13472J/1.128J/2158J/16940J COMPUTATIONAL GEOMETRY Lectures 4 and 5 N. M. Patrikalakis Massachusetts Institute of Technology Cambridge MA 02139-4307. USA Copyright 2003 Massachusetts Institute of Technology Contents 4 Introduction to Spline Curves 4.1 Introduction to parametric spline curves 4.2 Elastic deformation of a beam in bending 4.3 Parametric polynomial curves 4.3.1 Ferguson representation 4.3.2 Hermite- Coons curves 4.3.3 Matrix forms and change of basis 13. 4 bezier curves 4.3.5 Bezier surfaces 4.4 Composite curves 4.4.1 Motivation 2224457778889 4.4.3 Continuity conditions 4.4.4 Bezier composite curves(splines) 4.4.5 Uniform Cubic B-splines Bibliography Reading in the Textbook Chapter 1, pp13.472J/1.128J/2.158J/16.940J COMPUTATIONAL GEOMETRY Lectures 4 and 5 N. M. Patrikalakis Massachusetts Institute of Technology Cambridge, MA 02139-4307, USA Copyright c 2003 Massachusetts Institute of Technology Contents 4 Introduction to Spline Curves 2 4.1 Introduction to parametric spline curves . . . . . . . . . . . . . . . . . . . . . . 2 4.2 Elastic deformation of a beam in bending . . . . . . . . . . . . . . . . . . . . . 2 4.3 Parametric polynomial curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4.3.1 Ferguson representation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4.3.2 Hermite-Coons curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4.3.3 Matrix forms and change of basis . . . . . . . . . . . . . . . . . . . . . . 7 4.3.4 B´ezier curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.3.5 B´ezier surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.4 Composite curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.4.2 Lagrange basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.4.3 Continuity conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.4.4 B´ezier composite curves (splines) . . . . . . . . . . . . . . . . . . . . . . 20 4.4.5 Uniform Cubic B-splines . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Bibliography 28 Reading in the Textbook • Chapter 1, pp.6 - pp.33 1