Advanced Graphics Notes
Advanced Graphics
,
Dr Neil Dodgson
,
University of Cambridge
Computer Laboratory
Part II course, 1999
Part 3: Splines
A: Bezier curves
B: B-splines
C: NURBS
...back to part 2
|
on to part 4...
3B) B-splines.
B-splines are covered in some detail in
SMAG
section 3
and in
R&A
Section 5-9.
Why B-splines?
B-splines have many nice properties when compared to other families of curves which could be used. They:
minimise the order of the polynomial pieces (order k)
maximise the continuity between pieces (continuity C(k-2))
minimise the number of control points controlling a piece (k points)
have positive basis functions
have basis functions which partition unity, implying that each piece lies inside its control points' convex hull
are invarient with respect to affine transforms
Exercises
How many control points are required for a quartic Bezier and how many for a quartic B-spline?
Why are cubics the default for B-spline use?
Explain the difference between Uniform, Open Uniform, and Non-Uniform knot vectors. What are the advantages of each type?
Part 3: Splines
A: Bezier curves
B: B-splines
C: NURBS
...back to part 2
|
on to part 4...
Neil Dodgson
|
Advanced Graphics
|
Computer Laboratory
Source file: p3b.html
Page last updated on Thu Oct 7 17:02:59 BST 1999
by Neil Dodgson (
nad@cl.cam.ac.uk
)