
Precise Higher-Order Meshing of Curved 2D Domains - wowsig
http://graphics.cs.uos.de/bezierguarding.html
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donpdonp
After some skimming of the paper and googling of terms, I'm going to take a
whack at an ELI5 (note I have no special domain knowledge here): Some fields
such as GIS or CAD are given a polygon and need to represent the interior area
as a 'mesh' or set of triangles in order to perform certain operations on that
interior. The current approach to building a mesh gives an approximation of
that area where the method in the paper gives a mathematically exact
representation, which is a 'big deal' where accuracy counts. Corrections
welcome.

Fry: Hey, professor. What are you teaching this semester?

Prof. Farnsworth: Same thing I teach every semester: The Mathematics of
Quantum Neutrino Fields. I made up the title so that no student would dare
take it.

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whinvik
High order meshing is becoming increasing important in Computational Fluid
Dynamics since high order numerics requires the boundaries to be more
accurately represented. Would be interesting to know if this method could be
extended to generate quadrilaterals.

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snakeboy
As someone with only a basic knowledge of FEA, why would a quadrilateral mesh
ever make more sense than triangular?

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whinvik
There are multiple reasons but they all can be application specific.

First reason is that quadrilaterals can be mapped to a square and so you can
use "Tensor product" elements which is just a fancy way of saying that you can
uncouple the equations to be 1D for each direction. So you can think of your
problem in 1D and easily extend them to 2D by using quadrilaterals.

Second is somewhat related and is sparsity. The matrices generated for
quadrilaterals would be sparser and hence your performance will be higher.

Third is accuracy. Quadrilaterals are regarded to be more accurate however I
am not sure there are proofs or conclusive studies on this, more a rule of
thumb.

