# Thread: Prob with Bezier Curve Mathematical Example

1. Hi,
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.  2. 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.  3. 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.  4. 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)  5. 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.  6. Well done   Posting Permissions
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