Bezier Curve in Computer Graphics

Presentation on Bezier Curve

Presented By

Faruk AhmadDepartment of Computer Science & Engineering

Begum Rokeya University, Rangpur

MotiveThousands of points for a simple curve drawing !!!!

N = ?100? 1000? Or 10000…. ?

Oh No !!

What is the solution?

Got the solution !!!!A curve with only 4 Points!!

The Solution

BPk,n (t) = C(n,k) tk (1 – t) n - k

𝑃 (𝑡 )=∑𝑘=0

𝑛

𝑃 𝑘BPk,n (t)

C (n,k)

Bezier curve is the ultimate solution A few numbers of Control Points required

N is the number of Control Points

BP k,n (t) is the Bernstein polynomial, where t is the change variable

C (n,k) is the binomial coefficients

ExampleFor n = 3, we get,

B(t) = (1-t) 2 P0 + 2 (1-t) (t) P1 + t2P2

Where t = [0,1]

How it works?

Some scenario!

Applications of Bezier Curve

Computer Graphics Animation 2D & 3D Modeling

CAD(Computer Aided

Design)

CAGD(Computer Aided

Geometric Design)Robotics

Economic & Statistical Software Computer Games

Limitations

Most Efficient

Curve does not pass through all control points

Most Popular

Change in one point globally change the shape of curve

Though

But problems

are

Questions?

If you have any question ask me at: [email protected]

Thank You