Distributing Points on the Sphere, I

Katanforoush, Ali; Shahshahani, Mehrdad

doi:10.1080/10586458.2003.10504492

Cited by 64 publications

(42 citation statements)

References 8 publications

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“…This leads us to a challenging mathematic problem of symmetric distribution of n points on an m-dimensional hyper sphere (m-sphere), this problem has been discussed in mathematics, coding and graphics community specifically for R 3 . [22][23]. We solved the problem based on charge distribution and stable configurations and from that the vectors of the optimal fault tolerant of a 7DOF manipulators were obtained.…”

Section: B Optimal Fault Tolerant 7dof Jacobianmentioning

confidence: 99%

Designing optimal fault tolerant Jacobian for robotic manipulators

Asayesh

Nahavandi

2010

2010 IEEE/ASME International Conference on Advanced Intelligent Mechatronics

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Fault tolerance of robotic manipulators is determined based on the fault tolerance measures. In this study a Jacobian of a 7DOF optimal fault tolerant manipulator is designed based on optimality of worse case relative manipulability and worse case dexterity from geometric perspective instead of numerical solution of constrained optimisation problem or construction of optimal Jacobian through a desired null space. The proposed Jacobian matrix is optimal and equally fault tolerant for a single joint failure within any joint of the manipulators.

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Section: B Optimal Fault Tolerant 7dof Jacobianmentioning

confidence: 99%

Designing optimal fault tolerant Jacobian for robotic manipulators

Asayesh

Nahavandi

2010

2010 IEEE/ASME International Conference on Advanced Intelligent Mechatronics

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“…Andreev proved that, for n = 3 and λ = 1, the optimal configurations for m = 4, 6, 12 are respectively the regular tetrahedron, octahedron, and icosahedron (for λ = −1, 0, these configurations are also optimal [5,6,21]). Similar problems were also discussed in [15,19,20,24].…”

Section: Introductionmentioning

confidence: 60%

Spherical Distribution of 5 Points with Maximal Distance Sum

Hou

Shao

2010

Discrete Comput Geom

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In this paper, we consider the problem of spherical distribution of 5 points, that is, how to configure 5 points on the unit sphere such that the mutual distance sum is maximal. It is conjectured that the sum of distances is maximal if the 5 points form a bipyramid distribution with two points positioned at opposite poles of the sphere and the other three positioned uniformly on the equator. We study this problem using interval methods and related techniques, and give a computer-assisted proof.

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“…It is a hard problem called the "sphere packing problem [11,12]." However, our purpose was not to resolve this problem but to acquire a high-readability layout.…”

Section: Candidate Positions For Anchorsmentioning

confidence: 99%

Sphere Anchored Map: A Visualization Technique for Bipartite Graphs in 3D

Ito

Misue

Tanaka

2009

Lecture Notes in Computer Science

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Abstract. Circular anchored maps have been proposed as a drawing technique to acquire knowledge from bipartite graphs, where nodes in one set are arranged on a circumference. However, the readability decreases when large-scale graphs are drawn. To maintain the readability in drawing large-scale graphs, we developed "sphere anchored maps," in which nodes in one set are arranged on a sphere. We describe the layout method for sphere anchored maps and the results of our user study. The results of our study revealed that more clusters of free nodes can be found using sphere anchored maps than using circular anchored maps. Thus, our maps have high readability, particularly around anchors.

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Distributing Points on the Sphere, I

Abstract: Introduction 2. The Metrics 3. The Methods 4. Numerical Results References Acknowledgments

Cited by 64 publications

References 8 publications

Designing optimal fault tolerant Jacobian for robotic manipulators

Designing optimal fault tolerant Jacobian for robotic manipulators

Spherical Distribution of 5 Points with Maximal Distance Sum

Sphere Anchored Map: A Visualization Technique for Bipartite Graphs in 3D

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