Math Is Fun Forum

zak100

Member

Registered: 2014-02-11

Posts: 8

Solving Bezeir Curve Eq.

Hi,
I have tried to solve this eq. for n=1 (straight line):

P(u) = Σ Pk BEZk,n (u)
k=0 to n
BEZk,n(u) = C(n, k) uk (1-u)n-k, For n=1
BEZ0,1(u) = C(1, 0)u0 (1-u)1-0 = C(1,0) * (1-u) = 1!/(0!(1-0)! ) * (1-u) = 1-u)
BEZ1,1(u) = C(1,1)u1 (1-u)1-1 = C(1,1) u * (1-u)0 = 1!/(1! (1-1)!) * u = u
Now

P(u) = P0 BEZ0,1(u) + P1 BEZ1,1 (u) = (1-u)P0 + uP1

Plz guide me  if this is correct or not. Also tell me what this answer tells me?? How its sum would be 1? plz show me.

Zulfi.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solving Bezeir Curve Eq.

Hi zak100;

I am assuming that the BEZ n,k as you call them are the Bernstein polynomials and the Pk are the Hermite polynomials. I do not remember much about Bezier curves and I only can use the parametric form to solve a simple line one.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

zak100

Member

Registered: 2014-02-11

Posts: 8

Re: Solving Bezeir Curve Eq.

Yes. BEZn,k are the Berntein Polynomials but i dont know about Pk. Some body plz check whether my work is correct or not?

Zulfi.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solving Bezeir Curve Eq.

How can anybody check it when you do not even know what the symbols stand for?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

zak100

Member

Registered: 2014-02-11

Posts: 8

Re: Solving Bezeir Curve Eq.

Hi,
Thanks for your response. I have not studied Hermite curve. We have jmped directly on to the Bezeir curves.  I would tell you what the book says about Pk

Suppose we are given n+1 control -point positions: PK=(xK, xk, zk) with k varying from 0 to n. These coordinate points can be blended to produce the position vector P(u) (in the image its C(u)) which describes the path of an approximating Bezier polynomial function between p0 and pn.

In my view Pk is a point in 3d. Plz guide me about my work. If you familiar with parametric eq of line you can guide me.

Zulfi.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solving Bezeir Curve Eq.

According to my notes those are points. For a straight line there are only two. Sometimes you see Pn or Pk or P(x) meaning a polynomial, usually one of the orthogonal ones, that is why I asked.

I think the notes I have only cover points in the xy plane.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

zak100

Member

Registered: 2014-02-11

Posts: 8

Re: Solving Bezeir Curve Eq.

Hi,
Thanks for your response again. I dont think that this question is beyond the limits of your forum. I hope some body must have the notes for the solution of this eq.

Zulfi.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solving Bezeir Curve Eq.

Have you tried the SE?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

zak100

Member

Registered: 2014-02-11

Posts: 8

Re: Solving Bezeir Curve Eq.

Hi,
Thanks for your response. I dont know whats "SE". I have provided you my solution. If its wrong plz let me know.

Zulfi.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solving Bezeir Curve Eq.

SE equals the StackExchange. It is a math forum that might have someone who can answer your question.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

Re: Solving Bezeir Curve Eq.

Hi bobbym;

Are you sending away our people to SE?

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solving Bezeir Curve Eq.

I can not help him and maybe someone there can. The point is that the person gets help, it does not matter where.

Or it might jog someone over here who can solve it...

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

zak100

Member

Registered: 2014-02-11

Posts: 8

Re: Solving Bezeir Curve Eq.

Hi,
I did the google and i found my answer is correct.
Thanks for your advice. Actually it was not that difficult that i goto SE.

Zulfi.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solving Bezeir Curve Eq.

What was the link?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

zak100

Member

Registered: 2014-02-11

Posts: 8

Re: Solving Bezeir Curve Eq.

Hi,
Thanks for your response my friend. Actually i cant tell you the link. Its just for fun. However if somebody else ask me i would surely guide him. Actually i dont want to leave this thread incomplete.

Zulfi.