what is the selection criteria for control points in isogeometric analysis (IGA)? Especially in different geometries ...
The basics of constructing curves with NURBS implies placing control points on each turn of a curve, then you can extend this with tensor product elements to 3D geometries.
Hughes' book on isogeometric analysis has some example meshes for basic geometries. You can find other examples of NURBS models online. I also think you can use a CAD tool to model your geometry and extract the NURBS information.
So far I've only used example models from Hughes' book with some refinement as presented in The NURBS Book.
Dear Diego
Thank you very much for your helpful comments. I really appreciate your kind response.
I am currently working on the construction of different geometries using NURBS basic functions and read the NURBS and Hughes's book.
Regards,
Hamid
Also look at this book -> https://books.google.com.sa/books?hl=en&lr=&id=58KqCAAAQBAJ&oi=fnd&pg=PA1&dq=the+nurbs+book&ots=8KMXU9GflV&sig=h7E22N_lEh5WarhjLZU2gXNeOS4&redir_esc=y#v=onepage&q=the%20nurbs%20book&f=false
Great Diego. Very useful text book.
Thank you for sharing this valuable information with me.
Regards,
Hamid
you could also check the following link
http://www.sciencedirect.com/science/book/9780122490521
I would like to augment the discussion by talking about interia control points, or volumetric parametrizations as well. The answer to the question then depends on whether you are asking only about the boundary or about the interia of the object as well.
In the first case, we don't really choose anything since the spline data come from the CAD software, as Diego says above. However, to run IGA simulations we need the spline representation of the entire object, or domain, enclosed by the boundary. That we usually don't receive from CAD since only the boundary, or surface, of the object is designed with the CAD software. And this is actually one of the main bottlenecks of the entire IGA pipeline.
So the problem reads now as following: given the spline data for the boundary, how do we choose, or generate, the interia control points? Trivial though for simple geometries like unit square, it becomes rather difficult for more complicated objects. The location of the interia control points doesn't influence the boundary and therefore doesn't change the domain. But it defines the computational mesh for our IGA simulation, which in turn affects its accuracy.
A good paper I would recommend is this one:
Conference Paper Planar Parametrization in Isogeometric Analysis
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