1 /* This file is part of Evoral.
2 * Copyright (C) 2008 David Robillard <http://drobilla.net>
3 * Copyright (C) 2000-2008 Paul Davis
5 * Evoral is free software; you can redistribute it and/or modify it under the
6 * terms of the GNU General Public License as published by the Free Software
7 * Foundation; either version 2 of the License, or (at your option) any later
10 * Evoral is distributed in the hope that it will be useful, but WITHOUT ANY
11 * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
12 * FOR A PARTICULAR PURPOSE. See the GNU General Public License for details.
14 * You should have received a copy of the GNU General Public License along
15 * with this program; if not, write to the Free Software Foundation, Inc.,
16 * 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
26 #include <glibmm/threads.h>
28 #include "evoral/Curve.hpp"
29 #include "evoral/ControlList.hpp"
37 Curve::Curve (const ControlList& cl)
52 if ((npoints = _list.events().size()) > 2) {
54 /* Compute coefficients needed to efficiently compute a constrained spline
55 curve. See "Constrained Cubic Spline Interpolation" by CJC Kruger
56 (www.korf.co.uk/spline.pdf) for more details.
62 ControlList::EventList::const_iterator xx;
64 for (i = 0, xx = _list.events().begin(); xx != _list.events().end(); ++xx, ++i) {
65 x[i] = (double) (*xx)->when;
66 y[i] = (double) (*xx)->value;
69 double lp0, lp1, fpone;
71 lp0 = (x[1] - x[0])/(y[1] - y[0]);
72 lp1 = (x[2] - x[1])/(y[2] - y[1]);
77 fpone = 2 / (lp1 + lp0);
82 for (i = 0, xx = _list.events().begin(); xx != _list.events().end(); ++xx, ++i) {
84 double xdelta; /* gcc is wrong about possible uninitialized use */
85 double xdelta2; /* ditto */
86 double ydelta; /* ditto */
91 xdelta = x[i] - x[i-1];
92 xdelta2 = xdelta * xdelta;
93 ydelta = y[i] - y[i-1];
96 /* compute (constrained) first derivatives */
102 fplast = ((3 * (y[1] - y[0]) / (2 * (x[1] - x[0]))) - (fpone * 0.5));
104 /* we don't store coefficients for i = 0 */
108 } else if (i == npoints - 1) {
112 fpi = ((3 * ydelta) / (2 * xdelta)) - (fplast * 0.5);
116 /* all other segments */
118 double slope_before = ((x[i+1] - x[i]) / (y[i+1] - y[i]));
119 double slope_after = (xdelta / ydelta);
121 if (slope_after * slope_before < 0.0) {
122 /* slope changed sign */
125 fpi = 2 / (slope_before + slope_after);
129 /* compute second derivative for either side of control point `i' */
131 fppL = (((-2 * (fpi + (2 * fplast))) / (xdelta))) +
132 ((6 * ydelta) / xdelta2);
134 fppR = (2 * ((2 * fpi) + fplast) / xdelta) -
135 ((6 * ydelta) / xdelta2);
137 /* compute polynomial coefficients */
141 d = (fppR - fppL) / (6 * xdelta);
142 c = ((x[i] * fppL) - (x[i-1] * fppR))/(2 * xdelta);
147 xim12 = x[i-1] * x[i-1]; /* "x[i-1] squared" */
148 xim13 = xim12 * x[i-1]; /* "x[i-1] cubed" */
149 xi2 = x[i] * x[i]; /* "x[i] squared" */
150 xi3 = xi2 * x[i]; /* "x[i] cubed" */
152 b = (ydelta - (c * (xi2 - xim12)) - (d * (xi3 - xim13))) / xdelta;
156 (*xx)->create_coeffs();
157 (*xx)->coeff[0] = y[i-1] - (b * x[i-1]) - (c * xim12) - (d * xim13);
171 Curve::rt_safe_get_vector (double x0, double x1, float *vec, int32_t veclen)
173 Glib::Threads::Mutex::Lock lm(_list.lock(), Glib::Threads::TRY_LOCK);
178 _get_vector (x0, x1, vec, veclen);
184 Curve::get_vector (double x0, double x1, float *vec, int32_t veclen)
186 Glib::Threads::Mutex::Lock lm(_list.lock());
187 _get_vector (x0, x1, vec, veclen);
191 Curve::_get_vector (double x0, double x1, float *vec, int32_t veclen)
193 double rx, lx, hx, max_x, min_x;
195 int32_t original_veclen;
198 cerr << "Check1: veclen = " << veclen << endl;
200 if ((npoints = _list.events().size()) == 0) {
201 for (i = 0; i < veclen; ++i) {
202 vec[i] = _list.default_value();
207 cerr << "Check2: veclen = " << veclen << endl;
209 /* events is now known not to be empty */
211 max_x = _list.events().back()->when;
212 min_x = _list.events().front()->when;
214 lx = max (min_x, x0);
217 x1 = _list.events().back()->when;
220 hx = min (max_x, x1);
222 original_veclen = veclen;
224 cerr << "Check3: veclen = " << veclen << endl;
228 /* fill some beginning section of the array with the
229 initial (used to be default) value
232 double frac = (min_x - x0) / (x1 - x0);
233 int64_t subveclen = (int64_t) floor (veclen * frac);
235 cerr << "subveclen = " << subveclen << endl;
237 subveclen = min (subveclen, (int64_t)veclen);
239 cerr << "subveclen2 = " << subveclen << endl;
241 for (i = 0; i < subveclen; ++i) {
242 vec[i] = _list.events().front()->value;
245 cerr << "adjust veclen from " << veclen << " to ";
247 cerr << veclen << endl;
251 cerr << "Check4: veclen = " << veclen << endl;
253 if (veclen && x1 > max_x) {
255 /* fill some end section of the array with the default or final value */
257 double frac = (x1 - max_x) / (x1 - x0);
259 cerr << "compute subveclen from " << original_veclen << " * " << frac
260 << " taken from " << x0 << " .. " << x0
263 int64_t subveclen = (int64_t) floor (original_veclen * frac);
267 cerr << "subveclen3 = " << subveclen << endl;
268 subveclen = min (subveclen, (int64_t)veclen);
270 cerr << "subveclen4 = " << subveclen << endl;
271 val = _list.events().back()->value;
273 i = veclen - subveclen;
275 for (i = veclen - subveclen; i < veclen; ++i) {
279 cerr << "adjust veclen2 from " << veclen << " to ";
281 cerr << veclen << endl;
284 cerr << "Check5: veclen = " << veclen << endl;
292 for (i = 0; i < veclen; ++i) {
293 vec[i] = _list.events().front()->value;
298 cerr << "Check6: veclen = " << veclen << endl;
302 /* linear interpolation between 2 points */
304 /* XXX: this numerator / denominator stuff is pretty grim, but it's the only
305 way I could get the maths to be accurate; doing everything with pure doubles
306 gives ~1e-17 errors in the vec[i] computation.
309 /* gradient of the line */
310 double const m_num = _list.events().back()->value - _list.events().front()->value;
311 double const m_den = _list.events().back()->when - _list.events().front()->when;
313 /* y intercept of the line */
314 double const c = double (_list.events().back()->value) - (m_num * _list.events().back()->when / m_den);
316 /* dx that we are using */
325 for (int i = 0; i < veclen; ++i) {
326 vec[i] = (lx * (m_num / m_den) + m_num * i * dx_num / (m_den * dx_den)) + c;
335 cerr << "Check7: veclen = " << veclen << endl;
341 cerr << "Check8: veclen = " << veclen << endl;
347 dx = (hx - lx) / (veclen - 1);
350 cerr << "Check9: veclen = " << veclen << endl;
352 for (i = 0; i < veclen; ++i, rx += dx) {
353 vec[i] = multipoint_eval (rx);
358 Curve::unlocked_eval (double x)
360 // I don't see the point of this...
366 return _list.unlocked_eval (x);
370 Curve::multipoint_eval (double x)
372 pair<ControlList::EventList::const_iterator,ControlList::EventList::const_iterator> range;
374 ControlList::LookupCache& lookup_cache = _list.lookup_cache();
376 if ((lookup_cache.left < 0) ||
377 ((lookup_cache.left > x) ||
378 (lookup_cache.range.first == _list.events().end()) ||
379 ((*lookup_cache.range.second)->when < x))) {
381 ControlEvent cp (x, 0.0);
383 lookup_cache.range = equal_range (_list.events().begin(), _list.events().end(), &cp, ControlList::time_comparator);
386 range = lookup_cache.range;
390 a) x is an existing control point, so first == existing point, second == next point
394 b) x is between control points, so range is empty (first == second, points to where
399 if (range.first == range.second) {
401 /* x does not exist within the list as a control point */
403 lookup_cache.left = x;
405 if (range.first == _list.events().begin()) {
406 /* we're before the first point */
407 // return default_value;
408 return _list.events().front()->value;
411 if (range.second == _list.events().end()) {
412 /* we're after the last point */
413 return _list.events().back()->value;
417 ControlEvent* ev = *range.second;
419 return ev->coeff[0] + (ev->coeff[1] * x) + (ev->coeff[2] * x2) + (ev->coeff[3] * x2 * x);
422 /* x is a control point in the data */
423 /* invalidate the cached range because its not usable */
424 lookup_cache.left = -1;
425 return (*range.first)->value;
428 } // namespace Evoral
433 curve_get_vector_from_c (void *arg, double x0, double x1, float* vec, int32_t vecsize)
435 static_cast<Evoral::Curve*>(arg)->get_vector (x0, x1, vec, vecsize);