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+/*
+ * Copyright (C) 2008-2013 Paul Davis <paul@linuxaudiosystems.com>
+ * Copyright (C) 2008-2016 David Robillard <d@drobilla.net>
+ * Copyright (C) 2010-2012 Carl Hetherington <carl@carlh.net>
+ * Copyright (C) 2012-2018 Robin Gareus <robin@gareus.org>
+ *
+ * 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.,
+ * 51 Franklin Street, 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 "pbd/control_math.h"
+
+#include "evoral/Curve.h"
+#include "evoral/ControlList.h"
+
+using namespace std;
+using namespace sigc;
+
+namespace Evoral {
+
+
+Curve::Curve (const ControlList& cl)
+ : _dirty (true)
+ , _list (cl)
+{
+}
+
+void
+Curve::solve () const
+{
+ 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) const
+{
+ 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) const
+{
+ 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) const
+{
+ 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.descriptor().normal;
+ }
+ 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) {
+
+ const double lpos = _list.events().front()->when;
+ const double lval = _list.events().front()->value;
+ const double upos = _list.events().back()->when;
+ const double uval = _list.events().back()->value;
+
+ /* dx that we are using */
+ if (veclen > 1) {
+ const double dx_num = hx - lx;
+ const double dx_den = veclen - 1;
+ const double lower = _list.descriptor().lower;
+ const double upper = _list.descriptor().upper;
+
+ /* gradient of the line */
+ const double m_num = uval - lval;
+ const double m_den = upos - lpos;
+ /* y intercept of the line */
+ const double c = uval - (m_num * upos / m_den);
+
+ switch (_list.interpolation()) {
+ case ControlList::Logarithmic:
+ for (int i = 0; i < veclen; ++i) {
+ const double fraction = (lx - lpos + i * dx_num / dx_den) / m_den;
+ vec[i] = interpolate_logarithmic (lval, uval, fraction, lower, upper);
+ }
+ break;
+ case ControlList::Exponential:
+ for (int i = 0; i < veclen; ++i) {
+ const double fraction = (lx - lpos + i * dx_num / dx_den) / m_den;
+ vec[i] = interpolate_gain (lval, uval, fraction, upper);
+ }
+ break;
+ case ControlList::Discrete:
+ // any discrete vector curves somewhere?
+ assert (0);
+ case ControlList::Curved:
+ /* no 2 point spline */
+ /* fallthrough */
+ default: // Linear:
+ for (int i = 0; i < veclen; ++i) {
+ vec[i] = (lx * (m_num / m_den) + m_num * i * dx_num / (m_den * dx_den)) + c;
+ }
+ break;
+ }
+ } else {
+ double fraction = (lx - lpos) / (upos - lpos);
+ switch (_list.interpolation()) {
+ case ControlList::Logarithmic:
+ vec[0] = interpolate_logarithmic (lval, uval, fraction, _list.descriptor().lower, _list.descriptor().upper);
+ break;
+ case ControlList::Exponential:
+ vec[0] = interpolate_gain (lval, uval, fraction, _list.descriptor().upper);
+ break;
+ case ControlList::Discrete:
+ // any discrete vector curves somewhere?
+ assert (0);
+ case ControlList::Curved:
+ /* no 2 point spline */
+ /* fallthrough */
+ default: // Linear:
+ vec[0] = interpolate_linear (lval, uval, fraction);
+ break;
+ }
+ }
+
+ 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::multipoint_eval (double x) const
+{
+ 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;
+
+ switch (_list.interpolation()) {
+ case ControlList::Discrete:
+ return before->value;
+ case ControlList::Logarithmic:
+ return interpolate_logarithmic (before->value, after->value, tdelta / trange, _list.descriptor().lower, _list.descriptor().upper);
+ case ControlList::Exponential:
+ return interpolate_gain (before->value, after->value, tdelta / trange, _list.descriptor().upper);
+ case ControlList::Curved:
+ if (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);
+ }
+ /* fallthrough */
+ case ControlList::Linear:
+ 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
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