13472J/1.128J/2158J/16940J COMPUTATIONAL GEOMETRY Lecture 3 Kwanghee Ko T Maekawa N.M. Patrikalakis Massachusetts Institute of Technology Cambridge, MA 02139-4307, USA Copyright 2003 Massachusetts Institute of Technology Contents 3 Differential geometry of surfaces 3.1 Definition of surfaces 3.2 Curves on a surface 3.3 First fundamental form(arc length 3.4 Tangent plane 3.5 Normal vector 2234668 3.6 Second fundamental form II (curvature) 3.7 Principal curvatures Bibliography Reading in the Textbook Chapter 3, pp. 49-pp 7213.472J/1.128J/2.158J/16.940J COMPUTATIONAL GEOMETRY Lecture 3 Kwanghee Ko T. Maekawa N. M. Patrikalakis Massachusetts Institute of Technology Cambridge, MA 02139-4307, USA Copyright c 2003 Massachusetts Institute of Technology Contents 3 Differential geometry of surfaces 2 3.1 Definition of surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 Curves on a surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.3 First fundamental form (arc length) . . . . . . . . . . . . . . . . . . . . . . . . 4 3.4 Tangent plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.5 Normal vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.6 Second fundamental form II (curvature) . . . . . . . . . . . . . . . . . . . . . . 8 3.7 Principal curvatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Bibliography 13 Reading in the Textbook • Chapter 3, pp.49 - pp.72 1