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arXiv · 1403.7664

On Recursive Random Prolate Hyperspheroids

Jonathan D. Gammell·Siddhartha S. Srinivasa·Timothy D. Barfoot
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Abstract

This technical note analyzes the properties of a random sequence of prolate hyperspheroids with common foci. Each prolate hyperspheroid in the sequence is defined by a sample drawn randomly from the previous volume such that the sample lies on the new surface (Fig. 1). Section 1 defines the prolate hyperspheroid coordinate system and the resulting differential volume, Section 2 calculates the expected value of the new transverse diameter given a uniform distribution over the existing prolate hyperspheroid, and Section 3 calculates the convergence rate of this sequence. For clarity, the differential volume and some of the identities used in the integration are verified in Appendix A through a calculation of the volume of a general prolate hyperspheroid.

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Jonathan D. Gammell, Siddhartha S. Srinivasa, Timothy D. Barfoot. 2014-03-29. On Recursive Random Prolate Hyperspheroids. https://arxiv.org/abs/1403.7664

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