The exponential map for the group of similarity transformations and applications to motion interpolation

Spyridon Leonardos, Christine Allen-Blanchette, Jean Gallier

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

In this paper, we explore the exponential map and its inverse, the logarithm map, for the group SIM(n) of similarity transformations in n which are the composition of a rotation, a translation and a uniform scaling. We give a formula for the exponential map and we prove that it is surjective. We give an explicit formula for the case of n = 3 and show how to efficiently compute the logarithmic map. As an application, we use these algorithms to perform motion interpolation. Given a sequence of similarity transformations, we compute a sequence of logarithms, then fit a cubic spline that interpolates the logarithms and finally, we compute the interpolating curve in SIM(3).

Original languageEnglish (US)
Title of host publication2015 IEEE International Conference on Robotics and Automation, ICRA 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages377-382
Number of pages6
EditionJune
ISBN (Electronic)9781479969234
DOIs
StatePublished - Jun 29 2015
Externally publishedYes
Event2015 IEEE International Conference on Robotics and Automation, ICRA 2015 - Seattle, United States
Duration: May 26 2015May 30 2015

Publication series

NameProceedings - IEEE International Conference on Robotics and Automation
NumberJune
Volume2015-June
ISSN (Print)1050-4729

Conference

Conference2015 IEEE International Conference on Robotics and Automation, ICRA 2015
Country/TerritoryUnited States
CitySeattle
Period5/26/155/30/15

All Science Journal Classification (ASJC) codes

  • Software
  • Artificial Intelligence
  • Electrical and Electronic Engineering
  • Control and Systems Engineering

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