Bezier as part of another Bezier

Bezier as part of another Bezier

Post by Jacques De Scheppe » Sat, 24 Feb 2001 02:37:26



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

Post by Stephen Ma » Sat, 24 Feb 2001 06:31:26




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

 
 
 

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