Bézier curve

CS3241 Lab9

Bézier curve

Implementing Bézier curve using OpenGL

Recall L8, p34 Bézier Blending function

Bézier curve Trick: Generate n sample points

For n evenly distributed sample point in [0, 1] t = i/(n-1) (for i = 0….n-1)

Find B1[i], B2[i], B3[i], B4[i]

Sample point [x, y] = [ B1[i], B2[i], B3[i], B4[i] ] [P0, P1, P2, P3]T

Connect the dots!

Sample Point 0

t = 0

Bh1[0] = 1

Bh2[0] = 0

Bh3[0] = 0

Bh4[0] = 0

Sample Point n-1

t = 1

Bh1[n-1] = 0

Bh2[n-1] = 0

Bh3[n-1] = 0

Bh4[n-1] = 1

Sample Point i

t = i/(n-1)

Bh1[i] = (1-t)^3

Bh2[i] = 3(1-t)^2*t

Bh3[i] = 3(1-t)*t^2

Bh4[i] = t^3

x = Bh1[i]*p0.x + Bh2[i]*p1.x

+ Bh3[i]*p2.x + Bh4[i]*p3.x

y = ….

ti

Bézier curve

Task 1

Open bezierUI_todo.c

Implement Bézier curve after 4 control points

(constraint) are fixed

Please modify

computeBlendingBh – pre-compute Bh1..4 according to

func in Slide 2

drawCurve – find out the co-ordinate of sample point by

x = Bh1[i]*q.p[0].x + Bh2[i]*q.p[1].x + Bh3[i]*q.p[2].x + Bh4[i]*q.p[3].x;

y = Bh1[i]*q.p[0].y + Bh2[i]*q.p[1].y + Bh3[i]*q.p[2].y + Bh4[i]*q.p[3].y;

Bézier curve

Build-in in OpenGL

One-Dimensional Evaluators

Ch 12, Red book

Reference

http://www.glprogramming.com/red/chapter12.htm

l

http://en.wikipedia.org/wiki/B%C3%A9zier_curve