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fksmooth

$ \bigcirc$Name


fksmooth Apply Euclidean heat equation to a curve




$ \bigcirc$Command Synopsis


fksmooth [-n n] [-s std] [-t t] [-P] in out



-n n : number of iterations (default: 10)

-s std : standart deviation for Gaussian kernel (default: 2.)

-t t : space quantization step (default: 1.)

-P : to prevent Euclidean normalization

in : input curve (Flist)

out : output smoothed curve (Flist, modified input)




$ \bigcirc$Function Summary


Flist fksmooth (in , n , std , t , P )

Flist in ;

int *n ;

float *std , *t ;

char *P ;




$ \bigcirc$Description


This module applies to a plane curve C the non-linear heat equation [GH86] [Gra87]

$\displaystyle {\frac{{\partial C}}{{\partial t}}}$(s, t) = $\displaystyle {\frac{{\partial^2 C}}{{\partial s^2}}}$(s, t),

(s being the arlength parameterization of the curve) by alternatively convolving the function s $ \mapsto$ C(s) with a Gaussian kernel (see sgauss module) and reparameterizing it. This algorithm is described in [MM92]. With the -N option [MM86], no reparameterization is applied and the scheme is not consistant any more with the mean curvature motion

$\displaystyle {\frac{{\partial C}}{{\partial t}}}$(s, t) = $\displaystyle \kappa$(s, t)  N(s, t),

where $ \kappa$ and N are the local curvature and normal to the curve s $ \mapsto$ C(s, t).




$ \bigcirc$See Also


sgauss.

iter_fksmooth.


$ \bigcirc$Version 1.1


Last Modification date : Thu Nov 29 20:23:56 2001


$ \bigcirc$Author


Lionel Moisan






next up previous contents index
Next: gass Up: Reference Previous: km_savematchings   Contents   Index
mw 2004-05-05