Lecture 9 Notes:
Blending Surfaces
9.1
Examples and motivation
Blending surfaces, providing a smooth connection between various primary or functional surfaces, are very common in CAD. Examples include
Lecture 8 Notes:
Fitting, Fairing and Generalized
Cylinders
8.1
Least Squares Method of Curve Fitting
Example problem
Given N points Pi , i = 1, 2, ., N (N 4), construct an approximating cubic B
ezier
Lecture 6 Notes:
B-splines (Uniform and Non-uniform)
6.1
Introduction
The formulation of uniform B-splines can be generalized to accomplish certain objectives.
These include
_ Non-uniform parameteriza
Lecture 4 Notes:
Introduction to Spline Curves
4.1
Introduction to parametric spline curves
Parametric formulation
x = x(u); y = y(u); z = z(u)
or
R = R(u)
(vector notation)
Usually applications need
Lecture 1 Notes:
Introduction and classication of
geometric modeling forms
1.1
Motivation
Geometric modeling deals with the mathematical representation of curves, surfaces, and solids
necessary in the
Lecture 19 Notes: Decomposition
models
19.1
Introduction
Decomposition models are representations of solids via combinations (unions) of basic special
building blocks glued together. Alternatively, de
Lecture 20 Notes:
Advanced topics in dierential
geometry
20.1
Geodesics
In this section we study the computation of shortest path between two points on free-form
surfaces [14, 11].
20.1.1
Motivation
Lecture 13 Notes:
Osets of Parametric Curves and
Surfaces
13.1
Motivation
Osets are de_ned as the locus of points at a signed distance d along the normal of a planar
curve or surface. A literature sur
Lecture 2 Notes:
Dierential geometry of curves
2.1
De_nition of curves
2.1.1
Plane curves
_ Implicit curves f (x; y) = 0
Example: x2 + y 2 = a2
cfw_ It is di_cult to trace implicit curves.
cfw_ It is