Lecture 3 Differential geometry of surfaces 3.1 Definition of surfaces Implicit surfaces F(r,,a)=0 Example: 22+6+2=1 Ellipsoid, see Figure 3.1 Figure 3.1: Ellipsoid · Explicit surfaces If the implicit equation F(, y, a)=0 can be solved for one of the variables as a function

Lecture 9 Blending Surfaces 9.1 Examples and motivation Blending surfaces, providing a smooth connection between various primary or functional sur- faces, are very common in CAD. Examples include blending surfaces between Fuselage and wings of airplanes Propeller or turbine blade and hub Bulbous bow and ship hull Primary faces of solid models

Constructive Solid Geometry(CSG) 14.2 Primitives of CSG 14.3 Boolean operators 14.3.1 Regularized Boolean operators 14.4 Set membership classification 14.5 Properties of CSG

Cambridge MA 02139-4307 USA Copyright 2003 Massachusetts Institute of Technology Contents 8 Fitting, Fairing and Generalized Cylinders 8. 1 Least Squares Method of Curve Fitting 8.2 Fairing of Curves and Surfaces 8.2.1 Properties and Definition

19.2 Exhaustive enumeration 19.2.1 Definition and construction methods 19. 2.2 Applications 19.2.3 Properties of exhaustive enumeration methods 19.3 Space subdivision 19.3.1 Motivation and definitions 2233356677 19.3.2 Construction of octrees 19.3.3 Algorithms for octrees 19.3.4 Properties of octrees 19.3.5 Binary space subdivision