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## #1 2006-01-20 16:05:12

snyy
Member
Registered: 2005-12-29
Posts: 8

### intersection between cubic curve...

hi.. anyone know what is the formula to get the intersection point between cubic curve(Nurbs)?
thanks..

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## #2 2006-01-20 22:55:22

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: intersection between cubic curve...

Do you mean where one cubic curve crosses the x-axis or where two cubic curves cross each other?

If the first one, there's a cubic formula that you can use. It's very ugly, but it's usable. It would probably be easier to factorise it though, if you can.

If the second one, you just take one of the curves away from the other one to get a problem similar to the first case.

Why did the vector cross the road?
It wanted to be normal.

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## #3 2006-01-22 13:11:38

snyy
Member
Registered: 2005-12-29
Posts: 8

### Re: intersection between cubic curve...

yaya.. i want to know where 2 curve(Nurbs) cross each other. sorry, dont really get what you means. can explain futher to me ? thanks..

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## #4 2006-01-22 13:56:57

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: intersection between cubic curve...

What he means by cubic nurb is different than a cubic polynomial.

A nurb is a straight line with control points.  The control points work like gravity.  The closer it is to the line, the more it pulls it.  So placing a control point above a line will make it arc up, almost like -x^2.  Placing one above and below the line gives you a cubic nurb, it looks like a cubic polynomial.

You can move the control points to where ever you want, and it thus makes it easy to draw specific curves.  Very useful for modeling surfaces of things like cars.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #5 2006-01-23 02:49:21

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: intersection between cubic curve...

Ooh. Fair enough. I'd never heard of that terminology before. OK then, just ignore the above post, sorry!

Why did the vector cross the road?
It wanted to be normal.

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## #6 2006-01-23 03:22:27

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: intersection between cubic curve...

I believe I was partially wrong in the above.  I think the farther it is from the line, the more pull a single point has on it.  Although I'm sure you can implement it both ways.

As for finding the intersection, there isn't any formula you can use.  That's because there is no formula for a cubic nurb, besides knowing where the control points are.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #7 2006-01-23 14:45:23

snyy
Member
Registered: 2005-12-29
Posts: 8

### Re: intersection between cubic curve...

yes, i know where is the control point of my curve (nurbs). so, anywhere to get the intersec point?  then how to get the intersec point of the normal cubic curve?

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## #8 2006-01-23 16:15:42

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: intersection between cubic curve...

What are you creating nurbs in and for?

The only way I would know is to linearly search each nurb.  But I'll ask some friends I have, see if they can offer any advice.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #9 2006-01-24 19:13:00

snyy
Member
Registered: 2005-12-29
Posts: 8

### Re: intersection between cubic curve...

i doing a application which can draw nurbs, find the intersection and fill the nurbs...

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