Lie Groups for 2D and 3D Transformations
LieGroupsfor2Dand3DTransformationsEthanE adeUp datedMay20,2017*1Intro ductionThisdo ologicalgroupthatisalsoasmo othmanifold,withsomeotherniceprop ciatedwitheveryLiegroupisaLiealgebra,whi chisavectorspacediscussedb ortantly,aLiegroupanditsLiealgebraareint imatelyrelated,allowingcalculationsinone tob emapp cumentdo esnotgivearigorousintro ductiontoLiegroups,nordo esattempttoprovideenoughinformationthatt heLiegroupsrepresentingspatialtransforma tionscanb eemployedusefullyinrob (3)3DRotations33DrotationmatrixSE(3)3DRi gidtransformations6Lineartransformationo nhomogeneous4-vectorsSO(2)2DRotations12D rotationmatrixSE(2)2DRigidtransformation s3Lineartransformationonhomogeneous3-vec torsSim(3)3DSimilaritytransformations(ri gidmotion+scale)7Lineartransformationonh omogeneous4-vectorsForeachofthesegroups, therepresentationisdescrib ed,andtheexp oticsorcomputervision?
Lie Groups for 2D and 3D Transformations Ethan Eade Updated May 20, 2017 * 1 Introduction This document derives useful formulae for working with the Lie groups that represent transformations
Download Lie Groups for 2D and 3D Transformations
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document:
Related search queries
Datums, Coordinate Systems, Coordinate, Datums, Coordinate Systems, Coordinate Reference Systems, TRANSFORMATIONS, Guide to Duration, DV01, and, Guide to Duration, DV01, and Yield Curve Risk Transformations, Guidance Note Number 7, Coordinate, Coordinate Conversions and Transformations, Coordinate transformations, Rotational & Reflective Strip Patterns