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livetrax/libs/canvas/curve.cc

424 lines
9.8 KiB
C++

/*
Copyright (C) 2013 Paul Davis
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., 675 Mass Ave, Cambridge, MA 02139, USA.
*/
#include <exception>
#include <algorithm>
#include "canvas/curve.h"
using namespace ArdourCanvas;
using std::min;
using std::max;
Curve::Curve (Group* parent)
: Item (parent)
, PolyItem (parent)
, Fill (parent)
, n_samples (0)
, n_segments (512)
{
set_n_samples (256);
}
/** Set the number of points to compute when we smooth the data points into a
* curve.
*/
void
Curve::set_n_samples (Points::size_type n)
{
/* this only changes our appearance rather than the bounding box, so we
just need to schedule a redraw rather than notify the parent of any
changes
*/
n_samples = n;
samples.assign (n_samples, Duple (0.0, 0.0));
interpolate ();
}
/** When rendering the curve, we will always draw a fixed number of straight
* line segments to span the x-axis extent of the curve. More segments:
* smoother visual rendering. Less rendering: closer to a visibily poly-line
* render.
*/
void
Curve::set_n_segments (uint32_t n)
{
/* this only changes our appearance rather than the bounding box, so we
just need to schedule a redraw rather than notify the parent of any
changes
*/
n_segments = n;
redraw ();
}
void
Curve::compute_bounding_box () const
{
PolyItem::compute_bounding_box ();
/* possibly add extents of any point indicators here if we ever do that */
}
void
Curve::set (Points const& p)
{
PolyItem::set (p);
interpolate ();
}
void
Curve::interpolate ()
{
Points::size_type npoints = _points.size ();
if (npoints < 3) {
return;
}
Duple p;
double boundary;
const double xfront = _points.front().x;
const double xextent = _points.back().x - xfront;
/* initialize boundary curve points */
p = _points.front();
boundary = round (((p.x - xfront)/xextent) * (n_samples - 1));
for (Points::size_type i = 0; i < boundary; ++i) {
samples[i] = Duple (i, p.y);
}
p = _points.back();
boundary = round (((p.x - xfront)/xextent) * (n_samples - 1));
for (Points::size_type i = boundary; i < n_samples; ++i) {
samples[i] = Duple (i, p.y);
}
for (int i = 0; i < (int) npoints - 1; ++i) {
Points::size_type p1, p2, p3, p4;
p1 = max (i - 1, 0);
p2 = i;
p3 = i + 1;
p4 = min (i + 2, (int) npoints - 1);
smooth (p1, p2, p3, p4, xfront, xextent);
}
/* make sure that actual data points are used with their exact values */
for (Points::const_iterator p = _points.begin(); p != _points.end(); ++p) {
uint32_t idx = (((*p).x - xfront)/xextent) * (n_samples - 1);
samples[idx].y = (*p).y;
}
}
/*
* This function calculates the curve values between the control points
* p2 and p3, taking the potentially existing neighbors p1 and p4 into
* account.
*
* This function uses a cubic bezier curve for the individual segments and
* calculates the necessary intermediate control points depending on the
* neighbor curve control points.
*
*/
void
Curve::smooth (Points::size_type p1, Points::size_type p2, Points::size_type p3, Points::size_type p4,
double xfront, double xextent)
{
int i;
double x0, x3;
double y0, y1, y2, y3;
double dx, dy;
double slope;
/* the outer control points for the bezier curve. */
x0 = _points[p2].x;
y0 = _points[p2].y;
x3 = _points[p3].x;
y3 = _points[p3].y;
/*
* the x values of the inner control points are fixed at
* x1 = 2/3*x0 + 1/3*x3 and x2 = 1/3*x0 + 2/3*x3
* this ensures that the x values increase linearily with the
* parameter t and enables us to skip the calculation of the x
* values altogehter - just calculate y(t) evenly spaced.
*/
dx = x3 - x0;
dy = y3 - y0;
if (dx <= 0) {
/* error? */
return;
}
if (p1 == p2 && p3 == p4) {
/* No information about the neighbors,
* calculate y1 and y2 to get a straight line
*/
y1 = y0 + dy / 3.0;
y2 = y0 + dy * 2.0 / 3.0;
} else if (p1 == p2 && p3 != p4) {
/* only the right neighbor is available. Make the tangent at the
* right endpoint parallel to the line between the left endpoint
* and the right neighbor. Then point the tangent at the left towards
* the control handle of the right tangent, to ensure that the curve
* does not have an inflection point.
*/
slope = (_points[p4].y - y0) / (_points[p4].x - x0);
y2 = y3 - slope * dx / 3.0;
y1 = y0 + (y2 - y0) / 2.0;
} else if (p1 != p2 && p3 == p4) {
/* see previous case */
slope = (y3 - _points[p1].y) / (x3 - _points[p1].x);
y1 = y0 + slope * dx / 3.0;
y2 = y3 + (y1 - y3) / 2.0;
} else /* (p1 != p2 && p3 != p4) */ {
/* Both neighbors are available. Make the tangents at the endpoints
* parallel to the line between the opposite endpoint and the adjacent
* neighbor.
*/
slope = (y3 - _points[p1].y) / (x3 - _points[p1].x);
y1 = y0 + slope * dx / 3.0;
slope = (_points[p4].y - y0) / (_points[p4].x - x0);
y2 = y3 - slope * dx / 3.0;
}
/*
* finally calculate the y(t) values for the given bezier values. We can
* use homogenously distributed values for t, since x(t) increases linearily.
*/
dx = dx / xextent;
int limit = round (dx * (n_samples - 1));
const int idx_offset = round (((x0 - xfront)/xextent) * (n_samples - 1));
for (i = 0; i <= limit; i++) {
double y, t;
Points::size_type index;
t = i / dx / (n_samples - 1);
y = y0 * (1-t) * (1-t) * (1-t) +
3 * y1 * (1-t) * (1-t) * t +
3 * y2 * (1-t) * t * t +
y3 * t * t * t;
index = i + idx_offset;
if (index < n_samples) {
Duple d (i, max (y, 0.0));
samples[index] = d;
}
}
}
/** Given a position within the x-axis range of the
* curve, return the corresponding y-axis value
*/
double
Curve::map_value (double x) const
{
if (x > 0.0 && x < 1.0) {
double f;
Points::size_type index;
/* linearly interpolate between two of our smoothed "samples"
*/
x = x * (n_samples - 1);
index = (Points::size_type) x; // XXX: should we explicitly use floor()?
f = x - index;
return (1.0 - f) * samples[index].y + f * samples[index+1].y;
} else if (x >= 1.0) {
return samples.back().y;
} else {
return samples.front().y;
}
}
void
Curve::render (Rect const & area, Cairo::RefPtr<Cairo::Context> context) const
{
if (!_outline || _points.size() < 2) {
return;
}
/* Our approach is to always draw n_segments across our total size.
*
* This is very inefficient if we are asked to only draw a small
* section of the curve. For now we rely on cairo clipping to help
* with this.
*/
double x;
double y;
context->save ();
context->rectangle (area.x0, area.y0, area.width(),area.height());
context->clip ();
setup_outline_context (context);
if (_points.size() == 2) {
/* straight line */
Duple window_space;
window_space = item_to_window (_points.front());
context->move_to (window_space.x, window_space.y);
window_space = item_to_window (_points.back());
context->line_to (window_space.x, window_space.y);
} else {
/* curve of at least 3 points */
const double xfront = _points.front().x;
const double xextent = _points.back().x - xfront;
/* move through points to find the first one inside the
* rendering area
*/
Points::const_iterator edge = _points.end();
bool edge_found = false;
for (Points::const_iterator p = _points.begin(); p != _points.end(); ++p) {
Duple w (item_to_window (Duple ((*p).x, 0.0)));
if (w.x >= area.x0) {
edge_found = true;
break;
}
edge = p;
}
if (edge == _points.end()) {
if (edge_found) {
edge = _points.begin();
} else {
return;
}
}
std::cerr << "Start drawing " << distance (_points.begin(), edge) << " into points\n";
x = (*edge).x;
y = map_value (0.0);
Duple window_space = item_to_window (Duple (x, y));
context->move_to (window_space.x, window_space.y);
/* if the extent of this curve (in pixels) is small, then we don't need
* many segments.
*/
uint32_t nsegs = area.width();
double last_x = 0;
double xoffset = (x-xfront)/xextent;
// std::cerr << " draw " << nsegs << " segments\n";
for (uint32_t n = 1; n < nsegs; ++n) {
/* compute item space x coordinate of the start of this segment */
x = xoffset + (n / (double) nsegs);
y = map_value (x);
x += xfront + (xextent * x);
// std::cerr << "hspan @ " << x << ' ' << x - last_x << std::endl;
last_x = x;
window_space = item_to_window (Duple (x, y));
context->line_to (window_space.x, window_space.y);
if (window_space.x > area.x1) {
/* we're done - the last point was outside the redraw area along the x-axis */
break;
}
}
}
context->stroke ();
/* add points */
setup_fill_context (context);
for (Points::const_iterator p = _points.begin(); p != _points.end(); ++p) {
Duple window_space (item_to_window (*p));
context->arc (window_space.x, window_space.y, 5.0, 0.0, 2 * M_PI);
context->stroke ();
}
context->restore ();
}
bool
Curve::covers (Duple const & pc) const
{
Duple point = canvas_to_item (pc);
/* O(N) N = number of points, and not accurate */
for (Points::const_iterator p = _points.begin(); p != _points.end(); ++p) {
const Coord dx = point.x - (*p).x;
const Coord dy = point.y - (*p).y;
const Coord dx2 = dx * dx;
const Coord dy2 = dy * dy;
if ((dx2 < 2.0 && dy2 < 2.0) || (dx2 + dy2 < 4.0)) {
return true;
}
}
return false;
}