delabella

2D Delaunay triangulation (dela) - super stable (bella!)

• Bunch of credits must go to David for inventing such beautiful algorithm (Newton Apple Wrapper):

  http://www.s-hull.org/

• It is pretty well described in this paper:

  https://arxiv.org/ftp/arxiv/papers/1602/1602.04707.pdf

Example triangulation of signed distance field around some fancy font glyph

delabella usage:

#include "delabella.h"
// ...

	// somewhere in your code ...

	int POINTS = 1000000;

	struct MyPoint
	{
		char something;
		float x;
		int something_else;
		float y;
		float foo[5];
	};

	MyPoint* cloud = new MyPoint[POINTS];

	srand(36341);

	// gen some random input
	for (int i = 0; i < POINTS; i++)
	{
		cloud[i].x = rand();
		cloud[i].y = rand();
	}

	IDelaBella* idb = IDelaBella::Create();

	int verts = idb->Triangulate(POINTS, &cloud->x, &cloud->y, sizeof(MyPoint));

	// if positive, all ok 
	if (verts>0)
	{
		int tris = verts / 3;
		const DelaBella_Triangle* dela = idb->GetFirstDelaunayTriangle();
		for (int i = 0; i<tris; i++)
		{
			// do something with dela triangle 
			// ...
			dela = dela->next;
		}
	}
	else
	{
		// no points given or all points are colinear
		// make emergency call ...
	}

	delete[] cloud;
	idb->Destroy();

	// ...

performance comparison:

Output from speedtest.cpp

points	QHULL	S-HULL	S-HULL-3D	DELAUNATOR	DELABELLA
10	0.023 ms	0.009 ms	0.016 ms	0.004 ms	0.002 ms
25	0.068 ms	0.028 ms	0.033 ms	0.011 ms	0.006 ms
50	0.132 ms	0.065 ms	0.046 ms	0.022 ms	0.013 ms
100	0.256 ms	0.124 ms	0.096 ms	0.043 ms	0.028 ms
250	0.658 ms	0.375 ms	0.267 ms	0.118 ms	0.097 ms
500	1.354 ms	0.691 ms	0.620 ms	0.301 ms	0.181 ms
1,000	3.173 ms	1.442 ms	1.220 ms	0.527 ms	0.384 ms
2,500	8.709 ms	3.864 ms	3.175 ms	1.509 ms	1.191 ms
5,000	17.050 ms	8.891 ms	8.823 ms	3.231 ms	2.857 ms
10,000	34.756 ms	18.308 ms	17.732 ms	6.947 ms	5.957 ms
25,000	110.397 ms	53.015 ms	44.851 ms	19.349 ms	16.812 ms
50,000	215.183 ms	114.530 ms	94.747 ms	42.580 ms	35.093 ms
100,000	432.254 ms	231.915 ms	188.614 ms	85.278 ms	74.180 ms
250,000	1242.280 ms	652.245 ms	510.195 ms	255.369 ms	196.017 ms
500,000	2782.869 ms	1400.072 ms	1090.790 ms	567.055 ms	419.753 ms
1,000,000	5913.905 ms	3127.992 ms	2286.446 ms	1276.912 ms	897.941 ms
2,500,000	16091.611 ms	8820.593 ms	6203.232 ms	3747.699 ms	2405.105 ms
5,000,000	53809.487 ms	19320.767 ms	13289.362 ms	8374.141 ms	5056.733 ms