CGAL users discussion list

[Laurent Saboret <>]

Hi Jogging Song,

From the User Manual http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Surface_reconstruction_points_3/Chapter_main.html:
The computed implicit functions can be iso-contoured to reconstruct a surface by using the Cgal surface mesh generator [RY07, BO05]:
CGAL::make_surface_mesh
[RY07] Laurent Rineau and Mariette Yvinec. A generic software design for Delaunay refinement meshing. Comput. Geom. Theory Appl., 38:100-110, 2007.
[BO05] Jean-Daniel Boissonnat and Steve Oudot. Provably good sampling and meshing of surfaces. Graphical Models, 67:405-451, 2005

Then you have to search for these articles in Google Scholar.

Best regards,
Laurent Saboret

Le 30/09/2013 04:28, Jogging Song a écrit :

Hi, Jesse

Thanks for your reply. 

From the example code, poisson reconstruction algorithm is one kind of
implicit
function based method. Usually marching cube method is applied to the
implicit
function to get the triangle mesh. I am curious about how the Delaunay
triangulation
method is applied to the implicit function.

I am not an expert on computational geometry. Delaunay triangulation
algorithm takes
one point cloud as the input. 
The document says "Cgal implements a variant of this algorithm which solves
for a piecewise linear function on a 3D Delaunay triangulation instead of an
adaptive octree."
I don't understand what it means.
To understand it, I download the source code but it is hard to read it.

Thanks.
Regards
Jogging Song 

Jesse Louis-Rosenberg wrote

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 <

joggingsong@

> 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

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