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A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates


Gallego, Guillermo; Yezzi, Anthony (2015). A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates. Journal of Mathematical Imaging and Vision, 51(3):378-384.

Abstract

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.

Abstract

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:National licences > 142-005
Dewey Decimal Classification:Unspecified
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Physical Sciences > Modeling and Simulation
Physical Sciences > Condensed Matter Physics
Physical Sciences > Computer Vision and Pattern Recognition
Physical Sciences > Geometry and Topology
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Applied Mathematics, Geometry and Topology, Computer Vision and Pattern Recognition, Condensed Matter Physics, Modelling and Simulation, Statistics and Probability
Language:English
Date:1 March 2015
Deposited On:22 Oct 2021 07:30
Last Modified:26 Mar 2024 02:39
Publisher:Springer
ISSN:0924-9907
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s10851-014-0528-x
  • Content: Published Version
  • Language: English
  • Description: Nationallizenz 142-005