# 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)]

Return type

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.

Returns

Expected value of the area of the circle.

Return type

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.

Returns

An instance of the class that fits the points.

Return type

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.

Returns

Reflected points.

Return type

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.

Returns

Set to True for points in geometry.

Return type
property area

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

Type

float

property bound_max

maximum bounding n-sphere

Type

tuple

property bound_min

minimum interior n-sphere

Type

tuple

property d

diameter of n-sphere.

Type

float

property diameter

diameter of n-sphere.

Type

float

property limits

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

Type

list

property n_dim

number of dimensions, 2

Type

int

property position

position of n-sphere.

Type

list

Type

float

property sample_limits

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

Type

list

property size

size (diameter) of n-sphere.

Type

float

property volume

alias for area

Type

float