13472J/1.128J/2158J/16940J COMPUTATIONAL GEOMETRY Lecture 2 Kwanghee Ko T Maekawa N.M. Patrikalakis Massachusetts Institute of Technology Cambridge, MA 02139-4307, USA Copyright 2003 Massachusetts Institute of Technology Contents 2 Differential geometry of curves 2.1 Definition of curves 2 2.1.1 Plane curves 2.1.2 Space curves 4 2.2 Arc length 2.3 Tangent vector 2.4 Normal vector and curvature 2.5 Binormal vector and torsion 12 2.6 Serret-Frenet Bibliography Reading in the Textbook 3 Chapter 2, pp 36- pp 4813.472J/1.128J/2.158J/16.940J COMPUTATIONAL GEOMETRY Lecture 2 Kwanghee Ko T. Maekawa N. M. Patrikalakis Massachusetts Institute of Technology Cambridge, MA 02139-4307, USA Copyright c 2003 Massachusetts Institute of Technology Contents 2 Differential geometry of curves 2 2.1 Definition of curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1.1 Plane curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1.2 Space curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Arc length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Tangent vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Normal vector and curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.5 Binormal vector and torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.6 Serret-Frenet Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Bibliography 16 Reading in the Textbook • Chapter 1, pp.1 - pp.3 • Chapter 2, pp.36 - pp.48 1