title: 3D Mesh reconstruction triangulating input points only
body: <p>I am currently trying to solve the following problem, I have a set of points, which are the base point of some guide hair, I want to be able to triangulate those points so I can generate barycentric coordinates out of those points. I tried with delaunay triangulation using matlab, the only way I could make it to work was by doing the triangulation on a 2d plane like xz, but that is too much of a constraint for what I have in mind, here my test case:</p>
  
  <p>Here is my starting data set, the points i wish to triangulate are the 3d points at the base of the curves:
  <a href="https://i.stack.imgur.com/j4vdc.png" rel="nofollow"><img src="https://i.stack.imgur.com/j4vdc.png" alt=""></a></p>
  
  <p>Here the result of the triangulation on the 2D plane XZ which gives a decent result:
  <a href="https://i.stack.imgur.com/qH1fH.png" rel="nofollow"><img src="https://i.stack.imgur.com/qH1fH.png" alt="enter image description here"></a></p>
  
  <p>Unluckily this is way too much of a semplification, due to the fact that I might have to triangulate points sampled from a dog, cat ,monster mesh, where a 2D triangulation doesnt really fit. If I try to triangulate in 3D i get the following result:
  <a href="https://i.stack.imgur.com/ZsVEV.png" rel="nofollow"><img src="https://i.stack.imgur.com/ZsVEV.png" alt="enter image description here"></a></p>
  
  <p>As you can see there are triangles going in every direction not a consistant surface.</p>
  
  <p>Now, by googling around i found that my problem is more of a surface reconstruction and CGAL can actually help with it, so I did my homework and found this:
  <a href="http://doc.cgal.org/latest/Poisson_surface_reconstruction_3/index.html#title7" rel="nofollow">http://doc.cgal.org/latest/Poisson_surface_reconstruction_3/index.html#title7</a></p>
  
  <p>Which looks like exactly what I need, but the down side is that the limit surface is generated then tassellated, it does not triangulate the given input points, but the tassellation can actually be controlled with a distance parameter.
  Is there a way to constraint the tassellation using the given input point?
  I am also looking at other possibilities using other freamworks but if possible I would like to stick with cgal. 
  Thank you for your time.
  M</p>