Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Approximating the diameter, width, smallest enclosing cylinder, and minimum-width annulus
Proceedings of the sixteenth annual symposium on Computational geometry
Fast penetration depth computation for physically-based animation
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
Deformed distance fields for simulation of non-penetrating flexible bodies
Proceedings of the Eurographic workshop on Computer animation and simulation
Six-degree-of-freedom haptic rendering using incremental and localized computations
Presence: Teleoperators and Virtual Environments
Closest point query among the union of convex polytopes using rasterization hardware
Journal of Graphics Tools - Special on hardware-accelerated rendering techniques
Incremental Penetration Depth Estimation between Convex Polytopes Using Dual-Space Expansion
IEEE Transactions on Visualization and Computer Graphics
Faster core-set constructions and data stream algorithms in fixed dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Generalized penetration depth computation
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
Introduction to haptic rendering
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Generalized penetration depth computation
Computer-Aided Design
Removing Node Overlaps Using Multi-sphere Scheme
Graph Drawing
Performance Analysis of a Collision Detection Algorithm of Spheres Based on Slab Partitioning
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
Determining the directional contact range of two convex polyhedra
Computer-Aided Design
A multi-sphere scheme for 2D and 3D packing problems
SLS'07 Proceedings of the 2007 international conference on Engineering stochastic local search algorithms: designing, implementing and analyzing effective heuristics
PolyDepth: Real-time penetration depth computation using iterative contact-space projection
ACM Transactions on Graphics (TOG)
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Minimizing the error of linear separators on linearly inseparable data
Discrete Applied Mathematics
Nonlinear optimization to generate non-overlapping random dot patterns
Proceedings of the Winter Simulation Conference
ACM Transactions on Graphics (TOG)
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Let A and B be two convex polytopes in R3 with m and n facets, respectively. The penetration depth of A and B, denoted as π(A, B), is the minimum distance by which A has to be translated so that A and B do not intersect. We present a randomized algorithm that computes π(A, B) in O(m3/4+ε n3/4+ε +m1+ε + n1+ε) expected time, for any constant ε 0. It also computes a vector t such that ¶t¶ = π(A, B) and int(A + t) ∩ B = θ. We show that if the Minkowski sum B ⊕ (-A) has K facets, then the expected running time of our algorithm is O (K1/2+ε m1/4 n1/4 + m1+ε + n1+ε), for any ε 0.We also present an approximation algorithm for computing π(A, B). For any δ 0, we can compute, in time O(m + n + (log2 (m + n))/δ), a vector t such that ¶t¶ ≤ (1 + δ)π(A, B) and int(A + t) ∩ B = θ. Our result also gives a δ-approximation algorithm for computing the width of A in time O(n + (1/δ) log2(1/δ)), which is simpler and faster than the recent algorithm by Chan [3].