CS184 Section 7
Bezier Curves and De Casteljau's Algorithm
Brandon Wang
March 12, 2013
Material adapted from Fu-Chung Huang.
CS184 Section 7
Today
Midterm next week!
- Curves: Why?
- Curves Worksheet
- C, G continuity (maybe)
Curves
In the end, you'll be sending triangles to your GPU to render, so why represent things in this weird format?
- Scale/arbitrary precision (fonts, vector graphics)
- Some objects are easier to represent in this way
- The sampling algorithm isn't too bad.
Curves?
Smooth curves. Triangles are jagged, etc. Think of it as a continuous representation of a curve, whereas triangles are a discrete sample. (Demo later)
Mario Kart
Nice Curves
Geri's Game
De Casteljau's Algorithm
Calculate f(u) at a specific point u. (Easier to think between 0 and 1)
Split each line at u.
De Casteljau Animation
De Casteljau Animation
Finite Subdivision
Can't calculate f(u) for all u. That's silly.
Compute a few points, then draw lines between them.
AS3 demo
Pseudocode
Dynamic Programming
for i = 0:power
p[i][power] = control_points[i]
for power = degree-1:0
for i = 0:power
p[i][power] = (1-u) * p[i][power+1] + u*p[i+1][power+1]
return p[0][0]
Bezier Surfaces
Worksheet time
WorksheetGeometric, Parametric Continuity
