Bezier Curves

1
Bezier Curves

• and the man who loved them

2
Pierre Bezier

• French automobile engineer
• Every point of a curve needed
• Describe any 2D curve
• Uses only 4 points
• Great for CAM (computer aided manufacturing)

3
The Curves

• The Gimp
• Puts the graph of yx2 into a cube
• Transforms the Cube

http//members.cox.net/mathmistakes/bezier.htm
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Equations

• A bezier curve is defined from t (0-1) where
  point 0 and 3 are endpoints and 1 and 2 are their
  control points
• x(t) axt3 bxt2 cxt x0
• x1 x0 cx / 3x2 x1 (cx bx) / 3x3 x0
  cx bx ax
• y(t) ayt3 byt2 cyt y0
• y1 y0 cy / 3y2 y1 (cy by) / 3y3 y0
  cy by ay

5
Code

• Demonstration

6
Applications

• Graphics programs
• Engineering
• Animations

http//members.cox.net/mathmistakes/bezier.htm