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-vecto
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
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