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Thread: Prob with Bezier Curve Mathematical Example

  1. #1 Prob with Bezier Curve Mathematical Example 
    Junior Member
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    Hi,
    Can somebody plz guide me about this mathematical example:
    Q of Bezeir Curve.jpg

    I downloaded it from a web site. It also shows the solution. I have ddivided it into two parts:
    Part1

    Sol of Bezeir Curve Prob Part1.jpg

    Part2

    Sol of Bezeir Curve Prob Part2.jpg
    It has used the eq:
    P(u) = P0(1-u)3 + 3P1u(1-u)2+3P2u2(1-u)+P3u3


    For
    P(1/4) =27/64P0+27/64P1+9/64P2+1/64P3

    After that the solution shows the answer : [2.156 2.563 0]. I cant understand how to get this answer. Somebody plz guide me how can i get these values.

    Zulfi.
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  2. #2  
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    Substitute the points (2,2) )( 2,3) (3,3) (3,2) into that last equation and you get (138/64, 164,64). I haven't got a calculator on me but it looks like it would equal the answer.
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  3. #3  
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    Hi,
    Thanks for your time. Actually its not clear to me how to put values. The equation is in the form of P0 , P1 P2 and P3 but values are in terms of x & y. Plz guide me how to substitute the values.

    Zulfi.
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  4. #4  
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    Each P represents a different (x,y). So P(0)= (2,2) means the point where x=2 and y=2. So when you put all the P's into the equation, you are actually working with two equations at the same time. One for x and one for y. Here is an easy example:
    5(2,4)=(10,20) is saying
    5(x,y)=(5x,5y)
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  5. #5  
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    Hi,
    Thanks for your guidance. I have solved it.
    P(0) = P0
    For x-component:
    P(0) = x0 = 2
    For y-component
    P(0) = y0 = 2
    For z-component
    P(0) = z0 = 0
    Because no values are provided for z-component
    P(1/4) =27/64P0+27/64P1+9/64P2+1/64P3
    For x-component
    P(1/4) = 27/64x0 + 27/64x1 + 9/64x2 + 1/64x3
    = 27/64(2) + 27/64(2) + 9/64(3) + 1/64(3)
    =0.843 + 0.843 + .421 + .046
    = 2.153875
    For y-component
    P(1/4) = 27/64y0 + 27/64y1 + 9/64y2 + 1/64y3
    = 27/64(2) + 27/64(3) + 9/64(3) + 1/64(2)
    = 0.843 + 1.265 + 0.421 + 0.031 = 2.56
    For Z-component:
    No values are provided for z-component, so
    P(1/4) = 0
    [2.1538, 2.56, 0]
    P(1/2) = 1/8P0 + 3/8 P1 + 3/8P2 + 1/8P3
    For x-component
    P(1/2) = 1/8x0 + 3/8x1 + 3/8x2 + 1/8x3
    = 1/8(2) + 3/8(2) + 3/8 (3) + 1/8(3)
    = 0.25 + 0.75 + 1.125 + 0.375= 2.5
    For y-component
    P(1/2) = 1/8y0 + 3/8y1 + 3/8y2 + 1/8y3
    =1/8(2) + 3/8(3) + 3/8(3) + 1/8(2)
    = 0.25 + 1.125 + 1.125 + 0.25 = 2.75
    For z-component
    No values are provided for z-component, so its 0
    [2.5, 2.75, 0]
    P(3/4) = 1/64 x0 + 9/64 x1 + 27/64 x2 + 27/64 x3
    = 1/64(2) + 9/64 (2) + 27/64 (3) + 27/64 (3)
    = .0312 + 0.281 + 1.265 + 1.265 = 2.842
    P(3/4) = 1/64 y0 + 9/64 y1 + 27/64 y2 + 27/64 y3
    = 1/64 (2) + 9/64 (3) + 27/64 (3) + 27/64 (2) =
    = 0.0312 + 0.421 + 1.265 + 0.843 = 2.56
    [2.842, 2.56, 0]
    P(1) = P3
    For x-component
    P(1) = x3= 3
    For y-component
    P(1) = y3=2
    For z-component
    No values are provided z-component, so its value is 0
    [3, 2, 0]

    Zulfi.
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  6. #6  
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    Well done
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