490 lines
12 KiB
C++
490 lines
12 KiB
C++
/*
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* Copyright (C) 2008-2013 Paul Davis <paul@linuxaudiosystems.com>
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* Copyright (C) 2008-2016 David Robillard <d@drobilla.net>
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* Copyright (C) 2010-2012 Carl Hetherington <carl@carlh.net>
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* Copyright (C) 2012-2018 Robin Gareus <robin@gareus.org>
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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*/
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#include <iostream>
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#include <float.h>
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#include <cmath>
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#include <climits>
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#include <cfloat>
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#include <cmath>
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#include <vector>
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#include <glibmm/threads.h>
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#include "pbd/control_math.h"
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#include "evoral/Curve.h"
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#include "evoral/ControlList.h"
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using namespace std;
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using namespace sigc;
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namespace Evoral {
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Curve::Curve (const ControlList& cl)
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: _dirty (true)
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, _list (cl)
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{
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}
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void
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Curve::solve () const
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{
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uint32_t npoints;
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if (!_dirty) {
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return;
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}
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if ((npoints = _list.events().size()) > 2) {
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/* Compute coefficients needed to efficiently compute a constrained spline
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curve. See "Constrained Cubic Spline Interpolation" by CJC Kruger
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(www.korf.co.uk/spline.pdf) for more details.
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*/
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vector<Temporal::timepos_t> x (npoints);
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vector<double> y(npoints);
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uint32_t i;
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ControlList::EventList::const_iterator xx;
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for (i = 0, xx = _list.events().begin(); xx != _list.events().end(); ++xx, ++i) {
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x[i] = (*xx)->when;
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y[i] = (*xx)->value;
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}
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double lp0, lp1, fpone;
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double xd;
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xd = x[0].distance (x[1]).magnitude();
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lp0 = xd/(y[1] - y[0]);
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xd = x[1].distance (x[2]).magnitude();
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lp1 = xd/(y[2] - y[1]);
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if (lp0*lp1 < 0) {
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fpone = 0;
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} else {
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fpone = 2 / (lp1 + lp0);
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}
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double fplast = 0;
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for (i = 0, xx = _list.events().begin(); xx != _list.events().end(); ++xx, ++i) {
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double xi = x[i].val();
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if (i == 0) {
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/* first segment */
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fplast = ((3 * (y[1] - y[0]) / (2 * (x[1].val() - x[0].val()))) - (fpone * 0.5));
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/* we don't store coefficients for i = 0 */
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continue;
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}
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double xdelta; /* gcc is wrong about possible uninitialized use */
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double xdelta2; /* ditto */
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double ydelta; /* ditto */
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double fppL, fppR;
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double fpi;
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double xim1;
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xim1 = x[i-1].val();
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xdelta = xi - xim1;
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xdelta2 = xdelta * xdelta;
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ydelta = y[i] - y[i-1];
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/* compute (constrained) first derivatives */
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if (i == npoints - 1) {
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/* last segment */
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fpi = ((3 * ydelta) / (2 * xdelta)) - (fplast * 0.5);
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} else {
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/* all other segments */
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double slope_before = (x[i+1].val() - xi) / (y[i+1] - y[i]);
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double slope_after = (xdelta / ydelta);
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if (slope_after * slope_before < 0.0) {
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/* slope changed sign */
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fpi = 0.0;
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} else {
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fpi = 2 / (slope_before + slope_after);
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}
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}
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/* compute second derivative for either side of control point `i' */
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fppL = -2 * (fpi + 2 * fplast) / xdelta +
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6 * ydelta / xdelta2;
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fppR = 2 * (2 * fpi + fplast) / xdelta -
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6 * ydelta / xdelta2;
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/* compute polynomial coefficients */
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double b, c, d;
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d = (fppR - fppL) / (6 * xdelta);
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c = ((xi * fppL) - (xim1 * fppR))/(2 * xdelta);
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double xim12, xim13;
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double xi2, xi3;
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xim12 = xim1 * xim1; /* "x[i-1] squared" */
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xim13 = xim12 * xim1; /* "x[i-1] cubed" */
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xi2 = xi * xi; /* "x[i] squared" */
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xi3 = xi2 * xi; /* "x[i] cubed" */
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b = (ydelta - (c * (xi2 - xim12)) - (d * (xi3 - xim13))) / xdelta;
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/* store */
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(*xx)->create_coeffs();
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(*xx)->coeff[0] = y[i-1] - (b * xim1) - (c * xim12) - (d * xim13);
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(*xx)->coeff[1] = b;
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(*xx)->coeff[2] = c;
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(*xx)->coeff[3] = d;
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fplast = fpi;
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}
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}
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_dirty = false;
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}
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bool
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Curve::rt_safe_get_vector (Temporal::timepos_t const & x0, Temporal::timepos_t const & x1, float *vec, int32_t veclen) const
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{
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Glib::Threads::RWLock::ReaderLock lm(_list.lock(), Glib::Threads::TRY_LOCK);
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if (!lm.locked()) {
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return false;
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} else {
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_get_vector (x0, x1, vec, veclen);
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return true;
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}
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}
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void
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Curve::get_vector (Temporal::timepos_t const & x0, Temporal::timepos_t const & x1, float *vec, int32_t veclen) const
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{
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Glib::Threads::RWLock::ReaderLock lm(_list.lock());
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_get_vector (x0, x1, vec, veclen);
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}
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void
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Curve::_get_vector (Temporal::timepos_t x0, Temporal::timepos_t x1, float *vec, int32_t veclen) const
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{
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x0.set_time_domain (_list.time_domain());
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x1.set_time_domain (_list.time_domain());
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double rx, lx, hx;
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const double start = x0.val();
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const double end = x1.val();
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double max_x;
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double min_x;
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int32_t i;
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int32_t original_veclen;
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int32_t npoints;
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if (veclen == 0) {
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return;
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}
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if ((npoints = _list.events().size()) == 0) {
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/* no events in list, so just fill the entire array with the default value */
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for (int32_t i = 0; i < veclen; ++i) {
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vec[i] = _list.descriptor().normal;
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}
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return;
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}
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if (npoints == 1) {
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for (int32_t i = 0; i < veclen; ++i) {
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vec[i] = _list.events().front()->value;
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}
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return;
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}
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/* events is now known not to be empty */
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max_x = _list.events().back()->when.val();
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min_x = _list.events().front()->when.val();
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if (start > max_x) {
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/* totally past the end - just fill the entire array with the final value */
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for (int32_t i = 0; i < veclen; ++i) {
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vec[i] = _list.events().back()->value;
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}
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return;
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}
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if (end < min_x) {
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/* totally before the first event - fill the entire array with
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* the initial value.
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*/
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for (int32_t i = 0; i < veclen; ++i) {
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vec[i] = _list.events().front()->value;
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}
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return;
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}
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original_veclen = veclen;
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if (start < min_x) {
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/* fill some beginning section of the array with the
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initial (used to be default) value
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*/
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double frac = (min_x - start) / (end - start);
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int64_t fill_len = (int64_t) floor (veclen * frac);
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fill_len = min (fill_len, (int64_t)veclen);
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for (i = 0; i < fill_len; ++i) {
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vec[i] = _list.events().front()->value;
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}
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veclen -= fill_len;
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vec += fill_len;
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}
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if (veclen && end > max_x) {
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/* fill some end section of the array with the default or final value */
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double frac = (end - max_x) / (end - start);
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int64_t fill_len = (int64_t) floor (original_veclen * frac);
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float val;
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fill_len = min (fill_len, (int64_t)veclen);
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val = _list.events().back()->value;
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for (i = veclen - fill_len; i < veclen; ++i) {
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vec[i] = val;
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}
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veclen -= fill_len;
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}
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lx = max (min_x, start);
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hx = min (max_x, end);
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if (npoints == 2) {
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const double lpos = _list.events().front()->when.val();
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const double lval = _list.events().front()->value;
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const double upos = _list.events().back()->when.val();
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const double uval = _list.events().back()->value;
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/* dx that we are using */
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if (veclen > 1) {
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const double dx_num = hx - lx;
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const double dx_den = veclen - 1;
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const double lower = _list.descriptor().lower;
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const double upper = _list.descriptor().upper;
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/* gradient of the line */
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const double m_num = uval - lval;
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const double m_den = upos - lpos;
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/* y intercept of the line */
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const double c = uval - (m_num * upos / m_den);
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switch (_list.interpolation()) {
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case ControlList::Logarithmic:
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for (int i = 0; i < veclen; ++i) {
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const double fraction = (lx - lpos + i * dx_num / dx_den) / m_den;
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vec[i] = interpolate_logarithmic (lval, uval, fraction, lower, upper);
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}
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break;
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case ControlList::Exponential:
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for (int i = 0; i < veclen; ++i) {
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const double fraction = (lx - lpos + i * dx_num / dx_den) / m_den;
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vec[i] = interpolate_gain (lval, uval, fraction, upper);
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}
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break;
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case ControlList::Discrete:
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// any discrete vector curves somewhere?
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assert (0);
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case ControlList::Curved:
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/* no 2 point spline */
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/* fallthrough */
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default: // Linear:
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for (int i = 0; i < veclen; ++i) {
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vec[i] = (lx * (m_num / m_den) + m_num * i * dx_num / (m_den * dx_den)) + c;
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}
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break;
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}
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} else {
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double fraction = (lx - lpos) / (upos - lpos);
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switch (_list.interpolation()) {
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case ControlList::Logarithmic:
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vec[0] = interpolate_logarithmic (lval, uval, fraction, _list.descriptor().lower, _list.descriptor().upper);
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break;
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case ControlList::Exponential:
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vec[0] = interpolate_gain (lval, uval, fraction, _list.descriptor().upper);
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break;
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case ControlList::Discrete:
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// any discrete vector curves somewhere?
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assert (0);
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case ControlList::Curved:
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/* no 2 point spline */
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/* fallthrough */
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default: // Linear:
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vec[0] = interpolate_linear (lval, uval, fraction);
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break;
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}
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}
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return;
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}
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if (_dirty) {
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solve ();
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}
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rx = lx;
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double dx = 0.;
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if (veclen > 1) {
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dx = (hx - lx) / (veclen - 1);
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}
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for (i = 0; i < veclen; ++i, rx += dx) {
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vec[i] = multipoint_eval (x0.is_beats() ? Temporal::timepos_t::from_ticks (rx) : Temporal::timepos_t::from_superclock (rx));
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}
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}
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double
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Curve::multipoint_eval (Temporal::timepos_t const & x) const
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{
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pair<ControlList::EventList::const_iterator,ControlList::EventList::const_iterator> range;
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ControlList::LookupCache& lookup_cache = _list.lookup_cache();
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if ((lookup_cache.left == Temporal::timepos_t::max (_list.time_domain())) ||
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((lookup_cache.left > x) ||
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(lookup_cache.range.first == _list.events().end()) ||
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((*lookup_cache.range.second)->when < x))) {
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ControlEvent cp (x, 0.0);
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lookup_cache.range = equal_range (_list.events().begin(), _list.events().end(), &cp, ControlList::time_comparator);
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}
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range = lookup_cache.range;
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/* EITHER
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a) x is an existing control point, so first == existing point, second == next point
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OR
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b) x is between control points, so range is empty (first == second, points to where
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to insert x)
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*/
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if (range.first == range.second) {
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/* x does not exist within the list as a control point */
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lookup_cache.left = x;
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if (range.first == _list.events().begin()) {
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/* we're before the first point */
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// return default_value;
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return _list.events().front()->value;
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}
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if (range.second == _list.events().end()) {
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/* we're after the last point */
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return _list.events().back()->value;
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}
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ControlEvent* after = (*range.second);
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range.second--;
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ControlEvent* before = (*range.second);
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double vdelta = after->value - before->value;
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if (vdelta == 0.0) {
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return before->value;
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}
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double aw = after->when.val();
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double bw = before->when.val();
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double tdelta = x.val() - bw;
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double trange = aw - bw;
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switch (_list.interpolation()) {
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case ControlList::Discrete:
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return before->value;
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case ControlList::Logarithmic:
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return interpolate_logarithmic (before->value, after->value, tdelta / trange, _list.descriptor().lower, _list.descriptor().upper);
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case ControlList::Exponential:
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return interpolate_gain (before->value, after->value, tdelta / trange, _list.descriptor().upper);
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case ControlList::Curved:
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if (after->coeff) {
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ControlEvent* ev = after;
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/* As of Jan 2020, we only use Curved
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* for fade in/out curves (of audio
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* regions).
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*
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* This means that x is a relatively
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* small value (an offset into the
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* fade) amd we do not need to worry
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* about the square or cube overflowing
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* a double type. They can overflow an
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* int64_t by around 6 seconds.
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*/
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const double xv = x.val();
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double xv2 = xv * xv;
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return ev->coeff[0] + (ev->coeff[1] * xv) + (ev->coeff[2] * xv2) + (ev->coeff[3] * xv2 * xv);
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}
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/* fallthrough */
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case ControlList::Linear:
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return before->value + (vdelta * (tdelta / trange));
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}
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}
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/* x is a control point in the data */
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/* invalidate the cached range because its not usable */
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lookup_cache.left = Temporal::timepos_t::max (_list.time_domain());
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return (*range.first)->value;
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}
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} // namespace Evoral
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