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

23 F.E. and B.E. Meshing Algorithms 23.1 General 23.1.1 Finite Element Method(FEM) 23.1.2Mesh 23. 1.3 Some Criteria for a Good Meshin 23. 1.4 Finite Element Analysis in a CAD Environment

20.1 Geodesics .... 20.1.1 Motivation 20.1.2 Definition ..:. 20.1.3 Governing equations 20.1.4 Two-point boundary value problem 20.1.5 Example 20.2 Developable surface