# microstructpy.geometry.Circle¶

class microstructpy.geometry.Circle(**kwargs)[source]

A 2D circle.

This class represents a two-dimensional circle. It is defined by a center point and size parameter, which can be either radius or diameter.

Without parameters, this returns a unit circle centered on the origin.

Parameters: r (float) – (optional) The radius of the circle. Defaults to 1. center (list) – (optional) The coordinates of the center. Defaults to (0, 0). diameter – (optional) Alias for 2*r. radius – (optional) Alias for r. d – (optional) Alias for 2*r. size – (optional) Alias for 2*r. position – (optional) Alias for center.
approximate()

Approximate the n-sphere with itself

Other geometries can be approximated by a set of circles or spheres. For the n-sphere, this approximation is exact.

Returns: A list containing [(x, y, z, …, r)] list
classmethod area_expectation(**kwargs)[source]

Expected value of area.

This function computes the expected value for the area of a circle. The keyword arguments are the same as the class parameters. The values can be constants (ints or floats), or a distribution from the SciPy scipy.stats module.

The expected value is computed by the following formula:

$\mathbb{E}[A] = \pi \mathbb{E}[R^2] = \pi (\mu_R^2 + \sigma_R^2)$

For example:

>>> from microstructpy.geometry import Circle
>>> Circle.area_expectation(r=1)
3.141592653589793
>>> from scipy.stats import norm
>>> Circle.area_expectation(r=norm(1, 1))
6.283185307179586

Parameters: **kwargs – Keyword arguments, see Circle. Expected value of the area of the circle. float
classmethod best_fit(points)

Find n-sphere of best fit for set of points.

This function takes a list of points and computes an n-sphere of best fit, in an algebraic sense. This method was developed using the a published writeup, which was extended from 2D to ND. [1]

Parameters: points (list, numpy.ndarray) – List of points to fit. An instance of the class that fits the points. NSphere
 [1] Circle fitting writup by Randy Bullock, https://dtcenter.org/met/users/docs/write_ups/circle_fit.pdf
plot(**kwargs)[source]

Plot the circle.

This function adds a matplotlib.patches.Circle to the current axes. The keyword arguments are passed through to the circle patch.

Parameters: **kwargs (dict) – Keyword arguments for matplotlib.
reflect(points)

Reflect points across surface.

This function reflects a point or set of points across the surface of the n-sphere. Points at the center of the n-sphere are not reflected.

Parameters: points (list or numpy.ndarray) – Points to reflect. Reflected points. numpy.ndarray
within(points)

Test if points are within n-sphere.

This function tests whether a point or set of points are within the n-sphere. For the set of points, a list of booleans is returned to indicate which points are within the n-sphere.

Parameters: points (list or numpy.ndarray) – Point or list of points. Set to True for points in geometry. bool or numpy.ndarray
area

area of cirle, $$A=\pi r^2$$

Type: float
bound_max

maximum bounding n-sphere

Type: tuple
bound_min

minimum interior n-sphere

Type: tuple
d

diameter of n-sphere.

Type: float
diameter

diameter of n-sphere.

Type: float
limits

list of (lower, upper) bounds for the bounding box

Type: list
n_dim

number of dimensions, 2

Type: int
position

position of n-sphere.

Type: list
radius

Type: float
sample_limits

list of (lower, upper) bounds for the sampling region

Type: list
size

size (diameter) of n-sphere.

Type: float
volume

alias for area

Type: float