## Bezier as part of another Bezier

### Bezier as part of another Bezier

I have two cubic Bezier, each with their four control points. What I'd like
to know is, if there is a quick way to check if one of the Beziers is a part
of the other, just by their four control points.

### Bezier as part of another Bezier

Quote:>I have two cubic Bezier, each with their four control points. What I'd like
>to know is, if there is a quick way to check if one of the Beziers is a part
>of the other, just by their four control points.

Yes.  Assuming they are both unit length parameterized with
control points P0,P1,P2,P3 and Q0,Q1,Q2,Q3, then they are the
same curve if the following hold (note that these conditions
are equivalent to C3 conditions):

P3=Q0
P3-P2 = Q1-Q0
R := P2+(P2-P1) = Q2-(Q3-Q2)
R - (P1+(P1-P0)) = (Q3-(Q4-Q3)) - R

If your curves do not have equal paramaterizations, then there
are scaling factors involved.

Steve

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

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