livetrax/libs/canvas/canvas/interpolated_curve.h

/*
 * Copyright (C) 2014 Robin Gareus <robin@gareus.org>
 *
 * 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.,
 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
 */

#ifndef __CANVAS_INTERPOLATED_CURVE_H__
#define __CANVAS_INTERPOLATED_CURVE_H__

#include "canvas/visibility.h"
#include "canvas/types.h"

namespace ArdourCanvas {

class LIBCANVAS_API InterpolatedCurve
{
public:
    enum SplineType {
	    CatmullRomUniform,
	    CatmullRomCentripetal,
    };

protected:

	/**
	 * 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.
	 */
	static void
		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());
		}
	}

private:
	/**
	 * 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, 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 != 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 == 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]);
	}
};

}

#endif