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/*
* interpolation.h - fast implementations of several interpolation-algorithms
*
* Copyright (c) 2004-2005 Tobias Doerffel <tobydox/at/users.sourceforge.net>
*
* This file is part of LMMS - https://lmms.io
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public
* License as published by the Free Software Foundation; either
* version 2 of the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public
* License along with this program (see COPYING); if not, write to the
* Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
* Boston, MA 02110-1301 USA.
*
*/
#ifndef INTERPOLATION_H
#define INTERPOLATION_H
#ifndef __USE_XOPEN
#define __USE_XOPEN
#endif
#include <math.h>
#include "lmms_constants.h"
#include "lmms_math.h"
inline float hermiteInterpolate( float x0, float x1, float x2, float x3,
float frac_pos )
{
const float frsq = frac_pos*frac_pos;
const float frsq2 = 2*frsq;
return( ( (x2-x0) *0.5f ) * ( frac_pos * (frsq+1) -frsq2 ) +
( frsq2*frac_pos - 3*frsq ) * ( x1-x2 ) +
frsq2 * (frac_pos-1) * ( ( x3-x1 ) * 0.25f ) + x1 );
/*
const float frsq = frac_pos*frac_pos;
//const float frsq2 = 2*frsq;
frac_pos *= 0.5;
const float frcu = frsq*frac_pos;
return (
(frcu - frsq + frac_pos) * ((x2 - x0)) +
(4*frcu - 3*frsq) * (x1 - x2)
//frsq*(2*frac_pos-3) * (x1 - x2)
+ (frcu - 0.5*frsq)*((x3 - x1))
+ x1
);
*/
}
inline float cubicInterpolate( float v0, float v1, float v2, float v3, float x )
{
float frsq = x*x;
float frcu = frsq*v0;
float t1 = v3 + 3*v1;
return( v1 + fastFmaf( 0.5f, frcu, x ) * ( v2 - frcu * ( 1.0f/6.0f ) -
fastFmaf( t1, ( 1.0f/6.0f ), -v0 ) * ( 1.0f/3.0f ) ) + frsq * x * ( t1 *
( 1.0f/6.0f ) - 0.5f * v2 ) + frsq * fastFmaf( 0.5f, v2, -v1 ) );
}
inline float cosinusInterpolate( float v0, float v1, float x )
{
const float f = ( 1.0f - cosf( x * F_PI ) ) * 0.5f;
return fastFmaf( f, v1-v0, v0 );
}
inline float linearInterpolate( float v0, float v1, float x )
{
return fastFmaf( x, v1-v0, v0 );
}
inline float optimalInterpolate( float v0, float v1, float x )
{
const float z = x - 0.5f;
const float even = v1 + v0;
const float odd = v1 - v0;
const float c0 = even * 0.50037842517188658;
const float c1 = odd * 1.00621089801788210;
const float c2 = even * -0.004541102062639801;
const float c3 = odd * -1.57015627178718420;
return fastFmaf( fastFmaf( fastFmaf( c3, z, c2 ), z, c1 ), z, c0 );
}
inline float optimal4pInterpolate( float v0, float v1, float v2, float v3, float x )
{
const float z = x - 0.5f;
const float even1 = v2 + v1;
const float odd1 = v2 - v1;
const float even2 = v3 + v0;
const float odd2 = v3 - v0;
const float c0 = even1 * 0.45868970870461956 + even2 * 0.04131401926395584;
const float c1 = odd1 * 0.48068024766578432 + odd2 * 0.17577925564495955;
const float c2 = even1 * -0.246185007019907091 + even2 * 0.24614027139700284;
const float c3 = odd1 * -0.36030925263849456 + odd2 * 0.10174985775982505;
return fastFmaf( fastFmaf( fastFmaf( c3, z, c2 ), z, c1 ), z, c0 );
}
inline float lagrangeInterpolate( float v0, float v1, float v2, float v3, float x )
{
const float c0 = v1;
const float c1 = v2 - v0 * ( 1.0f / 3.0f ) - v1 * 0.5f - v3 * ( 1.0f / 6.0f );
const float c2 = 0.5f * (v0 + v2) - v1;
const float c3 = ( 1.0f/6.0f ) * ( v3 - v0 ) + 0.5f * ( v1 - v2 );
return fastFmaf( fastFmaf( fastFmaf( c3, x, c2 ), x, c1 ), x, c0 );
}
#endif
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