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livetrax/libs/evoral/src/Curve.cpp

429 lines
9.6 KiB
C++

/* This file is part of Evoral.
* Copyright (C) 2008 David Robillard <http://drobilla.net>
* Copyright (C) 2000-2008 Paul Davis
*
* Evoral 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.
*
* Evoral 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 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 St, 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 "evoral/Curve.hpp"
#include "evoral/ControlList.hpp"
using namespace std;
using namespace sigc;
namespace Evoral {
Curve::Curve (const ControlList& cl)
: _dirty (true)
, _list (cl)
{
}
void
Curve::solve ()
{
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)
{
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)
{
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)
{
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.default_value();
}
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) {
/* linear interpolation between 2 points */
/* XXX: this numerator / denominator stuff is pretty grim, but it's the only
way I could get the maths to be accurate; doing everything with pure doubles
gives ~1e-17 errors in the vec[i] computation.
*/
/* gradient of the line */
double const m_num = _list.events().back()->value - _list.events().front()->value;
double const m_den = _list.events().back()->when - _list.events().front()->when;
/* y intercept of the line */
double const c = double (_list.events().back()->value) - (m_num * _list.events().back()->when / m_den);
/* dx that we are using */
double dx_num = 0;
double dx_den = 1;
if (veclen > 1) {
dx_num = hx - lx;
dx_den = veclen - 1;
for (int i = 0; i < veclen; ++i) {
vec[i] = (lx * (m_num / m_den) + m_num * i * dx_num / (m_den * dx_den)) + c;
}
} else {
vec[0] = lx * (m_num / m_den) + c;
}
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::unlocked_eval (double x)
{
// I don't see the point of this...
if (_dirty) {
solve ();
}
return _list.unlocked_eval (x);
}
double
Curve::multipoint_eval (double x)
{
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;
if (_list.interpolation() == ControlList::Curved && 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);
} else {
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
extern "C" {
void
curve_get_vector_from_c (void *arg, double x0, double x1, float* vec, int32_t vecsize)
{
static_cast<Evoral::Curve*>(arg)->get_vector (x0, x1, vec, vecsize);
}
}