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livetrax/libs/canvas/curve.cc

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/*
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 <cmath>
#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)
, points_per_segment (16)
, curve_type (CatmullRomCentripetal)
{
}
/** 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_points_per_segment (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
*/
points_per_segment = n;
interpolate ();
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 ()
{
samples.clear ();
interpolate (_points, points_per_segment, CatmullRomCentripetal, false, samples);
n_samples = samples.size();
}
/* Cartmull-Rom code from http://stackoverflow.com/questions/9489736/catmull-rom-curve-with-no-cusps-and-no-self-intersections/19283471#19283471
*
* Thanks to Ted for his Java version, which I translated into Ardour-idiomatic
* C++ here.
*/
/**
* Calculate the same values but introduces the ability to "parameterize" the t
* values used in the calculation. This is based on Figure 3 from
* http://www.cemyuksel.com/research/catmullrom_param/catmullrom.pdf
*
* @param p An array of double values of length 4, where interpolation
* occurs from p1 to p2.
* @param time An array of time measures of length 4, corresponding to each
* p value.
* @param t the actual interpolation ratio from 0 to 1 representing the
* position between p1 and p2 to interpolate the value.
*/
static double
__interpolate (double p[4], double time[4], double t)
{
const double L01 = p[0] * (time[1] - t) / (time[1] - time[0]) + p[1] * (t - time[0]) / (time[1] - time[0]);
const double L12 = p[1] * (time[2] - t) / (time[2] - time[1]) + p[2] * (t - time[1]) / (time[2] - time[1]);
const double L23 = p[2] * (time[3] - t) / (time[3] - time[2]) + p[3] * (t - time[2]) / (time[3] - time[2]);
const double L012 = L01 * (time[2] - t) / (time[2] - time[0]) + L12 * (t - time[0]) / (time[2] - time[0]);
const double L123 = L12 * (time[3] - t) / (time[3] - time[1]) + L23 * (t - time[1]) / (time[3] - time[1]);
const double C12 = L012 * (time[2] - t) / (time[2] - time[1]) + L123 * (t - time[1]) / (time[2] - time[1]);
return C12;
}
/**
* Given a list of control points, this will create a list of points_per_segment
* points spaced uniformly along the resulting Catmull-Rom curve.
*
* @param points The list of control points, leading and ending with a
* coordinate that is only used for controling the spline and is not visualized.
* @param index The index of control point p0, where p0, p1, p2, and p3 are
* used in order to create a curve between p1 and p2.
* @param points_per_segment The total number of uniformly spaced interpolated
* points to calculate for each segment. The larger this number, the
* smoother the resulting curve.
* @param curve_type Clarifies whether the curve should use uniform, chordal
* or centripetal curve types. Uniform can produce loops, chordal can
* produce large distortions from the original lines, and centripetal is an
* optimal balance without spaces.
* @return the list of coordinates that define the CatmullRom curve
* between the points defined by index+1 and index+2.
*/
static void
_interpolate (const Points& points, Points::size_type index, int points_per_segment, Curve::SplineType curve_type, Points& results)
{
double x[4];
double y[4];
double time[4];
for (int i = 0; i < 4; i++) {
x[i] = points[index + i].x;
y[i] = points[index + i].y;
time[i] = i;
}
double tstart = 1;
double tend = 2;
if (curve_type != Curve::CatmullRomUniform) {
double total = 0;
for (int i = 1; i < 4; i++) {
double dx = x[i] - x[i - 1];
double dy = y[i] - y[i - 1];
if (curve_type == Curve::CatmullRomCentripetal) {
total += pow (dx * dx + dy * dy, .25);
} else {
total += pow (dx * dx + dy * dy, .5);
}
time[i] = total;
}
tstart = time[1];
tend = time[2];
}
int segments = points_per_segment - 1;
results.push_back (points[index + 1]);
for (int i = 1; i < segments; i++) {
double xi = __interpolate (x, time, tstart + (i * (tend - tstart)) / segments);
double yi = __interpolate (y, time, tstart + (i * (tend - tstart)) / segments);
results.push_back (Duple (xi, yi));
}
results.push_back (points[index + 2]);
}
/**
* This method will calculate the Catmull-Rom interpolation curve, returning
* it as a list of Coord coordinate objects. This method in particular
* adds the first and last control points which are not visible, but required
* for calculating the spline.
*
* @param coordinates The list of original straight line points to calculate
* an interpolation from.
* @param points_per_segment The integer number of equally spaced points to
* return along each curve. The actual distance between each
* point will depend on the spacing between the control points.
* @return The list of interpolated coordinates.
* @param curve_type Chordal (stiff), Uniform(floppy), or Centripetal(medium)
* @throws gov.ca.water.shapelite.analysis.CatmullRomException if
* points_per_segment is less than 2.
*/
void
Curve::interpolate (const Points& coordinates, uint32_t points_per_segment, SplineType curve_type, bool closed, Points& results)
{
if (points_per_segment < 2) {
return;
}
// Cannot interpolate curves given only two points. Two points
// is best represented as a simple line segment.
if (coordinates.size() < 3) {
results = coordinates;
return;
}
// Copy the incoming coordinates. We need to modify it during interpolation
Points vertices = coordinates;
// Test whether the shape is open or closed by checking to see if
// the first point intersects with the last point. M and Z are ignored.
if (closed) {
// Use the second and second from last points as control points.
// get the second point.
Duple p2 = vertices[1];
// get the point before the last point
Duple pn1 = vertices[vertices.size() - 2];
// insert the second from the last point as the first point in the list
// because when the shape is closed it keeps wrapping around to
// the second point.
vertices.insert(vertices.begin(), pn1);
// add the second point to the end.
vertices.push_back(p2);
} else {
// The shape is open, so use control points that simply extend
// the first and last segments
// Get the change in x and y between the first and second coordinates.
double dx = vertices[1].x - vertices[0].x;
double dy = vertices[1].y - vertices[0].y;
// Then using the change, extrapolate backwards to find a control point.
double x1 = vertices[0].x - dx;
double y1 = vertices[0].y - dy;
// Actaully create the start point from the extrapolated values.
Duple start (x1, y1);
// Repeat for the end control point.
int n = vertices.size() - 1;
dx = vertices[n].x - vertices[n - 1].x;
dy = vertices[n].y - vertices[n - 1].y;
double xn = vertices[n].x + dx;
double yn = vertices[n].y + dy;
Duple end (xn, yn);
// insert the start control point at the start of the vertices list.
vertices.insert (vertices.begin(), start);
// append the end control ponit to the end of the vertices list.
vertices.push_back (end);
}
// When looping, remember that each cycle requires 4 points, starting
// with i and ending with i+3. So we don't loop through all the points.
for (Points::size_type i = 0; i < vertices.size() - 3; i++) {
// Actually calculate the Catmull-Rom curve for one segment.
Points r;
_interpolate (vertices, i, points_per_segment, curve_type, r);
// Since the middle points are added twice, once for each bordering
// segment, we only add the 0 index result point for the first
// segment. Otherwise we will have duplicate points.
if (results.size() > 0) {
r.erase (r.begin());
}
// Add the coordinates for the segment to the result list.
results.insert (results.end(), r.begin(), r.end());
}
}
/** Given a fractional 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 || !_bounding_box) {
return;
}
Rect self = item_to_window (_bounding_box.get());
boost::optional<Rect> d = self.intersection (area);
assert (d);
Rect draw = d.get ();
/* 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.
*/
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);
context->stroke ();
} else {
/* curve of at least 3 points */
/* x-axis limits of the curve, in window space coordinates */
Duple w1 = item_to_window (Duple (_points.front().x, 0.0));
Duple w2 = item_to_window (Duple (_points.back().x, 0.0));
/* clamp actual draw to area bound by points, rather than our bounding box which is slightly different */
context->save ();
context->rectangle (draw.x0, draw.y0, draw.width(), draw.height());
context->clip ();
/* expand drawing area by several pixels on each side to avoid cairo stroking effects at the boundary.
they will still occur, but cairo's clipping will hide them.
*/
draw = draw.expand (4.0);
/* now clip it to the actual points in the curve */
if (draw.x0 < w1.x) {
draw.x0 = w1.x;
}
if (draw.x1 >= w2.x) {
draw.x1 = w2.x;
}
/* full width of the curve */
const double xextent = _points.back().x - _points.front().x;
/* Determine where the first drawn point will be */
Duple item_space = window_to_item (Duple (draw.x0, 0)); /* y value is irrelevant */
/* determine the fractional offset of this location into the overall extent of the curve */
const double xfract_offset = (item_space.x - _points.front().x)/xextent;
const uint32_t pixels = draw.width ();
Duple window_space;
/* draw the first point */
for (uint32_t pixel = 0; pixel < pixels; ++pixel) {
/* fractional distance into the total horizontal extent of the curve */
double xfract = xfract_offset + (pixel / xextent);
/* compute vertical coordinate (item-space) at that location */
double y = map_value (xfract);
/* convert to window space for drawing */
window_space = item_to_window (Duple (0.0, y)); /* x-value is irrelevant */
/* we are moving across the draw area pixel-by-pixel */
window_space.x = draw.x0 + pixel;
/* plot this point */
if (pixel == 0) {
context->move_to (window_space.x, window_space.y);
} else {
context->line_to (window_space.x, window_space.y);
}
}
context->stroke ();
context->restore ();
}
#if 0
/* 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 ();
}
#endif
}
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;
}