13472J/1.128J/2158J/16940J COMPUTATIONAL GEOMETRY Lecture 13 N. M. Patrikalakis Massachusetts Institute of Technology Cambridge MA 02139-4307. USA Copyright @2003 Massachusetts Institute of Technology Contents 1 3 Offsets of Parametric curves and surfaces 13.1 Motivation 13.2 Parametric offset curves 13.2.1 Differential geometry of parametric offset curves 13.2.2 Singularities of parametric offset curves 13.2.3 Approximations 13.3 Parametric offset surfaces 3.1 Differential geometry of parametric offset surfaces 13.3.2 Singularities of parametric offse et surfaces 13.3.3 Tracing algorithm 13 13.3.4 Self-intersections of offsets of explicit quadratic surfaces 13.3.5 Approximations Bibliography Reading in the Textbook Chapter 11, pp. 293-35313.472J/1.128J/2.158J/16.940J COMPUTATIONAL GEOMETRY Lecture 13 N. M. Patrikalakis Massachusetts Institute of Technology Cambridge, MA 02139-4307, USA Copyright c 2003 Massachusetts Institute of Technology Contents 13 Offsets of Parametric Curves and Surfaces 2 13.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 13.2 Parametric offset curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 13.2.1 Differential geometry of parametric offset curves . . . . . . . . . . . . . 5 13.2.2 Singularities of parametric offset curves . . . . . . . . . . . . . . . . . . 6 13.2.3 Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 13.3 Parametric offset surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 13.3.1 Differential geometry of parametric offset surfaces . . . . . . . . . . . . 10 13.3.2 Singularities of parametric offset surfaces . . . . . . . . . . . . . . . . . 11 13.3.3 Tracing algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 13.3.4 Self-intersections of offsets of explicit quadratic surfaces . . . . . . . . . 14 13.3.5 Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Bibliography 22 Reading in the Textbook • Chapter 11, pp. 293 - 353 1