replace sin curve with sections of lines

line_curve.java

package demo;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;

import processing.core.PApplet;
import processing.core.PVector;
import demo.DmPoint;

public class Demo extends PApplet {

	private static final long serialVersionUID = 7426719630987497221L;
	private DmPoint _locations[];
	private ArrayList<DmPoint> _path;

	public double getDistance(PVector x, PVector y, PVector z) {
		PVector s1 = PVector.sub(y, x);
		PVector s2 = PVector.sub(z, x);
		return s1.cross(s2).mag() / s1.mag();
	}

	private void findMax(PVector p[], int length) {
		PVector s1 = PVector.sub(p[length - 1], p[0]);
		double max = 0;
		int index = 0;
		for (int i = 1; i < length - 1; i++) {
			PVector s2 = PVector.sub(p[i], p[0]);
			double distance = s1.cross(s2).mag() / s1.mag();
			if (max < distance) {
				max = distance;
				index = i;
			}
		}

		if (max > 0.1) {
			_path.add((DmPoint) p[index]);
			findMax(p, index);
			findMax(Arrays.copyOfRange(p, index, length), length - index - 1);
		}
	}

	private void output() {
		for (DmPoint p : _path) {
			print(p.getIndex());
			print(p);
		}
	}

	public void setup() {
		this.size(720, 200);

		this.scale(2);
		noSmooth();

		_locations = new DmPoint[360];
		for (int i = 0; i < _locations.length; i++) {
			_locations[i] = new DmPoint(this, i, i, 50 + sin(i * PI / 180) * 40);
			_locations[i].draw();
		}

		_path = new ArrayList<DmPoint>();
		_path.clear();
		_path.add((DmPoint) _locations[0]);

		stroke(255, 0, 0);		
		findMax(_locations, _locations.length);

		Collections.sort(_path, new DmPoint.DmPointComparator());

		_path.add((DmPoint) _locations[_locations.length - 1]);
		output();

		for (int i = 0; i < _path.size() - 1; i++) {
			DmPoint.line(_path.get(i), _path.get(i + 1));
		}
		
		print("total ");
		print(_path.size());		
		println(" points.");
	}

	public void draw() {

	}
}