Question

Given a Bezier curve with 4 control points-

B0[1 0] , B1[3 3] , B2[6 3] , B3[8 1]

Determine any 5 points lying on the curve. Also, draw a rough sketch of the curve.

Answer 1

The calculated points are coordinates on the Bezier curve. Rough sketch: Starting at B0, the curve ascends towards B1, then turns towards B2 before descending to B3. The curve is smooth.

To determine points on the Bezier curve defined by control points B0[1 0], B1[3 3], B2[6 3], and B3[8 1], we can use the parametric equation for a cubic Bezier curve:

P(t)=
`(1-t)^(3)`.
`B_(0)` +3t
`(1-t)^(2)`.
`B_(1)` +
`3t^(2)` (1-t) .
`B_(2)` +
`t^(3)` .
`B_(3)`

where t varies from 0 to 1.

1. t=0: P(0)=
`B_(0)` =[1,0]

2. t=0.25 : Calculate P(0.25)

3. t=0.5 : Calculate P (0.5)

4. t=0.75: Calculate P (0.75)

5. t= 1 : P(1) =
`B_(3)` = [8,1]

The calculated points are coordinates on the Bezier curve.

Rough sketch: Starting at B0, the curve ascends towards B1, then turns towards B2 before descending to B3. The curve is smooth.

Now, let's plot these points on a coordinate system to create a rough sketch of the Bezier curve.