Collision Detection of Cylindrical Rigid Bodies Using Line Geometry

2005 ◽  
Author(s):  
John S. Ketchel ◽  
Pierre M. Larochelle
Keyword(s):  
Collision Detection ◽  
Nuclear Physics ◽  
Detection Algorithm ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Necessary Condition ◽  
Infinite Length ◽  
Line Geometry ◽  
Well Drilling ◽  
Necessary And Sufficient

This paper presents a novel methodology for detecting collisions of cylindrically shaped rigid bodies moving in three dimensions. This algorithm uses line geometry and dual number algebra to exploit the geometry of right circular cylindrical objects to facilitate the detection of collisions. First, the rigid bodies are modelled with infinite length cylinders and a necessary condition for collision is evaluated. If the necessary condition is not satisfied then the two bodies are not capable of collision. If the necessary condition is satisfied then a collision between the bodies may occur and we proceed to the next stage of the algorithm. In the second stage the bodies are modelled with finite length cylinders and a definitive necessary and sufficient collision detection algorithm is employed. The result is a straight-forward and efficient means of detecting collisions of cylindrically shaped bodies moving in three dimensions. This methodology has applications in spatial mechanism design, robot motion planning, workspace analysis of parallel kinematic machines such as Stewart-Gough platforms, nuclear physics, medical research, computer graphics and well drilling. A case study examining a spatial 4C robotic mechanism for self collisions is included.

Line Based Collision Detection of Cylindrical Rigid Bodies

2004 ◽  
Author(s):  
John S. Ketchel ◽  
Pierre M. Larochelle
Keyword(s):  
Collision Detection ◽  
Detection Algorithm ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Necessary Condition ◽  
Second Stage ◽  
Parallel Kinematic ◽  
Necessary And Sufficient ◽  
Two Bodies

This paper presents a novel methodology for detecting collisions of cylindrically shaped rigid bodies moving in three dimensions. This algorithm uses line geometry and dual number algebra to exploit the geometry of cylindrical objects to facilitate the detection of collisions. First, the rigid bodies are modelled with infinite cylinders and a necessary condition for collision is evaluated. If the necessary condition is not satisfied then the two bodies do not collide. If the necessary condition is satisfied then a collision between the bodies may occur and we proceed to the next stage of the algorithm. In the second stage the bodies are modelled with finite cylinders and a definitive necessary and sufficient collision detection algorithm is employed. The result is a straight-forward and efficient means of detecting collisions of cylindrically shaped bodies moving in three dimensions. This methodology has applications in spatial mechanism design, robot motion planning, and workspace analyses of parallel kinematic machines such as Stewart-Gough platforms. A case study examining a spatial 4C mechanism for self collisions is included.

Self-Collision Detection in Spatial Closed Chains

2008 ◽  
Vol 130 (9) ◽  
Author(s):  
John S. Ketchel ◽  
Pierre M. Larochelle
Keyword(s):  
Motion Planning ◽  
Finite Length ◽  
Collision Detection ◽  
Three Dimensional ◽  
Detection Algorithm ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Circular Cylinders ◽  
Infinite Length ◽  
Kinematic Chains

A novel methodology for detecting self-collisions in spatial closed kinematic chains is presented. In general these chains generate complex three dimensional motions in which their own links will collide with each other (i.e., a self-collision) without effective motion planning. The self-collision detection is accomplished via a novel algorithm for definitively detecting collisions of right circular, cylindrically shaped, rigid bodies moving in three dimensions. The algorithm uses line geometry and dual number algebra to exploit the geometry of right circular cylindrical objects to facilitate the detection of collisions. In the first stage of the algorithm, cylindrically shaped rigid bodies are modeled by infinite length right circular cylinders. Sufficient and necessary conditions are then used to determine if a pair of infinite length cylinders collide. If the actual finite length rigid bodies collide, then it is necessary that their associate infinite length cylinder models collide, and we proceed to the next stage of the algorithm where the bodies are modeled with finite length cylinders and a definitive necessary and sufficient collision detection algorithm is employed. The result is an efficient approach of detecting collisions of cylindrically shaped bodies moving in three dimensions that has applications in spatial mechanism design and motion planning. A case study examining a spatial 4C mechanism for self-collisions is included.

Research on Collision Detection Algorithm Based on OBB

2013 ◽  
Vol 433-435 ◽  
pp. 936-939 ◽  
Author(s):  
Xue Jing Ding
Keyword(s):  
Real Time ◽  
Virtual Environment ◽  
Collision Detection ◽  
Detection Algorithm ◽  
Rigid Bodies ◽  
The Real ◽  
Bounding Box

To enhance the real-time and accuracy of collision detection in virtual environment, introduces oriented bounding box (OBB) technology of hierarchical bounding box collision detection algorithm:construction of bounding box, generation of bounding box tree, implementation of collision detection algorithm,overlap judgement of bounding box. Collision detection algorithm based on OBB in this article is applied to solve the problem of collision detection between rigid bodies.

Some generalized characters associated to a transitive permutation group

2020 ◽  
Vol 23 (3) ◽  
pp. 393-397
Author(s):  
Wolfgang Knapp ◽  
Peter Schmid
Keyword(s):  
Positive Integer ◽  
Permutation Group ◽  
Frobenius Group ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Transitive Permutation Group ◽  
Point Stabilizer ◽  
Necessary And Sufficient ◽  
Regular Character ◽  
Permutation Character

AbstractLet G be a finite transitive permutation group of degree n, with point stabilizer {H\neq 1} and permutation character π. For every positive integer t, we consider the generalized character {\psi_{t}=\rho_{G}-t(\pi-1_{G})}, where {\rho_{G}} is the regular character of G and {1_{G}} the 1-character. We give necessary and sufficient conditions on t (and G) which guarantee that {\psi_{t}} is a character of G. A necessary condition is that {t\leq\min\{n-1,\lvert H\rvert\}}, and it turns out that {\psi_{t}} is a character of G for {t=n-1} resp. {t=\lvert H\rvert} precisely when G is 2-transitive resp. a Frobenius group.

scholarly journals On the forces that cable webs under tension can support and how to design cable webs to channel stresses

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180781 ◽  
Author(s):  
Guy Bouchitté ◽  
Ornella Mattei ◽  
Graeme W. Milton ◽  
Pierre Seppecher
Keyword(s):  
Linear Programming ◽  
Convex Hull ◽  
Structural Engineering ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Dimensional ◽  
Necessary And Sufficient

In many applications of structural engineering, the following question arises: given a set of forces f 1 ,  f 2 , …,  f N applied at prescribed points x 1 ,  x 2 , …,  x N , under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points x 1 ,  x 2 , …,  x N in the two- and three-dimensional cases. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two dimensions, we show that any such web can be replaced by one in which there are at most P elementary loops, where elementary means that the loop cannot be subdivided into subloops, and where P is the number of forces f 1 ,  f 2 , …,  f N applied at points strictly within the convex hull of x 1 ,  x 2 , …,  x N . In three dimensions, we show that, by slightly perturbing f 1 ,  f 2 , …,  f N , there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for channelling stress in desired ways.

scholarly journals On circulant codes with prescribed distances

1977 ◽  
Vol 16 (3) ◽  
pp. 361-369
Author(s):  
M. Deza ◽  
Peter Eades
Keyword(s):  
Sufficient Conditions ◽  
Difference Sets ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Weighing Matrices ◽  
Cyclic Difference Sets ◽  
The Matrix ◽  
Circulant Codes ◽  
Necessary And Sufficient ◽  
Square Matrix

Necessary and sufficient conditions are given for a square matrix to te the matrix of distances of a circulant code. These conditions are used to obtain some inequalities for cyclic difference sets, and a necessary condition for the existence of circulant weighing matrices.

Separability criteria based on the Bloch representation of density matrices

2007 ◽  
Vol 7 (7) ◽  
pp. 624-638
Author(s):  
J. de Vicente
Keyword(s):  
Sufficient Conditions ◽  
Quantum Systems ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Pure Product ◽  
Separability Problem ◽  
Arbitrary Dimensions ◽  
Necessary And Sufficient ◽  
Bloch Representation

We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which we derive a necessary condition and sufficient conditions for separability. For a certain class of states the necessary condition and a sufficient condition turn out to be equivalent, therefore yielding a necessary and sufficient condition. The proofs of the sufficient conditions are constructive, thus providing decompositions in pure product states for the states that satisfy them. We provide examples that show the ability of these conditions to detect entanglement. In particular, the necessary condition is proved to be strong enough to detect bound entangled states.

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