Aegisub/FexTrackerSource/FexGenericFilter.cpp

87 lines
1.6 KiB
C++

// This file is part of FexGenericFilter and (C) 2006 by Hajo Krabbenhöft (tentacle)
// All rights reserved but the aegisub project is allowed to use it.
#include <math.h>
#include "FexGenericFilter_Include.h"
FexFilter::FexFilter()
{
Width = 3;
}
FexFilter::~FexFilter()
{
}
double FexFilter::Filter( double t )
{
return t/Width;
}
/*
f(x) = e^(-x^2 / (2 s^2) )
f(x) = e^(-x^2 / t)
width:
SOLVE(0.1 = f(x), x, Real)
x = - sqrt(t LN(10) ? x = sqrt(t LN(10)
x = - 1.517427129·sqrt t ? x = 1.517427129·sqrt t
x = - sqrt(2*s*s* LN(10)) ? x = sqrt(2*s*s* LN(10))
x = - 2.145966026·s ? x = 2.145966026·s
sum:
Integral from -sqrt(t LN(10) to sqrt(t LN(10) of f(x) dx
1.715955662·sqrt(t)
2.426727768·s
*/
FexFilter_Gauss::FexFilter_Gauss( double sigma )
{
Sigma = sigma;
TwoSigmaSq = 2*sigma*sigma;
Width = 2.145966026 * sigma;
Normalize = 1.0 / (2.426727768 * sigma);
Normalize *= 1.0 + 0.1 / Width; //its the 0.1 we left out
}
FexFilter_Gauss::~FexFilter_Gauss()
{
}
double FexFilter_Gauss::Filter( double t )
{
return exp( -t*t / TwoSigmaSq ) * Normalize;
}
/*
f(x) = -x * e^(-x^2 / (2 s^2) )
f(x) = -x * e^(-x^2 / t)
width:
use the width of gauss since i'm clueless here
sum:
Integral from -sqrt(t LN(10) to sqrt(t LN(10) of -x*f(x) dx
0.7062351183·t^1.5
*/
FexFilter_GaussDerivation::FexFilter_GaussDerivation( double sigma )
{
Sigma = sigma;
TwoSigmaSq = 2*sigma*sigma;
Width = 2.145966026 * sigma;
Normalize = 1.0 / (0.7062351183 * pow( TwoSigmaSq, 1.5 ));
}
FexFilter_GaussDerivation::~FexFilter_GaussDerivation()
{
}
double FexFilter_GaussDerivation::Filter( double t )
{
return -t * exp( -t*t / TwoSigmaSq ) * Normalize;
}