2 Copyright (C) 2001-2003 Paul Davis
4 Contains ideas derived from "Constrained Cubic Spline Interpolation"
5 by CJC Kruger (www.korf.co.uk/spline.pdf).
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.
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.
17 You should have received a copy of the GNU General Public License
18 along with this program; if not, write to the Free Software
19 Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
30 #include <glibmm/thread.h>
31 #include <sigc++/bind.h>
33 #include "ardour/curve.h"
38 using namespace ARDOUR;
42 Curve::Curve (double minv, double maxv, double canv, bool nostate)
43 : AutomationList (canv)
49 Curve::Curve (const Curve& other)
50 : AutomationList (other)
52 min_yval = other.min_yval;
53 max_yval = other.max_yval;
56 Curve::Curve (const Curve& other, double start, double end)
57 : AutomationList (other, start, end)
59 min_yval = other.min_yval;
60 max_yval = other.max_yval;
63 Curve::Curve (const XMLNode& node)
64 : AutomationList (node)
73 Curve::operator= (const Curve& other)
76 *((AutomationList*)this) = other;
77 min_yval = other.min_yval;
78 max_yval = other.max_yval;
92 if ((npoints = events.size()) > 2) {
94 /* Compute coefficients needed to efficiently compute a constrained spline
95 curve. See "Constrained Cubic Spline Interpolation" by CJC Kruger
96 (www.korf.co.uk/spline.pdf) for more details.
102 AutomationEventList::iterator xx;
104 for (i = 0, xx = events.begin(); xx != events.end(); ++xx, ++i) {
105 x[i] = (double) (*xx)->when;
106 y[i] = (double) (*xx)->value;
109 double lp0, lp1, fpone;
111 lp0 =(x[1] - x[0])/(y[1] - y[0]);
112 lp1 = (x[2] - x[1])/(y[2] - y[1]);
117 fpone = 2 / (lp1 + lp0);
122 for (i = 0, xx = events.begin(); xx != events.end(); ++xx, ++i) {
124 CurvePoint* cp = dynamic_cast<CurvePoint*>(*xx);
127 fatal << _("programming error: ")
128 << X_("non-CurvePoint event found in event list for a Curve")
133 double xdelta; /* gcc is wrong about possible uninitialized use */
134 double xdelta2; /* ditto */
135 double ydelta; /* ditto */
140 xdelta = x[i] - x[i-1];
141 xdelta2 = xdelta * xdelta;
142 ydelta = y[i] - y[i-1];
145 /* compute (constrained) first derivatives */
151 fplast = ((3 * (y[1] - y[0]) / (2 * (x[1] - x[0]))) - (fpone * 0.5));
153 /* we don't store coefficients for i = 0 */
157 } else if (i == npoints - 1) {
161 fpi = ((3 * ydelta) / (2 * xdelta)) - (fplast * 0.5);
165 /* all other segments */
167 double slope_before = ((x[i+1] - x[i]) / (y[i+1] - y[i]));
168 double slope_after = (xdelta / ydelta);
170 if (slope_after * slope_before < 0.0) {
171 /* slope changed sign */
174 fpi = 2 / (slope_before + slope_after);
179 /* compute second derivative for either side of control point `i' */
181 fppL = (((-2 * (fpi + (2 * fplast))) / (xdelta))) +
182 ((6 * ydelta) / xdelta2);
184 fppR = (2 * ((2 * fpi) + fplast) / xdelta) -
185 ((6 * ydelta) / xdelta2);
187 /* compute polynomial coefficients */
191 d = (fppR - fppL) / (6 * xdelta);
192 c = ((x[i] * fppL) - (x[i-1] * fppR))/(2 * xdelta);
197 xim12 = x[i-1] * x[i-1]; /* "x[i-1] squared" */
198 xim13 = xim12 * x[i-1]; /* "x[i-1] cubed" */
199 xi2 = x[i] * x[i]; /* "x[i] squared" */
200 xi3 = xi2 * x[i]; /* "x[i] cubed" */
202 b = (ydelta - (c * (xi2 - xim12)) - (d * (xi3 - xim13))) / xdelta;
206 cp->coeff[0] = y[i-1] - (b * x[i-1]) - (c * xim12) - (d * xim13);
220 Curve::rt_safe_get_vector (double x0, double x1, float *vec, int64_t veclen)
222 Glib::Mutex::Lock lm (lock, Glib::TRY_LOCK);
227 _get_vector (x0, x1, vec, veclen);
233 Curve::get_vector (double x0, double x1, float *vec, int64_t veclen)
235 Glib::Mutex::Lock lm (lock);
236 _get_vector (x0, x1, vec, veclen);
240 Curve::_get_vector (double x0, double x1, float *vec, int64_t veclen)
242 double rx, dx, lx, hx, max_x, min_x;
244 int64_t original_veclen;
247 if ((npoints = events.size()) == 0) {
248 for (i = 0; i < veclen; ++i) {
249 vec[i] = default_value;
254 /* events is now known not to be empty */
256 max_x = events.back()->when;
257 min_x = events.front()->when;
259 lx = max (min_x, x0);
262 x1 = events.back()->when;
265 hx = min (max_x, x1);
267 original_veclen = veclen;
271 /* fill some beginning section of the array with the
272 initial (used to be default) value
275 double frac = (min_x - x0) / (x1 - x0);
276 int64_t subveclen = (int64_t) floor (veclen * frac);
278 subveclen = min (subveclen, veclen);
280 for (i = 0; i < subveclen; ++i) {
281 vec[i] = events.front()->value;
288 if (veclen && x1 > max_x) {
290 /* fill some end section of the array with the default or final value */
292 double frac = (x1 - max_x) / (x1 - x0);
294 int64_t subveclen = (int64_t) floor (original_veclen * frac);
298 subveclen = min (subveclen, veclen);
300 val = events.back()->value;
302 i = veclen - subveclen;
304 for (i = veclen - subveclen; i < veclen; ++i) {
317 for (i = 0; i < veclen; ++i) {
318 vec[i] = events.front()->value;
326 /* linear interpolation between 2 points */
328 /* XXX I'm not sure that this is the right thing to
329 do here. but its not a common case for the envisaged
334 dx = (hx - lx) / (veclen - 1) ;
339 double slope = (events.back()->value - events.front()->value)/
340 (events.back()->when - events.front()->when);
341 double yfrac = dx*slope;
343 vec[0] = events.front()->value + slope * (lx - events.front()->when);
345 for (i = 1; i < veclen; ++i) {
346 vec[i] = vec[i-1] + yfrac;
360 /* note: if there are veclen elements in the output,
361 there are only veclen-1 steps between them.
364 dx = (hx - lx) / (veclen-1);
366 for (i = 0; i < veclen; ++i, rx += dx) {
367 vec[i] = multipoint_eval (rx);
373 Curve::unlocked_eval (double x)
379 return shared_eval (x);
383 Curve::multipoint_eval (double x)
385 pair<AutomationEventList::iterator,AutomationEventList::iterator> range;
387 if ((lookup_cache.left < 0) ||
388 ((lookup_cache.left > x) ||
389 (lookup_cache.range.first == events.end()) ||
390 ((*lookup_cache.range.second)->when < x))) {
393 ControlEvent cp (x, 0.0);
395 lookup_cache.range = equal_range (events.begin(), events.end(), &cp, cmp);
398 range = lookup_cache.range;
402 a) x is an existing control point, so first == existing point, second == next point
406 b) x is between control points, so range is empty (first == second, points to where
411 if (range.first == range.second) {
413 /* x does not exist within the list as a control point */
415 lookup_cache.left = x;
417 if (range.first == events.begin()) {
418 /* we're before the first point */
419 // return default_value;
420 events.front()->value;
423 if (range.second == events.end()) {
424 /* we're after the last point */
425 return events.back()->value;
429 CurvePoint* cp = dynamic_cast<CurvePoint*> (*range.second);
431 return cp->coeff[0] + (cp->coeff[1] * x) + (cp->coeff[2] * x2) + (cp->coeff[3] * x2 * x);
434 /* x is a control point in the data */
435 /* invalidate the cached range because its not usable */
436 lookup_cache.left = -1;
437 return (*range.first)->value;
441 Curve::point_factory (double when, double val) const
443 return new CurvePoint (when, val);
447 Curve::point_factory (const ControlEvent& other) const
449 return new CurvePoint (other.when, other.value);
455 curve_get_vector_from_c (void *arg, double x0, double x1, float* vec, int64_t vecsize)
457 static_cast<Curve*>(arg)->get_vector (x0, x1, vec, vecsize);