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A model of concept MinSphereOfSpheresTraits must provide the following constants, types, predicates and operations.
| MinSphereOfSpheresTraits::D | |
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specifies the dimension of the spheres you want to
compute the minsphere of.
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| MinSphereOfSpheresTraits::Sphere | |||
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is a typedef to to some class representing a sphere.
(The package will compute the minsphere of spheres of type
Sphere.) The type Sphere must provide a copy constructor.
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| MinSphereOfSpheresTraits::FT | |||
is a (exact or inexact) field number type.
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| MinSphereOfSpheresTraits::Cartesian_const_iterator | |||
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non-mutable model of the STL
concept ForwardIterator with value type FT. Used
to access the center coordinates of a sphere.
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| MinSphereOfSpheresTraits::Use_square_roots | |||
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must typedef to either
CGAL::Tag_true or CGAL::Tag_false. The algorithm
uses (depending on the type
MinSphereOfSpheresTraits::Algorithm) floating-point arithmetic
internally for some intermediate computations. The type
Use_square_roots affects how these calculations are done: When
Use_square_roots is Tag_true, the algorithm computing
the minsphere will perform square-root operations on doubles
and floats where appropriate. On the other hand, if
Use_square_roots is CGAL::Tag_false, the algorithm will
work without doing square-roots. Note: On some platforms the algorithm is much faster when square-roots are disabled (due to lacking hardware support).
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| MinSphereOfSpheresTraits::Algorithm | |||
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selects the method to compute the minsphere
with. It must typedef to either CGAL::Default_algorithm,
CGAL::LP_algorithm or CGAL::Farthest_first_heuristic.
The recommended choice is the first, which is a synonym to the one
of the other two methods which we consider ``the best in practice.''
In case of CGAL::LP_algorithm, the minsphere will be computed
using the LP-algorithm [MSW92], which in our
implementation has maximal expected running time O(2d n) (in the
number of operations on the number type FT). In case of
CGAL::Farthest_first_heuristic, a simple heuristic will be
used instead which seems to work fine in practice, but comes without
a guarantee on the running time. For an inexact number type
FT we strongly recommend CGAL::Default_algorithm, or, if
you want, CGAL::Farthest_first_heuristic, since these handle
most degeneracies in a satisfying manner. Notice that this
compile-time flag is taken as a hint only. Should one of the
methods not be available anymore in a future release, then the
default algorithm will be chosen.
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