Generate Non-Parallel Axes
Generates n axes-of-rotation that are 'well-spaced', that is all axes are as far from being parallel as possible. The resulting axes minimize clustering. This is one way to generate a uniform sampling of 3D rotation axes.
INPUTS:
n, the number of axis to uniformly sample.
BACKGROUND:
This is a generalization of the Thomson problem (J.J. Thomson 1904). The Thomson problem determines the minimum energy configuration for n electrons confined to the surface of a sphere: http://en.wikipedia.org/wiki/Thomson_problem
To generate well-spaced axes, additional constraints are imposed by "coupling" each electron with an additional electron at its antipodal point, i.e. x and -x in 3-space.
The solution generates "maximally" separated directions in 3-space, where maximally means that the directions are as far from being parallel as possible.
CREDITS:
Based on code from Hao Peng and Yongyang Yu and their unpublished “Optimization on the surface of a hyper sphere”, https://www.cs.purdue.edu/homes/pengh/reports/590OP.pdf
Zitieren als
Aaron T. Becker's Robot Swarm Lab (2024). Generate Non-Parallel Axes (https://www.mathworks.com/matlabcentral/fileexchange/44515-generate-non-parallel-axes), MATLAB Central File Exchange. Abgerufen .
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- MATLAB > Graphics > 2-D and 3-D Plots > Surfaces, Volumes, and Polygons > Volume Visualization > Scalar Volume Data >
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Inspiriert von: Suite of functions to perform uniform sampling of a sphere
Inspiriert: Control n MRI-powered actuators
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Version | Veröffentlicht | Versionshinweise | |
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1.1.0.0 | On advice from Anton Semechko, vectorized the code for a 10x speedup and explained the difference between uniform_axes and points_on_a_sphere sampling. |
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1.0.0.0 |