Dr Neil Dodgson,
University of Cambridge
Computer Laboratory
Part II course, 1998
Lecture 5 Index
...back to lecture 4
NURBS
on to lecture 6...
5) NURBS
NURBS are covered in some detail in R&A Section 5-13.
Non-uniform rational B-splines are the curves that are currently used
in any graphics application that requires curves and surfaces with
more functionality than Bezier curves can offer. In addition to the
features listed in Lecture 4B, NURBS are
invarient with respect to perspective transforms.
NURBS curves incorporate -- as special cases -- uniform B-splines,
non-rational B-splines, Bezier curves, lines, and conics. NURBS
surfaces incorporate planes, quadrics, and tori.
Exercises
- Review from IB: What are homogeneous
coordinates and what are they used for in computer graphics?
- Explain how to use homegeneous coordinates to get rational
B-splines given that you know how to produce non-rational B-splines.
- Convince your supervisor that you understand why NURBS includes
Uniform B-splines, Non-Rational B-splines, Beziers, lines, conics,
quadrics, and tori.
- When would you use Bezier curves and when would you use B-splines?
(i.e. why have B-splines, in general, replaced Bezier curves in CAD?)
- [1998/7/12] Consider the design of a user interface for a NURBS
drawing system. Users should have access to the full expressive power
of the NURBS representation. What things should users be able to
modify to give them such access and what effect does each have on the
resulting shape?
- For each of the items (in the previous question) that the user can
edit: (i) Give sensible default values; (ii) Explain how they would be
constrained if a `demo' version of the software was to be limited to
cubic Uniform Non-rational B-Splines.
|
Lecture 5 Index
...back to lecture 4
NURBS
on to lecture 6...
Neil Dodgson |
Advanced Graphics |
Computer Laboratory
Source file: l5a.html
Page last updated on Tue Sep 8 16:01:43 BST 1998
by Neil Dodgson
(nad@cl.cam.ac.uk)