Efficiently computes the smallest bounding ball of a point set, in arbitrary number of dimensions.

## miniball

A Python module to efficiently compute the smallest bounding ball of a point set, in arbitrary number of dimensions.

The algorithm runs in approximatively linear time in respects to the number of input points. This is NOT a derivative nor a port of Bernd Gaertner’s C++ library.

### Requirements

miniball 1.2 requires

• Python >= 3.5

• Numpy >= 1.17

### Installation

\$ pip install miniball

### Usage

Here is how you can get the smallest bounding ball of a set of points S

>>> import numpy
>>> import miniball
>>> S = numpy.random.randn(100, 2)
>>> C, r2 = miniball.get_bounding_ball(S)

The center of the bounding ball is C, its radius is the square root of r2. The input coordinates S can be integer, they will automatically cast to floating point internally.

And that’s it ! miniball does only one thing with one function.

#### Result accuracy

Although the algorithm returns exact results in theory, in practice it returns result only exact up to a given precision. The epsilon keyword argument allows to control that precision, it is set to 1e-7 by default.

>>> import numpy
>>> import miniball
>>> S = numpy.random.randn(100, 2)
>>> C, r2 = miniball.get_bounding_ball(S, epsilon=1e-7)

#### Repeatability

The algorithm to compute bounding balls relies on a pseudo-random number generator. Although the algorithms return an exact solution, it is only exact up to the epsilon parameter. As a consequence, running the get_bounding_ball function twice on the same input might not return exactly the same output.

By default, each call to get_bounding_ball pull out a new, freshly seeded pseudo-random number generator. Therefore, if you wish to get repeatable results from get_bounding_ball, you have to (and only have to) pass the same pseudo-random number generator, using with the rng keyword argument

>>> import numpy
>>> import miniball
>>> S = numpy.random.randn(100, 2)
>>> rng = numpy.random.RandomState(42)
>>> C, r2 = miniball.get_bounding_ball(S, rng = rng)

#### Duplicated input points

Duplicated input points might trigger failures. This implementation do not check for duplicated input points, the guaranty of non-duplication is defered to you, the programmer. This is by design, to avoid to pay the cost of de-duplication when we are sure that the input has no duplicates.

### Implementation notes

The algorithm implemented is Welzl’s algorithm. It is a pure Python implementation, it is not a binding of the popular C++ package Bernd Gaertner’s miniball.

The algorithm, although often presented in its recursive form, is here implemented in an iterative fashion. Python have an hard-coded recursion limit, therefore a recursive implementation of Welzl’s algorithm would have an artificially limited number of point it could process.

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