and present two acceleration techniques to speed up the computation: 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 describe its application to proximity queries and motion planning.