Bezier curves

### 19.8.1 Bezier curves

The Bezier curve with the control points P0,P1,…,Pn is the curve parameterized by

n
∑
j=0
⎛ ⎜ ⎝ |
n,j
t
| ⎞ ⎟ ⎠ |
j
| (1−t)n−j Pj.

The bezier command plots Bezier curves.

- bezier takes a sequence of arguments:
  - controls, a sequence of control points.
  - plot, the symbol.
- bezier(controls,plot) plots the Bezier curve with the given control points.

#### Examples

bezier(1,1+i,2+i,3-i,plot)

bezier(point(0,0,0),point(1,1,0),point(0,1,1),plot)

To get the parameterization of the curve, use the parameq command (see Section 26.12.8).

#### Examples

parameq(bezier(1,1+i,2+i,3-i))

| ⎛ ⎝ | 1−t | ⎞ ⎠ | 3+3 t | ⎛ ⎝ | 1−t | ⎞ ⎠ | 2 | ⎛ ⎝ | 1+i | ⎞ ⎠ | +3 t2 | ⎛ ⎝ | 1−t | ⎞ ⎠ | ⎛ ⎝ | 2+i | ⎞ ⎠ | +t3 | ⎛ ⎝ | 3−i | ⎞ ⎠

parameq(bezier(point([0,0,0]),point([1,1,0]),point([0,1,1])))

| ⎡ ⎣ | 2 t | ⎛ ⎝ | 1−t | ⎞ ⎠ | ,2 t | ⎛ ⎝ | 1−t | ⎞ ⎠ | +t2,t2 | ⎤ ⎦