Smoothing a curve: bezier curves, b-splines and Alejandro's PenTool Script

François Chaplais francois.chaplais at mines-paristech.fr
Fri Oct 2 15:28:12 EDT 2009


Le 2 oct. 09 à 19:15, Hugh Senior a écrit :

>
> I am also trying to plot a curved line through coordinate points, so a
> Bezier curve is not an appropriate route as it intentionally misses  
> the
> coordinate point. Similarly, with potentially big distances between  
> points,
> how 'smooth' is 'smooth'? A sharp, angular curve at each point or a  
> more
> flattened, rounded curve? And this assumes that no curve is  
> possible at all
> for the first and last points because there is no way of knowing  
> the shape
> at all.
>
> One math guru I spoke to said it's not doable with coordinate data  
> anyway,
> only statistical data. I hope he is incorrect.
>
IF the Bezier curve is a function y=f(x) of the horizontal pixel  
number N, the the best you can on screen (or printer fror that  
matter) do is draw a line (hopefully anti aliased) from each point  
(x,integer((f(x))) to point (x+1,integer(f(x+1))). f is a polynomial.

To manage the general case, you can search for the mathematical (i.e.  
maybe non integer) points at which the tangent of the curves is  
vertical.

Best regards,
	François




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