🚀 go-pugleaf

The parametric equation is 
	x = x0*(1-t)^3 + x1*3*t*(1-t)^2 + x2*3*t^2*(1-t) + x3*t^3

Same thing for y. You can plot by just letting t go from 0 to 1 in some  
increment and draw lines at the (x,y) points.

A more common plot is to recursively subdivide until the spline is close  
enough to just a line between (x0,y0) & (x3,y3).

control points for half of split
s0 = X0
s1 = .5*(x0 + x1)
s2 = .25*(x0 + 2*x1 + x2)
s3 = .125*(x0 + 3*x1 + 3*x2 + x3)

second half of split

t0 = .125*(x0 + 3*x1 + 3*x2 + x3)
t1 = .25*(x1 + 2*x2 + x3)
t2 = .5*(x2+x3)
t3 = x3

A good book is 
Splines for use in computer graphics & gemoetric modeling
Bartels,Beatty,Barsky
IBSN 0-934613-27-3

	-greg.

Brian C. Hobbs writes
> 
> 	If I constrained a bezier curve to conform to a function (as in
> "every x value has one and only one y value"), and plotted it out via a 
> curveto operator, is there any way that I could find out what the y  
value
> for a point along the curve would be for any x value?  Either the  
relevant
> equations for a Bezier curve or some ps code to trace it would be very  
> helpful.
> 
> 	This would sort of be like the functionality of the gamma curve
> manipulator in Scene.
> 
> 	Thanks.
> 
> 
> --
> Brian C. Hobbs				|	"I am Number Two."
> Chromagrafx Imaging Systems	|	"Who is Number One?"
> brian@chromagrafx.com		|	"You are, Number Six."
-- 

Greg Cockroft                       greg@agog.com    
Agog, Inc.                          (517) 627-2186   fax 2673
13780 North River Highway