Robin Gareus
c03b658531
use cairo for anti-aliasing, and ignore explicit Catmull-Rom points for that fall on the same x-cordinate.
454 lines
15 KiB
C++
454 lines
15 KiB
C++
/*
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Copyright (C) 2013 Paul Davis
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program; if not, write to the Free Software
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Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
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*/
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#include <cmath>
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#include <exception>
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#include <algorithm>
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#include "canvas/curve.h"
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using namespace ArdourCanvas;
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using std::min;
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using std::max;
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Curve::Curve (Group* parent)
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: Item (parent)
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, PolyItem (parent)
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, Fill (parent)
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, n_samples (0)
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, points_per_segment (16)
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, curve_type (CatmullRomCentripetal)
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, curve_fill (None)
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{
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}
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/** When rendering the curve, we will always draw a fixed number of straight
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* line segments to span the x-axis extent of the curve. More segments:
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* smoother visual rendering. Less rendering: closer to a visibily poly-line
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* render.
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*/
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void
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Curve::set_points_per_segment (uint32_t n)
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{
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/* this only changes our appearance rather than the bounding box, so we
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just need to schedule a redraw rather than notify the parent of any
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changes
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*/
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points_per_segment = n;
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interpolate ();
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redraw ();
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}
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void
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Curve::compute_bounding_box () const
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{
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PolyItem::compute_bounding_box ();
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/* possibly add extents of any point indicators here if we ever do that */
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}
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void
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Curve::set (Points const& p)
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{
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PolyItem::set (p);
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interpolate ();
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}
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void
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Curve::interpolate ()
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{
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samples.clear ();
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interpolate (_points, points_per_segment, CatmullRomCentripetal, false, samples);
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n_samples = samples.size();
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}
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/* Cartmull-Rom code from http://stackoverflow.com/questions/9489736/catmull-rom-curve-with-no-cusps-and-no-self-intersections/19283471#19283471
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*
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* Thanks to Ted for his Java version, which I translated into Ardour-idiomatic
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* C++ here.
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*/
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/**
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* Calculate the same values but introduces the ability to "parameterize" the t
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* values used in the calculation. This is based on Figure 3 from
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* http://www.cemyuksel.com/research/catmullrom_param/catmullrom.pdf
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*
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* @param p An array of double values of length 4, where interpolation
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* occurs from p1 to p2.
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* @param time An array of time measures of length 4, corresponding to each
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* p value.
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* @param t the actual interpolation ratio from 0 to 1 representing the
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* position between p1 and p2 to interpolate the value.
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*/
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static double
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__interpolate (double p[4], double time[4], double t)
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{
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const double L01 = p[0] * (time[1] - t) / (time[1] - time[0]) + p[1] * (t - time[0]) / (time[1] - time[0]);
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const double L12 = p[1] * (time[2] - t) / (time[2] - time[1]) + p[2] * (t - time[1]) / (time[2] - time[1]);
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const double L23 = p[2] * (time[3] - t) / (time[3] - time[2]) + p[3] * (t - time[2]) / (time[3] - time[2]);
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const double L012 = L01 * (time[2] - t) / (time[2] - time[0]) + L12 * (t - time[0]) / (time[2] - time[0]);
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const double L123 = L12 * (time[3] - t) / (time[3] - time[1]) + L23 * (t - time[1]) / (time[3] - time[1]);
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const double C12 = L012 * (time[2] - t) / (time[2] - time[1]) + L123 * (t - time[1]) / (time[2] - time[1]);
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return C12;
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}
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/**
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* Given a list of control points, this will create a list of points_per_segment
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* points spaced uniformly along the resulting Catmull-Rom curve.
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*
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* @param points The list of control points, leading and ending with a
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* coordinate that is only used for controling the spline and is not visualized.
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* @param index The index of control point p0, where p0, p1, p2, and p3 are
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* used in order to create a curve between p1 and p2.
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* @param points_per_segment The total number of uniformly spaced interpolated
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* points to calculate for each segment. The larger this number, the
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* smoother the resulting curve.
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* @param curve_type Clarifies whether the curve should use uniform, chordal
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* or centripetal curve types. Uniform can produce loops, chordal can
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* produce large distortions from the original lines, and centripetal is an
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* optimal balance without spaces.
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* @return the list of coordinates that define the CatmullRom curve
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* between the points defined by index+1 and index+2.
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*/
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static void
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_interpolate (const Points& points, Points::size_type index, int points_per_segment, Curve::SplineType curve_type, Points& results)
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{
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double x[4];
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double y[4];
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double time[4];
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for (int i = 0; i < 4; i++) {
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x[i] = points[index + i].x;
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y[i] = points[index + i].y;
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time[i] = i;
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}
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double tstart = 1;
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double tend = 2;
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if (curve_type != Curve::CatmullRomUniform) {
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double total = 0;
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for (int i = 1; i < 4; i++) {
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double dx = x[i] - x[i - 1];
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double dy = y[i] - y[i - 1];
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if (curve_type == Curve::CatmullRomCentripetal) {
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total += pow (dx * dx + dy * dy, .25);
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} else {
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total += pow (dx * dx + dy * dy, .5);
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}
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time[i] = total;
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}
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tstart = time[1];
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tend = time[2];
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}
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int segments = points_per_segment - 1;
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results.push_back (points[index + 1]);
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for (int i = 1; i < segments; i++) {
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double xi = __interpolate (x, time, tstart + (i * (tend - tstart)) / segments);
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double yi = __interpolate (y, time, tstart + (i * (tend - tstart)) / segments);
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results.push_back (Duple (xi, yi));
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}
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results.push_back (points[index + 2]);
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}
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/**
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* This method will calculate the Catmull-Rom interpolation curve, returning
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* it as a list of Coord coordinate objects. This method in particular
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* adds the first and last control points which are not visible, but required
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* for calculating the spline.
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*
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* @param coordinates The list of original straight line points to calculate
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* an interpolation from.
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* @param points_per_segment The integer number of equally spaced points to
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* return along each curve. The actual distance between each
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* point will depend on the spacing between the control points.
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* @return The list of interpolated coordinates.
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* @param curve_type Chordal (stiff), Uniform(floppy), or Centripetal(medium)
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* @throws gov.ca.water.shapelite.analysis.CatmullRomException if
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* points_per_segment is less than 2.
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*/
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void
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Curve::interpolate (const Points& coordinates, uint32_t points_per_segment, SplineType curve_type, bool closed, Points& results)
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{
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if (points_per_segment < 2) {
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return;
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}
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// Cannot interpolate curves given only two points. Two points
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// is best represented as a simple line segment.
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if (coordinates.size() < 3) {
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results = coordinates;
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return;
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}
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// Copy the incoming coordinates. We need to modify it during interpolation
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Points vertices = coordinates;
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// Test whether the shape is open or closed by checking to see if
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// the first point intersects with the last point. M and Z are ignored.
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if (closed) {
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// Use the second and second from last points as control points.
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// get the second point.
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Duple p2 = vertices[1];
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// get the point before the last point
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Duple pn1 = vertices[vertices.size() - 2];
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// insert the second from the last point as the first point in the list
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// because when the shape is closed it keeps wrapping around to
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// the second point.
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vertices.insert(vertices.begin(), pn1);
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// add the second point to the end.
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vertices.push_back(p2);
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} else {
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// The shape is open, so use control points that simply extend
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// the first and last segments
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// Get the change in x and y between the first and second coordinates.
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double dx = vertices[1].x - vertices[0].x;
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double dy = vertices[1].y - vertices[0].y;
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// Then using the change, extrapolate backwards to find a control point.
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double x1 = vertices[0].x - dx;
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double y1 = vertices[0].y - dy;
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// Actaully create the start point from the extrapolated values.
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Duple start (x1, y1);
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// Repeat for the end control point.
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int n = vertices.size() - 1;
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dx = vertices[n].x - vertices[n - 1].x;
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dy = vertices[n].y - vertices[n - 1].y;
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double xn = vertices[n].x + dx;
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double yn = vertices[n].y + dy;
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Duple end (xn, yn);
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// insert the start control point at the start of the vertices list.
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vertices.insert (vertices.begin(), start);
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// append the end control ponit to the end of the vertices list.
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vertices.push_back (end);
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}
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// When looping, remember that each cycle requires 4 points, starting
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// with i and ending with i+3. So we don't loop through all the points.
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for (Points::size_type i = 0; i < vertices.size() - 3; i++) {
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// Actually calculate the Catmull-Rom curve for one segment.
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Points r;
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_interpolate (vertices, i, points_per_segment, curve_type, r);
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// Since the middle points are added twice, once for each bordering
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// segment, we only add the 0 index result point for the first
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// segment. Otherwise we will have duplicate points.
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if (results.size() > 0) {
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r.erase (r.begin());
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}
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// Add the coordinates for the segment to the result list.
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results.insert (results.end(), r.begin(), r.end());
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}
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}
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void
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Curve::render (Rect const & area, Cairo::RefPtr<Cairo::Context> context) const
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{
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if (!_outline || _points.size() < 2 || !_bounding_box) {
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return;
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}
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Rect self = item_to_window (_bounding_box.get());
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boost::optional<Rect> d = self.intersection (area);
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assert (d);
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Rect draw = d.get ();
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/* Our approach is to always draw n_segments across our total size.
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*
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* This is very inefficient if we are asked to only draw a small
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* section of the curve. For now we rely on cairo clipping to help
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* with this.
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*/
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setup_outline_context (context);
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if (_points.size() == 2) {
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/* straight line */
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Duple window_space;
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window_space = item_to_window (_points.front());
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context->move_to (window_space.x, window_space.y);
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window_space = item_to_window (_points.back());
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context->line_to (window_space.x, window_space.y);
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switch (curve_fill) {
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case None:
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context->stroke();
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break;
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case Inside:
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context->stroke_preserve ();
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window_space = item_to_window (Duple(_points.back().x, draw.height()));
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context->line_to (window_space.x, window_space.y);
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window_space = item_to_window (Duple(_points.front().x, draw.height()));
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context->line_to (window_space.x, window_space.y);
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context->close_path();
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setup_fill_context(context);
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context->fill ();
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break;
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case Outside:
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context->stroke_preserve ();
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window_space = item_to_window (Duple(_points.back().x, 0.0));
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context->line_to (window_space.x, window_space.y);
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window_space = item_to_window (Duple(_points.front().x, 0.0));
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context->line_to (window_space.x, window_space.y);
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context->close_path();
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setup_fill_context(context);
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context->fill ();
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break;
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}
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} else {
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/* curve of at least 3 points */
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/* x-axis limits of the curve, in window space coordinates */
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Duple w1 = item_to_window (Duple (_points.front().x, 0.0));
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Duple w2 = item_to_window (Duple (_points.back().x, 0.0));
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/* clamp actual draw to area bound by points, rather than our bounding box which is slightly different */
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context->save ();
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context->rectangle (draw.x0, draw.y0, draw.width(), draw.height());
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context->clip ();
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/* expand drawing area by several pixels on each side to avoid cairo stroking effects at the boundary.
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they will still occur, but cairo's clipping will hide them.
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*/
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draw = draw.expand (4.0);
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/* now clip it to the actual points in the curve */
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if (draw.x0 < w1.x) {
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draw.x0 = w1.x;
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}
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if (draw.x1 >= w2.x) {
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draw.x1 = w2.x;
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}
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/* find left and right-most sample */
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Duple window_space;
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Points::size_type left = 0;
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Points::size_type right = n_samples;
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for (Points::size_type idx = 0; idx < n_samples - 1; ++idx) {
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left = idx;
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window_space = item_to_window (Duple (samples[idx].x, 0.0));
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if (window_space.x >= draw.x0) break;
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}
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for (Points::size_type idx = n_samples; idx > left + 1; --idx) {
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window_space = item_to_window (Duple (samples[idx].x, 0.0));
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if (window_space.x <= draw.x1) break;
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right = idx;
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}
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/* draw line between samples */
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window_space = item_to_window (Duple (samples[left].x, samples[left].y));
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context->move_to (window_space.x, window_space.y);
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Coord last_x = round(window_space.x);
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for (uint32_t idx = left + 1; idx < right; ++idx) {
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window_space = item_to_window (Duple (samples[idx].x, samples[idx].y));
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if (last_x == round(window_space.x)) continue;
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last_x = round(window_space.x);
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context->line_to (last_x - .5 , window_space.y);
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}
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switch (curve_fill) {
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case None:
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context->stroke();
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break;
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case Inside:
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context->stroke_preserve ();
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window_space = item_to_window (Duple (samples[right-1].x, draw.height()));
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context->line_to (window_space.x, window_space.y);
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window_space = item_to_window (Duple (samples[left].x, draw.height()));
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context->line_to (window_space.x, window_space.y);
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context->close_path();
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setup_fill_context(context);
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context->fill ();
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break;
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case Outside:
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context->stroke_preserve ();
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window_space = item_to_window (Duple (samples[right-1].x, 0.0));
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context->line_to (window_space.x, window_space.y);
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window_space = item_to_window (Duple (samples[left].x, 0.0));
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context->line_to (window_space.x, window_space.y);
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context->close_path();
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setup_fill_context(context);
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context->fill ();
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break;
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}
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context->restore ();
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}
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#if 0
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/* add points */
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setup_outline_context (context);
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for (Points::const_iterator p = _points.begin(); p != _points.end(); ++p) {
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Duple window_space (item_to_window (*p));
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context->arc (window_space.x, window_space.y, 5.0, 0.0, 2 * M_PI);
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context->stroke ();
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}
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#endif
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}
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bool
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Curve::covers (Duple const & pc) const
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{
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Duple point = canvas_to_item (pc);
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/* O(N) N = number of points, and not accurate */
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for (Points::const_iterator p = _points.begin(); p != _points.end(); ++p) {
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const Coord dx = point.x - (*p).x;
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const Coord dy = point.y - (*p).y;
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const Coord dx2 = dx * dx;
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const Coord dy2 = dy * dy;
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if ((dx2 < 2.0 && dy2 < 2.0) || (dx2 + dy2 < 4.0)) {
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return true;
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}
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}
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return false;
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}
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