2 Quadratic Bezier Curves = 1 Cubic Bezier Curve????

2 Quadratic Bezier Curves = 1 Cubic Bezier Curve????

Post by Olumi » Fri, 01 Nov 2002 09:13:18



I would like to know is it possible to use 2 quadratic bezier curves
to model a cubic bezier curve?

Thanks

- Olumide

 
 
 

2 Quadratic Bezier Curves = 1 Cubic Bezier Curve????

Post by Just d' FAQ » Fri, 01 Nov 2002 10:00:04



Quote:>I would like to know is it possible to use 2 quadratic bezier curves
>to model a cubic bezier curve?

Of course not. Or sure. It depends what you mean by "model".

A quadratic is always planar. A cubic can twist through space, like
  (t,t^2,t^3)
which in Bezier form for t IN [0,1] has control points
  (0,0,0) (1/3,0,0) (2/3,1/3,0) (1,1,1)
Two planar quadratics cannot possibly match that.

On the other hand, you can certainly blend two quadratics by linear
interpolation to produce a cubic; and you can always try approximating
just as you would with line segments. So a more liberal meaning of
"model" yields a yes.

 
 
 

2 Quadratic Bezier Curves = 1 Cubic Bezier Curve????

Post by Mikko 'memon' Monon » Fri, 01 Nov 2002 15:50:12



Quote:>I would like to know is it possible to use 2 quadratic bezier curves
>to model a cubic bezier curve?

I dont know how the math goes, but I once found this:

        http://www.openswf.org/code/cubic2quadratic.cpp

So, it's at least possible to fake/approximate it.

--memon


                            uow3W                 uow3w~/6Jo'3p15u1'mmm

 
 
 

1. How to Construct a NURBS curve from several (Cubic) Bezier Curves (joined end-on-end)

I have a series of Bezier Curves with Control vertices:

P0, P1, P2, P3
P3, P4, P5, P6
P6, P7, P8, P9
...
...
P(n), P(n+1), P(n+1), P(n+3)
P(n+3), P(n+4), P(n+5), P(n+6)
....

I would like to construct a single NURBS curve that "interpolates" all
points generated by all the above bezier curves?

I assume this involves lookind for De-Boor points?

Is there any standard way of doing this? (Generating De-Boor points
from Bezier Points that is.)

Thanks

- Olumide

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