DelaunayTriangulator is occasionally incorrect (6-point example)

Issue details

I am attempting to use the DelaunayTriangulator to calculate adjacency information in a voronoi diagram. Unfortunately, it appears that the triangulator occasionally triangulates quads in the wrong direction. Here’s a picture of one of the failing cases I’m encountering:

The background is the rasterized voronoi of the points, to emphasize the problem. The quad made up of points (0, 3, 1, 2) should be triangulated into (0, 3, 1) and (1, 2, 0), but instead it gets cut in the other direction. Adding another point somewhere else in the diagram (even far away) can sometimes flip this particular quad to be correct.

Reproduction steps/code

This test case reproduces the issue exactly as shown in the picture.

import com.badlogic.gdx.math.DelaunayTriangulator;
import com.badlogic.gdx.utils.ShortArray;

public class DelaunayTest {

	public static void main(String[] args) {
		float[] points = new float[12];
		points[0] = (float) 2000.7620849609375;
		points[1] = (float) 3044.865234375;
		points[2] = (float) 3121.152099609375;
		points[3] = (float) 2331.909912109375;
		points[4] = (float) 1909.64794921875;
		points[5] = (float) 1924.1240234375;
		points[6] = (float) 3096.233642578125;
		points[7] = (float) 2911.776611328125;
		points[8] = (float) 776.0308227539062;
		points[9] = (float) 658.64501953125;
		points[10] = (float) 3619.53564453125;
		points[11] = (float) 163.5050811767578;

		DelaunayTriangulator delaunay = new DelaunayTriangulator();
		ShortArray trigs = delaunay.computeTriangles(points, false);

		for (int c = 0, n = trigs.size; c < n; c += 3) {
			System.out.format("(%d, %d, %d)\n", trigs.get(c), trigs.get(c+1), trigs.get(c+2));
		}

		// Prints out:
		// (4, 2, 5)
		// (2, 3, 1) // wrong!
		// (2, 4, 0)
		// (3, 5, 1)
		// (2, 0, 3) // wrong!
		// (5, 2, 1)
	}

}

Version of LibGDX and/or relevant dependencies

master (as of 12/15/2016, commit 52bbab3)

Please select the affected platforms

• Android
• iOS (robovm)
• iOS (MOE)
• HTML/GWT
• Windows
• Linux
• MacOS I’ve only tested on Windows 7, but the problem seems algorithmic.

[tommyettinger]

So we contributors have been going through issues recently and closing any that no longer represent legitimate bugs. This is not one of those cases. The example code provided by @SpexGuy was very helpful in confirming the bug, but actually solving it was a can of worms, and I’m not certain I’ve got a fix for all buggy situations… But it’s something. What I found was that the point sorting code was sometimes not producing a correct ascending-x order, and while I’m not totally sure why this happens, an extra check is all that’s needed to make sure that the sort is correct. Once the sort is correct, the triangles match the diagram given in the first post. This is a two-line fix, and as long as there isn’t some extra unknown bug, it should be enough. I’ll PR the change in a few minutes.

[MrStahlfelge]

Fix is merged.