# [Gmsh] How to generate a parabaloid or surface from an equation?

Matthieu Lecouvez matthieu.lecouvez at gmail.com
Fri Dec 11 20:42:44 CET 2020

```Hi Paul,

I have not found a way to easily define a surface from an analytical
equation.

One thing you can do though, for axisymmetric objects, is to describe a
curve from a list of points using a spline and then extrude this curve by
rotation. In this way, the surface created by the extrusion will be
correctly described. This method should work for your parabolic reflector
but not for a generic surface.

For surfaces that can be described in some coordinate system as z = f(x,y),
one other option is to use several spline curves at fixed x0, x1, ..., xN,
then identically at fixed y0, y1, ..., yN and use ruled surfaces based on
theses curves. I have found that the accuracy of this method is not ideal,
but with enough splines it can work (you can use the compound feature to
mesh the whole surface and not be restricted by the NxN points chosen to
describe the surface).

Both methods are usable with .geo files, maybe using the API would provide
easier ways to do that. Please let me know if you find a more adequate way.

Matt.

Le lun. 7 déc. 2020 à 22:35, Paul K <paulklasmann at hotmail.com> a écrit :

> Dear All,
> I would like to generate a parabaloid surface, for example a parabolic
> reflector surface that is defined by an equation.  Is this possible? First
> I would use Gmsh on its own to generate the surface mesh that I plan to use
> in a physical optics PO and GTD simulation.  In a CAD program I would plot
> the curve from the vertex and rotate into a BOR object.
> Second, I'd like to be able generate any arbitary surface using a function
> so that I can simulate a shaped or distorted reflector.  Any advice would
> be greatly appreciated.
>
> My final goal is to write a C++ program with a wxWidgets GUI and to
> include gmsh as the mesh generator for the PO simulator and possibly have a
> way of visualising the reflector and mesh. Thank you.
>
> Kind Regards
> Paul
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