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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
Thank You
