Lecture 9 Notes:
Examples and motivation
Blending surfaces, providing a smooth connection between various primary or functional surfaces, are very common in CAD. Examples include blending surfaces between:
_ Fuselage and wings of air
Lecture 3 Notes:
Dierential geometry of surfaces
De_nition of surfaces
_ Implicit surfaces F (x; y; z) = 0
Example: a2 + b2 + c2 = 1 Ellipsoid, see Figure 3.1.
Figure 3.1: Ellipsoid.
_ Explicit surfaces
If the implicit equation F (x; y; z) = 0 c
Lecture 8 Notes:
Fitting, Fairing and Generalized
Least Squares Method of Curve Fitting
Given N points Pi , i = 1, 2, ., N (N 4), construct an approximating cubic B
ezier curve that interpolates P1 and PN (end points).
Lecture 6 Notes:
B-splines (Uniform and Non-uniform)
The formulation of uniform B-splines can be generalized to accomplish certain objectives.
_ Non-uniform parameterization.
_ Greater general
_ Change of one poly
Lecture 4 Notes:
Introduction to Spline Curves
Introduction to parametric spline curves
x = x(u); y = y(u); z = z(u)
R = R(u)
Usually applications need a _nite range for u (e.g. 0 _ u _ 1).
For free-form sha
Lecture 1 Notes:
Introduction and classication of
geometric modeling forms
Geometric modeling deals with the mathematical representation of curves, surfaces, and solids
necessary in the denition of complex physical or engineering objects. T
Lecture 19 Notes: Decomposition
Decomposition models are representations of solids via combinations (unions) of basic special
building blocks glued together. Alternatively, decomposition models may be considered to
Lecture 20 Notes:
Advanced topics in dierential
In this section we study the computation of shortest path between two points on free-form
surfaces [14, 11].
robot motion planning
Lecture 13 Notes:
Osets of Parametric Curves and
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 survey on oset curves and surfaces up to 1992 was carried
Lecture 2 Notes:
Dierential geometry of curves
De_nition of curves
_ Implicit curves f (x; y) = 0
Example: x2 + y 2 = a2
cfw_ It is di_cult to trace implicit curves.
cfw_ It is easy to check if a point lies on the curve.