Advanced Graphics Study Guide

Part 3: Splines
A: Bezier curves
B: B-splines
C: NURBS
...back to part 2 | on to part 4...

3B) B-splines

Why B-splines?

• 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...