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For my PhD work, I am using the dD Geometry Kernel provided by the C++ CGAL library.

  • My basic goal: I want to construct a sequence of dimension growing hyperspheres by sequentially adding one new point, until reaching arbitrary dimension d. The first hypersphere is 1-dimensional and the last one is d-dimensional. Each new point added leads to actual augmentation of the dimension (no coplanarity).

  • My problem: Using CGAL::Sphere_d class, I don't know how to construct a (d-k)-dimensional hypersphere (k < d) in a d-dimensional ambiant space (i.e d-dimensional points). Indeed, to construct a d'-sphere, it is necessary to provide d'+1 d'-points (which is normal). For instance, I would like to construct a disk (2-sphere) out of 3 3-dimensional points. Using directly this CGAL class would therefore imply that I provide 2-dimensional points, which is impossible (so far).

  • My question: As a very recent user of CGAL libraries, I don't know if this class might be the one I have to use or if it is necessary for me to find another one ? If not necessary, how to bypass my problem ?

Thanks in advance,

Octavio

Octavio
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  • this is most likely not what you searching for but anyway look here http://stackoverflow.com/a/21575035/2521214 for (C++ hypersphere filling) may be you can adapt it for CGAL somehow to satisfy your needs – Spektre Feb 25 '14 at 23:43

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