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curve.cc

/*
    Copyright (C) 2001-2003 Paul Davis 

    Contains ideas derived from "Constrained Cubic Spline Interpolation" 
    by CJC Kruger (www.korf.co.uk/spline.pdf).

    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; if not, write to the Free Software
    Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.

    $Id: curve.cc,v 1.52 2005/09/22 22:32:49 essej Exp $
*/

#include <iostream>
#include <float.h>
#include <cmath>
#include <climits>
#include <cfloat>
#include <cmath>

#include <pbd/lockmonitor.h>
#include <sigc++/bind.h>

#include "ardour/curve.h"

#include "i18n.h"

using namespace std;
using namespace ARDOUR;
using namespace PBD;
using namespace SigC;

Curve::Curve (double minv, double maxv, double canv, bool nostate)
      : AutomationList (canv, nostate)
{
      min_yval = minv;
      max_yval = maxv;
}

Curve::Curve (const Curve& other)
      : AutomationList (other)
{
      min_yval = other.min_yval;
      max_yval = other.max_yval;
}

Curve::Curve (const Curve& other, double start, double end)
      : AutomationList (other, start, end)
{
      min_yval = other.min_yval;
      max_yval = other.max_yval;
}

Curve::~Curve ()
{
}

void
Curve::solve ()
{
      uint32_t npoints;

      if (!_dirty) {
            return;
      }
      
      if ((npoints = events.size()) > 2) {
            
            /* Compute coefficients needed to efficiently compute a constrained spline
               curve. See "Constrained Cubic Spline Interpolation" by CJC Kruger
               (www.korf.co.uk/spline.pdf) for more details.
            */

            double x[npoints];
            double y[npoints];
            uint32_t i;
            AutomationEventList::iterator xx;

            for (i = 0, xx = events.begin(); xx != events.end(); ++xx, ++i) {
                  x[i] = (double) (*xx)->when;
                  y[i] = (double) (*xx)->value;
            }

            double lp0, lp1, fpone;

            lp0 =(x[1] - x[0])/(y[1] - y[0]);
            lp1 = (x[2] - x[1])/(y[2] - y[1]);

            if (lp0*lp1 < 0) {
                  fpone = 0;
            } else {
                  fpone = 2 / (lp1 + lp0);
            }

            double fplast = 0;

            for (i = 0, xx = events.begin(); xx != events.end(); ++xx, ++i) {
                  
                  CurvePoint* cp = dynamic_cast<CurvePoint*>(*xx);

                  if (cp == 0) {
                        fatal  << _("programming error: ")
                               << X_("non-CurvePoint event found in event list for a Curve")
                               << endmsg;
                        /*NOTREACHED*/
                  }
                  
                  double xdelta;   /* gcc is wrong about possible uninitialized use */
                  double xdelta2;  /* ditto */
                  double ydelta;   /* ditto */
                  double fppL, fppR;
                  double fpi;

                  if (i > 0) {
                        xdelta = x[i] - x[i-1];
                        xdelta2 = xdelta * xdelta;
                        ydelta = y[i] - y[i-1];
                  }

                  /* compute (constrained) first derivatives */
                  
                  if (i == 0) {

                        /* first segment */
                        
                        fplast = ((3 * (y[1] - y[0]) / (2 * (x[1] - x[0]))) - (fpone * 0.5));

                        /* we don't store coefficients for i = 0 */

                        continue;

                  } else if (i == npoints - 1) {

                        /* last segment */

                        fpi = ((3 * ydelta) / (2 * xdelta)) - (fplast * 0.5);
                        
                  } else {

                        /* all other segments */

                        double slope_before = ((x[i+1] - x[i]) / (y[i+1] - y[i]));
                        double slope_after = (xdelta / ydelta);

                        if (slope_after * slope_before < 0.0) {
                              /* slope changed sign */
                              fpi = 0.0;
                        } else {
                              fpi = 2 / (slope_before + slope_after);
                        }
                        
                  }

                  /* compute second derivative for either side of control point `i' */
                  
                  fppL = (((-2 * (fpi + (2 * fplast))) / (xdelta))) +
                        ((6 * ydelta) / xdelta2);
                  
                  fppR = (2 * ((2 * fpi) + fplast) / xdelta) -
                        ((6 * ydelta) / xdelta2);
                  
                  /* compute polynomial coefficients */

                  double b, c, d;

                  d = (fppR - fppL) / (6 * xdelta);   
                  c = ((x[i] * fppL) - (x[i-1] * fppR))/(2 * xdelta);
                  
                  double xim12, xim13;
                  double xi2, xi3;
                  
                  xim12 = x[i-1] * x[i-1];  /* "x[i-1] squared" */
                  xim13 = xim12 * x[i-1];   /* "x[i-1] cubed" */
                  xi2 = x[i] * x[i];        /* "x[i] squared" */
                  xi3 = xi2 * x[i];         /* "x[i] cubed" */
                  
                  b = (ydelta - (c * (xi2 - xim12)) - (d * (xi3 - xim13))) / xdelta;

                  /* store */

                  cp->coeff[0] = y[i-1] - (b * x[i-1]) - (c * xim12) - (d * xim13);
                  cp->coeff[1] = b;
                  cp->coeff[2] = c;
                  cp->coeff[3] = d;

                  fplast = fpi;
            }
            
      }

      _dirty = false;
}

bool
Curve::rt_safe_get_vector (double x0, double x1, float *vec, int32_t veclen)
{
      TentativeLockMonitor lm (lock, __LINE__, __FILE__);

      if (!lm.locked()) {
            return false;
      } else {
            _get_vector (x0, x1, vec, veclen);
            return true;
      }
}

void
Curve::get_vector (double x0, double x1, float *vec, int32_t veclen)
{
      LockMonitor lm (lock, __LINE__, __FILE__);
      _get_vector (x0, x1, vec, veclen);
}

void
Curve::_get_vector (double x0, double x1, float *vec, int32_t veclen)
{
      double rx, dx, lx, hx, max_x, min_x;
      int32_t i;
      int32_t original_veclen;
      int32_t npoints;

      if ((npoints = events.size()) == 0) {
            for (i = 0; i < veclen; ++i) {
                  vec[i] = default_value;
            }
            return;
      }

      /* events is now known not to be empty */

      max_x = events.back()->when;
      min_x = events.front()->when;

      lx = max (min_x, x0);

      if (x1 < 0) {
            x1 = events.back()->when;
      }

      hx = min (max_x, x1);
      
      
      original_veclen = veclen;

      if (x0 < min_x) {

            /* fill some beginning section of the array with the 
               initial (used to be default) value 
            */

            double frac = (min_x - x0) / (x1 - x0);
            int32_t subveclen = (int32_t) floor (veclen * frac);
            
            subveclen = min (subveclen, veclen);

            for (i = 0; i < subveclen; ++i) {
                  vec[i] = events.front()->value;
            }

            veclen -= subveclen;
            vec += subveclen;
      }

      if (veclen && x1 > max_x) {

            /* fill some end section of the array with the default or final value */

            double frac = (x1 - max_x) / (x1 - x0);

            int32_t subveclen = (int32_t) floor (original_veclen * frac);

            float val;
            
            subveclen = min (subveclen, veclen);

            val = events.back()->value;

            i = veclen - subveclen;

            for (i = veclen - subveclen; i < veclen; ++i) {
                  vec[i] = val;
            }

            veclen -= subveclen;
      }

      if (veclen == 0) {
            return;
      }

      if (npoints == 1 ) {
      
            for (i = 0; i < veclen; ++i) {
                  vec[i] = events.front()->value;
            }
            return;
      }
 
 
      if (npoints == 2) {
 
            /* linear interpolation between 2 points */
 
            /* XXX I'm not sure that this is the right thing to
               do here. but its not a common case for the envisaged
               uses.
            */
      
            if (veclen > 1) {
                  dx = (hx - lx) / (veclen - 1) ;
            } else {
                  dx = 0; // not used
            }
      
            double slope = (events.back()->value - events.front()->value)/  
                  (events.back()->when - events.front()->when);
            double yfrac = dx*slope;
 
            vec[0] = events.front()->value + slope * (lx - events.front()->when);
 
            for (i = 1; i < veclen; ++i) {
                  vec[i] = vec[i-1] + yfrac;
            }
 
            return;
      }
 
      if (_dirty) {
            solve ();
      }

      rx = lx;

      if (veclen > 1) {

            dx = (hx - lx) / veclen;

            for (i = 0; i < veclen; ++i, rx += dx) {
                  vec[i] = multipoint_eval (rx);
            }
      }
}

double
Curve::unlocked_eval (double x)
{
      if (_dirty) {
            solve ();
      }

      return shared_eval (x);
}

double
Curve::multipoint_eval (double x)
{     
      pair<AutomationEventList::iterator,AutomationEventList::iterator> range;

      if ((lookup_cache.left < 0) ||
          ((lookup_cache.left > x) || 
           (lookup_cache.range.first == events.end()) || 
           ((*lookup_cache.range.second)->when < x))) {
            
            TimeComparator cmp;
            ControlEvent cp (x, 0.0);

            lookup_cache.range = equal_range (events.begin(), events.end(), &cp, cmp);
      }

      range = lookup_cache.range;

      /* EITHER 
         
         a) x is an existing control point, so first == existing point, second == next point

         OR

         b) x is between control points, so range is empty (first == second, points to where
             to insert x)
         
      */

      if (range.first == range.second) {

            /* x does not exist within the list as a control point */
            
            lookup_cache.left = x;

            if (range.first == events.begin()) {
                  /* we're before the first point */
                  // return default_value;
                  events.front()->value;
            }
            
            if (range.second == events.end()) {
                  /* we're after the last point */
                  return events.back()->value;
            }

            double x2 = x * x;
            CurvePoint* cp = dynamic_cast<CurvePoint*> (*range.second);

            return cp->coeff[0] + (cp->coeff[1] * x) + (cp->coeff[2] * x2) + (cp->coeff[3] * x2 * x);
      } 

      /* x is a control point in the data */
      /* invalidate the cached range because its not usable */
      lookup_cache.left = -1;
      return (*range.first)->value;
}

ControlEvent*
Curve::point_factory (double when, double val) const
{
      return new CurvePoint (when, val);
}

ControlEvent*
Curve::point_factory (const ControlEvent& other) const
{
      return new CurvePoint (other.when, other.value);
}

Change
Curve::restore_state (StateManager::State& state)
{
      mark_dirty ();
      return AutomationList::restore_state (state);
}


extern "C" {

void 
curve_get_vector_from_c (void *arg, double x0, double x1, float* vec, int32_t vecsize)
{
      static_cast<Curve*>(arg)->get_vector (x0, x1, vec, vecsize);
}

}

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