CGAL users discussion list

[Jogging Song <>]

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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>> Sent from the cgal-discuss mailing list archive at Nabble.com.
>>
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>>
>>
> 
> 
> -- 
> Jesse Louis-Rosenberg
> Nervous System
> http://n-e-r-v-o-u-s.com
> 
> -- 
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