Uniform surface mesh generation

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Uniform surface mesh generation

Shankar Kulumani

I am using the tutorial here to generate a mesh given an implicit function (an ellipsoid).

I have two questions:

  1. Is there a method to relate the mesh generation parameters (angular_bound, radius_bound, and distance_bound) to the resulting number of vertices and/or faces of the resulting mesh?

  2. Is there a method to ensure a uniform mesh over the surface? For example, this Matlab code offers a uniform mesh generation function DistMesh.

Thank you



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Re: Uniform surface mesh generation

Sebastien Loriot (GeometryFactory)
On 03/27/2018 02:06 AM, Shankar Kulumani wrote:

> I am using the tutorialhere
> <https://doc.cgal.org/latest/Surface_mesher/Surface_mesher_2mesh_an_implicit_function_8cpp-example.html>to
> generate a mesh given an implicit function (an ellipsoid).
>
> I have two questions:
>
>  1.
>
>     Is there a method to relate the mesh generation parameters
>     (|angular_bound|,|radius_bound|, and|distance_bound|) to the
>     resulting number of vertices and/or faces of the resulting mesh?
>
No you can't, the criteria allos to control the size and shape of the
triangles, as well as the error of the mesh wrt the input.

>  2.
>
>     Is there a method to ensure a uniform mesh over the surface? For
>     example, this Matlab code offers a uniform mesh generation
>     functionDistMesh <http://persson.berkeley.edu/distmesh/>.

As described here:
https://doc.cgal.org/latest/Surface_mesher/classCGAL_1_1Surface__mesh__default__criteria__3.html

If you want something uniform, you should pass the expected size
to radius_bound. However, note that all the triangles generated will
all have to respect the error or angle criteria. So in some parts
of you mesh you might have triangles thiner than expected (basically
where you have curvature). If you put looser value for these criteria
then the radius_bound should be the one imposing the constraints on
triangles generated.

Sebastien.

>
> Thank you
>
>
>

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Re: Uniform surface mesh generation

Shankar Kulumani
Thank you for all the help.

On Tue, Mar 27, 2018, 03:34 Sebastien Loriot (GeometryFactory) <[hidden email]> wrote:
On 03/27/2018 02:06 AM, Shankar Kulumani wrote:
> I am using the tutorialhere
> <https://doc.cgal.org/latest/Surface_mesher/Surface_mesher_2mesh_an_implicit_function_8cpp-example.html>to
> generate a mesh given an implicit function (an ellipsoid).
>
> I have two questions:
>
>  1.
>
>     Is there a method to relate the mesh generation parameters
>     (|angular_bound|,|radius_bound|, and|distance_bound|) to the
>     resulting number of vertices and/or faces of the resulting mesh?
>
No you can't, the criteria allos to control the size and shape of the
triangles, as well as the error of the mesh wrt the input.

>  2.
>
>     Is there a method to ensure a uniform mesh over the surface? For
>     example, this Matlab code offers a uniform mesh generation
>     functionDistMesh <http://persson.berkeley.edu/distmesh/>.

As described here:
https://doc.cgal.org/latest/Surface_mesher/classCGAL_1_1Surface__mesh__default__criteria__3.html

If you want something uniform, you should pass the expected size
to radius_bound. However, note that all the triangles generated will
all have to respect the error or angle criteria. So in some parts
of you mesh you might have triangles thiner than expected (basically
where you have curvature). If you put looser value for these criteria
then the radius_bound should be the one imposing the constraints on
triangles generated.

Sebastien.

>
> Thank you
>
>
>

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