1 /*
2 * Copyright (C) 2008-2013 Paul Davis <paul@linuxaudiosystems.com>
3 * Copyright (C) 2008-2016 David Robillard <d@drobilla.net>
4 * Copyright (C) 2010-2012 Carl Hetherington <carl@carlh.net>
5 * Copyright (C) 2012-2018 Robin Gareus <robin@gareus.org>
6 *
7 * This program is free software; you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation; either version 2 of the License, or
10 * (at your option) any later version.
11 *
12 * This program is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License along
18 * with this program; if not, write to the Free Software Foundation, Inc.,
19 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
20 */
21
22 #include <iostream>
23 #include <float.h>
24 #include <cmath>
25 #include <climits>
26 #include <cfloat>
27 #include <cmath>
28 #include <vector>
29
30 #include <glibmm/threads.h>
31
32 #include "pbd/control_math.h"
33
34 #include "evoral/Curve.h"
35 #include "evoral/ControlList.h"
36
37 using namespace std;
38 using namespace sigc;
39
40 namespace Evoral {
41
42
Curve(const ControlList & cl)43 Curve::Curve (const ControlList& cl)
44 : _dirty (true)
45 , _list (cl)
46 {
47 }
48
49 void
solve() const50 Curve::solve () const
51 {
52 uint32_t npoints;
53
54 if (!_dirty) {
55 return;
56 }
57
58 if ((npoints = _list.events().size()) > 2) {
59
60 /* Compute coefficients needed to efficiently compute a constrained spline
61 curve. See "Constrained Cubic Spline Interpolation" by CJC Kruger
62 (www.korf.co.uk/spline.pdf) for more details.
63 */
64
65 vector<double> x(npoints);
66 vector<double> y(npoints);
67 uint32_t i;
68 ControlList::EventList::const_iterator xx;
69
70 for (i = 0, xx = _list.events().begin(); xx != _list.events().end(); ++xx, ++i) {
71 x[i] = (double) (*xx)->when;
72 y[i] = (double) (*xx)->value;
73 }
74
75 double lp0, lp1, fpone;
76
77 lp0 = (x[1] - x[0])/(y[1] - y[0]);
78 lp1 = (x[2] - x[1])/(y[2] - y[1]);
79
80 if (lp0*lp1 < 0) {
81 fpone = 0;
82 } else {
83 fpone = 2 / (lp1 + lp0);
84 }
85
86 double fplast = 0;
87
88 for (i = 0, xx = _list.events().begin(); xx != _list.events().end(); ++xx, ++i) {
89
90 double xdelta; /* gcc is wrong about possible uninitialized use */
91 double xdelta2; /* ditto */
92 double ydelta; /* ditto */
93 double fppL, fppR;
94 double fpi;
95
96 if (i > 0) {
97 xdelta = x[i] - x[i-1];
98 xdelta2 = xdelta * xdelta;
99 ydelta = y[i] - y[i-1];
100 }
101
102 /* compute (constrained) first derivatives */
103
104 if (i == 0) {
105
106 /* first segment */
107
108 fplast = ((3 * (y[1] - y[0]) / (2 * (x[1] - x[0]))) - (fpone * 0.5));
109
110 /* we don't store coefficients for i = 0 */
111
112 continue;
113
114 } else if (i == npoints - 1) {
115
116 /* last segment */
117
118 fpi = ((3 * ydelta) / (2 * xdelta)) - (fplast * 0.5);
119
120 } else {
121
122 /* all other segments */
123
124 double slope_before = ((x[i+1] - x[i]) / (y[i+1] - y[i]));
125 double slope_after = (xdelta / ydelta);
126
127 if (slope_after * slope_before < 0.0) {
128 /* slope changed sign */
129 fpi = 0.0;
130 } else {
131 fpi = 2 / (slope_before + slope_after);
132 }
133 }
134
135 /* compute second derivative for either side of control point `i' */
136
137 fppL = (((-2 * (fpi + (2 * fplast))) / (xdelta))) +
138 ((6 * ydelta) / xdelta2);
139
140 fppR = (2 * ((2 * fpi) + fplast) / xdelta) -
141 ((6 * ydelta) / xdelta2);
142
143 /* compute polynomial coefficients */
144
145 double b, c, d;
146
147 d = (fppR - fppL) / (6 * xdelta);
148 c = ((x[i] * fppL) - (x[i-1] * fppR))/(2 * xdelta);
149
150 double xim12, xim13;
151 double xi2, xi3;
152
153 xim12 = x[i-1] * x[i-1]; /* "x[i-1] squared" */
154 xim13 = xim12 * x[i-1]; /* "x[i-1] cubed" */
155 xi2 = x[i] * x[i]; /* "x[i] squared" */
156 xi3 = xi2 * x[i]; /* "x[i] cubed" */
157
158 b = (ydelta - (c * (xi2 - xim12)) - (d * (xi3 - xim13))) / xdelta;
159
160 /* store */
161
162 (*xx)->create_coeffs();
163 (*xx)->coeff[0] = y[i-1] - (b * x[i-1]) - (c * xim12) - (d * xim13);
164 (*xx)->coeff[1] = b;
165 (*xx)->coeff[2] = c;
166 (*xx)->coeff[3] = d;
167
168 fplast = fpi;
169 }
170
171 }
172
173 _dirty = false;
174 }
175
176 bool
rt_safe_get_vector(double x0,double x1,float * vec,int32_t veclen) const177 Curve::rt_safe_get_vector (double x0, double x1, float *vec, int32_t veclen) const
178 {
179 Glib::Threads::RWLock::ReaderLock lm(_list.lock(), Glib::Threads::TRY_LOCK);
180
181 if (!lm.locked()) {
182 return false;
183 } else {
184 _get_vector (x0, x1, vec, veclen);
185 return true;
186 }
187 }
188
189 void
get_vector(double x0,double x1,float * vec,int32_t veclen) const190 Curve::get_vector (double x0, double x1, float *vec, int32_t veclen) const
191 {
192 Glib::Threads::RWLock::ReaderLock lm(_list.lock());
193 _get_vector (x0, x1, vec, veclen);
194 }
195
196 void
_get_vector(double x0,double x1,float * vec,int32_t veclen) const197 Curve::_get_vector (double x0, double x1, float *vec, int32_t veclen) const
198 {
199 double rx, lx, hx, max_x, min_x;
200 int32_t i;
201 int32_t original_veclen;
202 int32_t npoints;
203
204 if (veclen == 0) {
205 return;
206 }
207
208 if ((npoints = _list.events().size()) == 0) {
209 /* no events in list, so just fill the entire array with the default value */
210 for (int32_t i = 0; i < veclen; ++i) {
211 vec[i] = _list.descriptor().normal;
212 }
213 return;
214 }
215
216 if (npoints == 1) {
217 for (int32_t i = 0; i < veclen; ++i) {
218 vec[i] = _list.events().front()->value;
219 }
220 return;
221 }
222
223 /* events is now known not to be empty */
224
225 max_x = _list.events().back()->when;
226 min_x = _list.events().front()->when;
227
228 if (x0 > max_x) {
229 /* totally past the end - just fill the entire array with the final value */
230 for (int32_t i = 0; i < veclen; ++i) {
231 vec[i] = _list.events().back()->value;
232 }
233 return;
234 }
235
236 if (x1 < min_x) {
237 /* totally before the first event - fill the entire array with
238 * the initial value.
239 */
240 for (int32_t i = 0; i < veclen; ++i) {
241 vec[i] = _list.events().front()->value;
242 }
243 return;
244 }
245
246 original_veclen = veclen;
247
248 if (x0 < min_x) {
249
250 /* fill some beginning section of the array with the
251 initial (used to be default) value
252 */
253
254 double frac = (min_x - x0) / (x1 - x0);
255 int64_t fill_len = (int64_t) floor (veclen * frac);
256
257 fill_len = min (fill_len, (int64_t)veclen);
258
259 for (i = 0; i < fill_len; ++i) {
260 vec[i] = _list.events().front()->value;
261 }
262
263 veclen -= fill_len;
264 vec += fill_len;
265 }
266
267 if (veclen && x1 > max_x) {
268
269 /* fill some end section of the array with the default or final value */
270
271 double frac = (x1 - max_x) / (x1 - x0);
272 int64_t fill_len = (int64_t) floor (original_veclen * frac);
273 float val;
274
275 fill_len = min (fill_len, (int64_t)veclen);
276 val = _list.events().back()->value;
277
278 for (i = veclen - fill_len; i < veclen; ++i) {
279 vec[i] = val;
280 }
281
282 veclen -= fill_len;
283 }
284
285 lx = max (min_x, x0);
286 hx = min (max_x, x1);
287
288 if (npoints == 2) {
289
290 const double lpos = _list.events().front()->when;
291 const double lval = _list.events().front()->value;
292 const double upos = _list.events().back()->when;
293 const double uval = _list.events().back()->value;
294
295 /* dx that we are using */
296 if (veclen > 1) {
297 const double dx_num = hx - lx;
298 const double dx_den = veclen - 1;
299 const double lower = _list.descriptor().lower;
300 const double upper = _list.descriptor().upper;
301
302 /* gradient of the line */
303 const double m_num = uval - lval;
304 const double m_den = upos - lpos;
305 /* y intercept of the line */
306 const double c = uval - (m_num * upos / m_den);
307
308 switch (_list.interpolation()) {
309 case ControlList::Logarithmic:
310 for (int i = 0; i < veclen; ++i) {
311 const double fraction = (lx - lpos + i * dx_num / dx_den) / m_den;
312 vec[i] = interpolate_logarithmic (lval, uval, fraction, lower, upper);
313 }
314 break;
315 case ControlList::Exponential:
316 for (int i = 0; i < veclen; ++i) {
317 const double fraction = (lx - lpos + i * dx_num / dx_den) / m_den;
318 vec[i] = interpolate_gain (lval, uval, fraction, upper);
319 }
320 break;
321 case ControlList::Discrete:
322 // any discrete vector curves somewhere?
323 assert (0);
324 case ControlList::Curved:
325 /* no 2 point spline */
326 /* fallthrough */
327 default: // Linear:
328 for (int i = 0; i < veclen; ++i) {
329 vec[i] = (lx * (m_num / m_den) + m_num * i * dx_num / (m_den * dx_den)) + c;
330 }
331 break;
332 }
333 } else {
334 double fraction = (lx - lpos) / (upos - lpos);
335 switch (_list.interpolation()) {
336 case ControlList::Logarithmic:
337 vec[0] = interpolate_logarithmic (lval, uval, fraction, _list.descriptor().lower, _list.descriptor().upper);
338 break;
339 case ControlList::Exponential:
340 vec[0] = interpolate_gain (lval, uval, fraction, _list.descriptor().upper);
341 break;
342 case ControlList::Discrete:
343 // any discrete vector curves somewhere?
344 assert (0);
345 case ControlList::Curved:
346 /* no 2 point spline */
347 /* fallthrough */
348 default: // Linear:
349 vec[0] = interpolate_linear (lval, uval, fraction);
350 break;
351 }
352 }
353
354 return;
355 }
356
357 if (_dirty) {
358 solve ();
359 }
360
361 rx = lx;
362
363 double dx = 0;
364 if (veclen > 1) {
365 dx = (hx - lx) / (veclen - 1);
366 }
367
368 for (i = 0; i < veclen; ++i, rx += dx) {
369 vec[i] = multipoint_eval (rx);
370 }
371 }
372
373 double
multipoint_eval(double x) const374 Curve::multipoint_eval (double x) const
375 {
376 pair<ControlList::EventList::const_iterator,ControlList::EventList::const_iterator> range;
377
378 ControlList::LookupCache& lookup_cache = _list.lookup_cache();
379
380 if ((lookup_cache.left < 0) ||
381 ((lookup_cache.left > x) ||
382 (lookup_cache.range.first == _list.events().end()) ||
383 ((*lookup_cache.range.second)->when < x))) {
384
385 ControlEvent cp (x, 0.0);
386
387 lookup_cache.range = equal_range (_list.events().begin(), _list.events().end(), &cp, ControlList::time_comparator);
388 }
389
390 range = lookup_cache.range;
391
392 /* EITHER
393
394 a) x is an existing control point, so first == existing point, second == next point
395
396 OR
397
398 b) x is between control points, so range is empty (first == second, points to where
399 to insert x)
400
401 */
402
403 if (range.first == range.second) {
404
405 /* x does not exist within the list as a control point */
406
407 lookup_cache.left = x;
408
409 if (range.first == _list.events().begin()) {
410 /* we're before the first point */
411 // return default_value;
412 return _list.events().front()->value;
413 }
414
415 if (range.second == _list.events().end()) {
416 /* we're after the last point */
417 return _list.events().back()->value;
418 }
419
420 ControlEvent* after = (*range.second);
421 range.second--;
422 ControlEvent* before = (*range.second);
423
424 double vdelta = after->value - before->value;
425
426 if (vdelta == 0.0) {
427 return before->value;
428 }
429
430 double tdelta = x - before->when;
431 double trange = after->when - before->when;
432
433 switch (_list.interpolation()) {
434 case ControlList::Discrete:
435 return before->value;
436 case ControlList::Logarithmic:
437 return interpolate_logarithmic (before->value, after->value, tdelta / trange, _list.descriptor().lower, _list.descriptor().upper);
438 case ControlList::Exponential:
439 return interpolate_gain (before->value, after->value, tdelta / trange, _list.descriptor().upper);
440 case ControlList::Curved:
441 if (after->coeff) {
442 ControlEvent* ev = after;
443 double x2 = x * x;
444 return ev->coeff[0] + (ev->coeff[1] * x) + (ev->coeff[2] * x2) + (ev->coeff[3] * x2 * x);
445 }
446 /* fallthrough */
447 case ControlList::Linear:
448 return before->value + (vdelta * (tdelta / trange));
449 }
450 }
451
452 /* x is a control point in the data */
453 /* invalidate the cached range because its not usable */
454 lookup_cache.left = -1;
455 return (*range.first)->value;
456 }
457
458 } // namespace Evoral
459