bezier curve in computer graphics
TRANSCRIPT
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Presentation on Bezier Curve
Presented By
Faruk AhmadDepartment of Computer Science & Engineering
Begum Rokeya University, Rangpur
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MotiveThousands of points for a simple curve drawing !!!!
N = ?100? 1000? Or 10000…. ?
Oh No !!
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What is the solution?
Got the solution !!!!A curve with only 4 Points!!
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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
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ExampleFor n = 3, we get,
B(t) = (1-t) 2 P0 + 2 (1-t) (t) P1 + t2P2
Where t = [0,1]
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How it works?
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Some scenario!
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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
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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
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Thank You