Curve.cpp

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/* This file is part of Evoral.
 * Copyright (C) 2008 David Robillard <http://drobilla.net>
 * Copyright (C) 2000-2008 Paul Davis
 *
 * Evoral 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.
 *
 * Evoral 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 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.,
 * 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
 */

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

#include <glibmm/threads.h>

#include "evoral/Curve.hpp"
#include "evoral/ControlList.hpp"

using namespace std;
using namespace sigc;

namespace Evoral {


Curve::Curve (const ControlList& cl)
        : _dirty (true)
        , _list (cl)
{
}

void
Curve::solve ()
{
        uint32_t npoints;

        if (!_dirty) {
                return;
        }

        if ((npoints = _list.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.
                */

                vector<double> x(npoints);
                vector<double> y(npoints);
                uint32_t i;
                ControlList::EventList::const_iterator xx;

                for (i = 0, xx = _list.events().begin(); xx != _list.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 = _list.events().begin(); xx != _list.events().end(); ++xx, ++i) {

                        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 */

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

                        fplast = fpi;
                }

        }

        _dirty = false;
}

bool
Curve::rt_safe_get_vector (double x0, double x1, float *vec, int32_t veclen)
{
        Glib::Threads::RWLock::ReaderLock lm(_list.lock(), Glib::Threads::TRY_LOCK);

        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)
{
        Glib::Threads::RWLock::ReaderLock lm(_list.lock());
        _get_vector (x0, x1, vec, veclen);
}

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

        if (veclen == 0) {
                return;
        }

        if ((npoints = _list.events().size()) == 0) {
                /* no events in list, so just fill the entire array with the default value */
                for (int32_t i = 0; i < veclen; ++i) {
                        vec[i] = _list.default_value();
                }
                return;
        }

        if (npoints == 1) {
                for (int32_t i = 0; i < veclen; ++i) {
                        vec[i] = _list.events().front()->value;
                }
                return;
        }

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

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

        if (x0 > max_x) {
                /* totally past the end - just fill the entire array with the final value */    
                for (int32_t i = 0; i < veclen; ++i) {
                        vec[i] = _list.events().back()->value;
                }
                return;
        }

        if (x1 < min_x) {
                /* totally before the first event - fill the entire array with
                 * the initial value.
                 */
                for (int32_t i = 0; i < veclen; ++i) {
                        vec[i] = _list.events().front()->value;
                }
                return;
        }

        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);
                int64_t fill_len = (int64_t) floor (veclen * frac);

                fill_len = min (fill_len, (int64_t)veclen);

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

                veclen -= fill_len;
                vec += fill_len;
        }

        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);
                int64_t fill_len = (int64_t) floor (original_veclen * frac);
                float val;

                fill_len = min (fill_len, (int64_t)veclen);
                val = _list.events().back()->value;

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

                veclen -= fill_len;
        }

        lx = max (min_x, x0);
        hx = min (max_x, x1);

        if (npoints == 2) {

                /* linear interpolation between 2 points */

                /* XXX: this numerator / denominator stuff is pretty grim, but it's the only
                   way I could get the maths to be accurate; doing everything with pure doubles
                   gives ~1e-17 errors in the vec[i] computation.
                */

                /* gradient of the line */
                double const m_num = _list.events().back()->value - _list.events().front()->value;
                double const m_den = _list.events().back()->when - _list.events().front()->when;

                /* y intercept of the line */
                double const c = double (_list.events().back()->value) - (m_num * _list.events().back()->when / m_den);

                /* dx that we are using */
                double dx_num = 0;
                double dx_den = 1;
                if (veclen > 1) {
                        dx_num = hx - lx;
                        dx_den = veclen - 1;
                        for (int i = 0; i < veclen; ++i) {
                                vec[i] = (lx * (m_num / m_den) + m_num * i * dx_num / (m_den * dx_den)) + c;
                        }
                } else {
                        vec[0] = lx * (m_num / m_den) + c;
                }

                return;
        }

        if (_dirty) {
                solve ();
        }

        rx = lx;

        double dx = 0;
        if (veclen > 1) {
                dx = (hx - lx) / (veclen - 1);
        }

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

double
Curve::unlocked_eval (double x)
{
        // I don't see the point of this...

        if (_dirty) {
                solve ();
        }

        return _list.unlocked_eval (x);
}

double
Curve::multipoint_eval (double x)
{
        pair<ControlList::EventList::const_iterator,ControlList::EventList::const_iterator> range;

        ControlList::LookupCache& lookup_cache = _list.lookup_cache();

        if ((lookup_cache.left < 0) ||
            ((lookup_cache.left > x) ||
             (lookup_cache.range.first == _list.events().end()) ||
             ((*lookup_cache.range.second)->when < x))) {

                ControlEvent cp (x, 0.0);

                lookup_cache.range = equal_range (_list.events().begin(), _list.events().end(), &cp, ControlList::time_comparator);
        }

        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 == _list.events().begin()) {
                        /* we're before the first point */
                        // return default_value;
                        return _list.events().front()->value;
                }

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

                ControlEvent* after = (*range.second);
                range.second--;
                ControlEvent* before = (*range.second);

                double vdelta = after->value - before->value;

                if (vdelta == 0.0) {
                        return before->value;
                }

                double tdelta = x - before->when;
                double trange = after->when - before->when;

                if (_list.interpolation() == ControlList::Curved && after->coeff) {
                                ControlEvent* ev = after;
                                double x2 = x * x;
                                return ev->coeff[0] + (ev->coeff[1] * x) + (ev->coeff[2] * x2) + (ev->coeff[3] * x2 * x);
                } else {
                        return before->value + (vdelta * (tdelta / trange));
                }
        }

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

} // namespace Evoral

extern "C" {

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

}