Smoothing a curve

[capellan]

Hi All,

Some time ago, i published this stack that shows two
algorithms for smoothing the straight sides of a polygon:

http://www.geocities.com/capellan2000/Two_smooth_polygon_algorithm.zip

This stack implements two polygon smoothing algorithms:
Chaikin and Shemanarev

Here is a screenshot:
http://www.geocities.com/capellan2000/Vector_algorithms.PNG

Hope it is useful.

alejandro


Hugh Senior-2 wrote:
> 
> Hello Francois,
> 
> I think we need a RevCoding mathematician! I struggle with elementary
> mathematics, let alone polynomial tangent functions!
> 
> /H
> 
> Le 2 oct. 09 ` 19:15, Hugh Senior a icrit :
> 
>>
>> 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,
> 	Frangois
> 
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