Efficiently computes the smallest bounding ball of a point set, in arbitrary number of dimensions.
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.
This project is licensed under the MIT License
miniball 1.1 requires
- Python >= 3.5
- Numpy >= 1.17
$ pip install miniball
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.
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)
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)
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.
This project is licensed under the MIT License - see the LICENSE file for details
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