13472J/1.128J/2158J/16940J COMPUTATIONAL GEOMETRY Lecture 9 N.M. Patrikalakis Massachusetts Institute of Technology Cambridge MA 02139-4307 USA Copyright 2003 Massachusetts Institute of Technology Contents 9 Blending Surfaces 2 9.1 Examples and motivation 2 9. 2 Blending surface approximation in terms of B-splines 9.2.1 Blend construction through a procedural "lofted"surface 9.3 Spherical and circular blending in terms of generalized cylinders 9.4 Blending of implicit algebraic surfaces 11 9.5 Blending as a boundary value problem 9.5.1 Introduction 12 9.5.2 Example: 2nd order(Laplace)equation 9.5.3 Mapping boundary value problem 17 9.5.4 Position and tangent plane continuity 9.5.5 Curvature continuity 9.5.6 Multisided blending surfaces Bibliography 2413.472J/1.128J/2.158J/16.940J COMPUTATIONAL GEOMETRY Lecture 9 N. M. Patrikalakis Massachusetts Institute of Technology Cambridge, MA 02139-4307, USA Copyright c 2003 Massachusetts Institute of Technology Contents 9 Blending Surfaces 2 9.1 Examples and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 9.2 Blending surface approximation in terms of B-splines . . . . . . . . . . . . . . 4 9.2.1 Blend construction through a procedural “lofted” surface . . . . . . . . 5 9.3 Spherical and circular blending in terms of generalized cylinders . . . . . . . . 7 9.4 Blending of implicit algebraic surfaces . . . . . . . . . . . . . . . . . . . . . . . 11 9.5 Blending as a boundary value problem . . . . . . . . . . . . . . . . . . . . . . 12 9.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 9.5.2 Example: 2 nd order (Laplace) equation . . . . . . . . . . . . . . . . . . 13 9.5.3 Mapping – boundary value problem . . . . . . . . . . . . . . . . . . . . 17 9.5.4 Position and tangent plane continuity . . . . . . . . . . . . . . . . . . . 19 9.5.5 Curvature continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 9.5.6 Multisided blending surfaces . . . . . . . . . . . . . . . . . . . . . . . . 21 Bibliography 24 1