Refer to the original stackoverflow post here:
I have been facing this dilemma for some months now, and made exhaustive research.
Mainly there are 2 categories of algorithms: computation geometry, and implicit surfaces.
They fit the mesh on the existing points.
Probably the most famous algorithm of this group is powercrust, because it is theoretically well-established – it guarantees watertight mesh.
Ball Pivoting is patented by IBM. Also, it is not suitable for pointclouds with varying point density.
One fits implicit functions on the pointcloud, then uses a marching-cube-like algorithm to extract the zero-set of the function into a mesh.
Methods in this category differ mainly by the different implicit functions used.
The algorithms of this category usually can be implemented so that they are able to process huge inputs very efficiently, and one can scale their quality<->speed trade-off. They are not disturbed by noise, varying point-density, holes. A disadvantage of them is that they require consistently oriented surface normals at the input points.
You will find small number of free implementations. However it depends on whether You are going to integrate it into free software (in this case GPL license is acceptable for You) or into a commercial software (in this case You need a more liberal license). The latter is very rare.
One is in VTK. I suspect it to be difficult to integrate (no documentation is available for free), it has a strange, over-complicated architecture, and is not designed for high-performance applications. Also has some limitations for the allowed input pointclouds.
Take a look at this Poisson implementation, and after that share your experience about it with me please.
Also: here are a few high-performance algorithms, with surface reconstruction among them.
CGAL is a famous 3d library, but it is free only for free projects. Meshlab is a famous application with GPL.
Also (Added August 2013): The library PCL has a module dedicated to surface reconstruction and is in active development (and is part of Google’s Summer of Code). The surface module contains a number of different algorithms for reconstruction. PCL also has the ability to estimate surface normals, incase you do not have them provided with your point data, this functionality can be found in the features module. PCL is released under the terms of the BSD license and is open source software, it is free for commercial and research use.