interpolation.h

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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 LMMS_INTERPOLATION_H
#define LMMS_INTERPOLATION_H
 
#include <cmath>
#include <numbers>
 
namespace lmms
{
 
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 = v1 * 3.f + v3;
 
        return v1 + (0.5f * frcu + x) * (v2 - frcu * (1.0f / 6.0f) -
                (t1 * (1.0f / 6.0f) - v0) * (1.0f / 3.0f)) + frsq * x * (t1 *
                (1.0f / 6.0f) - 0.5f * v2) + frsq * (0.5f * v2 - v1);
}
 
 
 
inline float cosinusInterpolate( float v0, float v1, float x )
{
        const float f = (1.0f - std::cos(x * std::numbers::pi_v<float>)) * 0.5f;
        return f * (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 ((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 ((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 ((c3 * x + c2) * x + c1) * x + c0;
}
 
 
 
} // namespace lmms
 
#endif // LMMS_INTERPOLATION_H