## intersection bezier/bezier &bezier/conic ?

### intersection bezier/bezier &bezier/conic ?

hi there,

I am trying to solve the problem to intersect bezier curves and bezier curves
and algebraic curves, can somebody please point me towards information that can
help me to do that efficiently?

the solution I need, needs to be precise so polygonization of the curves
doesn't work. from reading books and scanning certain magazines, I think I
should be using an algorithm that utilizes implicitization of the parametric
curves.

thanks for any kind of input

ove

### intersection bezier/bezier &bezier/conic ?

Quote:

>hi there,

>I am trying to solve the problem to intersect bezier curves and bezier curves
>and algebraic curves, can somebody please point me towards information that can
>help me to do that efficiently?

>the solution I need, needs to be precise so polygonization of the curves
>doesn't work. from reading books and scanning certain magazines, I think I
>should be using an algorithm that utilizes implicitization of the parametric
>curves.

Check out the article:
"Comparison of three curve intersection algorithm"
Thomas W Sederberg and Scott R Parry,
Computer-Aided Design, 1986, pg 58-63

It discusses Bezier Subdivision, Interval Subdivision and Implicitization.

According to the article, for two degree 3 beziers, Implicitization is
4.1 times faster than Interval subdivision and 6.9 times faster than
bezier subdivision. However, for degree 5 beziers, Interval subdivision
is the fastest and implicitization is the slowest.

If you do implement the implicitization algorithm, I would really like

--
----------------------------------------------------------------------

TKK Inc.                                Compuserve: 76167,2273
Oakville, Ontario
Voice (905) 338-9103
FAX   (905) 338-9108
----------------------------------------------------------------------

Hi
Is there any algebraic method to find the intersection between two
Cubic Beziers

Thank u