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MathGroup Archive 2003

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RE: Mesh generation in 2D

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44746] RE: [mg44669] Mesh generation in 2D
  • From: "Ingolf Dahl" <ingolf.dahl at telia.com>
  • Date: Mon, 24 Nov 2003 00:05:33 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,
I have made a small Mathematica routine to split a triangle, or a list of
triangles, into small triangles with all sides less than the variable d. It
complements the package by Martin Kraus. The triangles can be 2D or 3D. You
might find it useful for your point one. It should be possible to modify it
to also suit your point two: the argument d could be replaced by some
function of the position of the triangle. If you define the lines inside the
region as double walls parts of the initial border, I believe that you can
also satisfy point three. You can download the routine from
http://w1.318.telia.com/~u31815170/Mathematica/DivideTriangle.nb.

Ingolf Dahl
Sweden


>-----Original Message-----
>From: Goyder Dr HGD [mailto:H.Goyder at rmcs.cranfield.ac.uk]
To: mathgroup at smc.vnet.net
>Sent: Thursday, November 20, 2003 09:17
>To: mathgroup at smc.vnet.net
>Subject: [mg44746] [mg44669] Mesh generation in 2D
>
>
>Dear MathGroup,
>
>What is the best way to generate a mesh of triangles for a 2D grid on a
>general nonconvex region?
>
>I know that in version 4.2 there is a computational geometry
>add-on and that
>there is a package for polygon triangulation at
>http://library.wolfram.com/packages/polygontriangulation/  by Martin Kraus
>and also there is the book and packages by Tom Wickham-Jones
>http://library.wolfram.com/infocenter/Books/3753/ . However, I
>cannot find a
>procedure for putting this altogether to make a triangular mesh.
>
>What I am looking for is:
>
>1. The ability to put grid nodes in a general nonconvex region so that the
>triangles are all about the same size and the triangles are as close as
>possible to equilateral.
>
>2. The ability to weight the size of the triangles so that I can put more
>grid where it is needed.
>
>3. The ability to enforce lines within the region (not necessarily
>straight)
>so that I can have barriers with no thickness.
>
>4. Everything implemented in Mathematica.
>
>Has this all been done or am I asking for the impossible?
>
>Thanks for your comments.
>
>Hugh Goyder
>
>
>--
>This message has been scanned for viruses and
>dangerous content by the Cranfield MailScanner, and is
>believed to be clean.
>


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