How can I generate a mesh of quadrilaterals for a given 2D surface using MATLAB?

Does somebody know, how to simply and theoretically generate a mesh of quadrilaterals on a given surface?

The surface is in the x,y-plane and might also have curved borders.

I have searched on google and found like tons and tons of informations and also free software to take over this Job, but I really would like to know, how I can generate a mesh of quadrilateral elements which corresponds to a given surface just on my own.

So where is the best place to start? I need to develop my own understanding and also my own spaghetti code for this task.

Given the borders of and the interior of a 2D surface, how or where should I start in order to get my 'new' vertices on the interior of the surface? How do I know, how many quadrilateral elements and corresponding vertices do I need?

Thank you for your help and support in advance.

Regards

Ahmed Hossam

[Ahmed Hossam]

http://math.stackexchange.com/questions/2210037/generating-a-mesh-on-a-2d-surface

Answer 1

[KSSV]

You have to use Transfinite Interpolation. Check the following links:

http://in.mathworks.com/matlabcentral/fileexchange/40681-transfinite-interpolation

http://in.mathworks.com/matlabcentral/fileexchange/40618-grid-generation

http://in.mathworks.com/matlabcentral/fileexchange/33731-meshing-a-plate-using-four-noded-elements

http://in.mathworks.com/matlabcentral/fileexchange/34143-meshing-thin-shells-using-four-noded-elements

http://in.mathworks.com/matlabcentral/fileexchange/44670-mesh-a-plate-with-hole

[Ahmed Hossam]

I remember reading about this algebraic method. But I couldn't find enough explanations for this method in the textbooks. I will check these links and answer you later.

[Ahmed Hossam]

What I need is the detailed mathematical theory of the transfinite interpolation in order for me to be able to generate my own code based on this theory.

[Ahmed Hossam]

I believe in gmsh.

Answer 2

[Jiexian Ma]

A general way is using Gmsh to generate quasi-structured or unstructured quadrilateral mesh.

In Im2mesh (an open-source Matlab package), I demostrate how to define 2d geometry in Matlab and then generate unstructured quadrilateral mesh via Gmsh.

Please check these two examples: demo11 demo12

To run demo, you need to download Im2mesh package and Gmsh sofware.