CGAL users discussion list

[Jesse Louis-Rosenberg <>]

Hi Jogging Song,

I think your understanding is mistaken. The point cloud is not directly triangulated. Instead Poisson reconstruction generates an implicit function which estimates the surface from the point cloud. Surface mesh triangulation takes an implicit function (which is now independent from you point cloud) and generates a triangle mesh using Delaunay refinement.

Best,

Jesse Louis-Rosenberg

Nervous System

On Thu, Sep 26, 2013 at 1:16 AM, Jogging Song <> wrote:

Hi, all

Currently I hope to use CGAL to obtain one adaptive non-manifold mesh from
my input point cloud. I try to learn more about poisson reconstruction in
CGAL.
From the following link:
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Surface_reconstruction_points_3/Chapter_main.html
/"Cgal implements a variant of this algorithm which solves for a piecewise
linear function on a 3D Delaunay triangulation instead of an adaptive
octree. The algorithm takes as input a set of 3D oriented points. It builds
a 3D Delaunay triangulation from these points and refines it by Delaunay
refinement so as to remove all badly shaped (non isotropic) tetrahedra and
to tessellate a loose bounding box of the input oriented points. The normal
of each Steiner point added during refinement is set to zero. It then solves
for a scalar indicator function f represented as a piecewise linear function
over the refined triangulation. More specifically, it solves for the Poisson
equation Δf = div(n) at each vertex of the triangulation using a sparse
linear solver. Eventually, the Cgal surface mesh generator extracts an
isosurface with function value set by default to be the median value of f at
all input points. "/

From my understanding of the above description, for the oriented point cloud
I provide, Delaunay triangulation is employed to obtain one triangle mesh,
and Delaunay refinement will be applied to resultant triangle mesh. Poisson
reconstruction will use the new mesh as the input.

In the demo code poisson_reconstruction_example.cpp, the input oriented
point cloud is input to poisson reconstruction and the implicit function is
got. The function named make_surface_mesh is called to generate the triangle
mesh, and I find that the argument lists doesn't contain the information
about point cloud.

Is my understand correct? Where is Delaunay triangulation applied?

Thanks.
Regards
Jogging Song



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Jesse Louis-Rosenberg
Nervous System
http://n-e-r-v-o-u-s.com