Fast triangulation of unordered point clouds

This tutorial explains how to run a greedy surface triangulation algorithm on a PointCloud with normals, to obtain a triangle mesh based on projections of the local neighborhoods. An example of the method's output can be seen here:

Background: algorithm and parameters

The method works by maintaining a list of points from which the mesh can be grown ("fringe" points) and extending it until all possible points are connected. It can deal with unorganized points, coming from one or multiple scans, and having multiple connected parts. It works best if the surface is locally smooth and there are smooth transitions between areas with different point densities.

Triangulation is performed locally, by projecting the local neighborhood of a point along the point's normal, and connecting unconnected points. Thus, the following parameters can be set:

setMaximumNearestNeighbors(unsigned) and setMu(double) control the size of the neighborhood. The former defines how many neighbors are searched for, while the latter specifies the maximum acceptable distance for a point to be considered, relative to the distance of the nearest point (in order to adjust to changing densities). Typical values are 50-100 and 2.5-3 (or 1.5 for grids).
setSearchRadius(double) is practically the maximum edge length for every triangle. This has to be set by the user such that to allow for the biggest triangles that should be possible.
setMinimumAngle(double) and setMaximumAngle(double) are the minimum and maximum angles in each triangle. While the first is not guaranteed, the second is. Typical values are 10 and 120 degrees (in radians).
setMaximumSurfaceAgle(double) and setNormalConsistency(bool) are meant to deal with the cases where there are sharp edges or corners and where two sides of a surface run very close to each other. To achieve this, points are not connected to the current point if their normals deviate more than the specified angle (note that most surface normal estimation methods produce smooth transitions between normal angles even at sharp edges). This angle is computed as the angle between the lines defined by the normals (disregarding the normal's direction) if the normal-consistency-flag is not set, as not all normal estimation methods can guarantee consistently oriented normals. Typically, 45 degrees (in radians) and false works on most datasets.

Please see the example below, and you can consult the following paper and its references for more details:

@InProceedings{Marton09ICRA,
  author    = {Zoltan Csaba Marton and Radu Bogdan Rusu and Michael Beetz},
  title     = {{On Fast Surface Reconstruction Methods for Large and Noisy Datasets}},
  booktitle = {Proceedings of the IEEE International Conference on Robotics and Automation (ICRA)},
  month     = {May 12-17},
  year      = {2009},
  address   = {Kobe, Japan},
}

The code

First, create a file, let's say, greedy_projection.cpp in your favorite editor, and place the following code inside it: