microstructpy.geometry.Rectangle

class microstructpy.geometry.Rectangle(**kwargs)

Bases: microstructpy.geometry.n_box.NBox

This class contains a generic, 2D rectangle. The position and dimensions of the box can be specified using any of the parameters below.

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

Parameters:

• length (float) – (optional) Length of the rectangle.
• width (float) – (optional) Width of the rectangle. (optional)
• side_lengths (list) – (optional) Side lengths. Defaults to (1, 1).
• center (list) – (optional) Center of rectangle. Defaults to (0, 0).
• corner (list) – (optional) Bottom-left corner.
• bounds (list) – (optional) Bounds of rectangle. Expected to be in the format [(xmin, xmax), (ymin, ymax)].
• limits – Alias for bounds.
• angle (float) – (optional) The rotation angle, in degrees.
• angle_deg (float) – (optional) The rotation angle, in degrees.
• angle_rad (float) – (optional) The rotation angle, in radians.
• matrix (numpy.ndarray) – (optional) The 2x2 rotation matrix.

approximate(x1=None)

Approximate rectangle with a set of circles.

This method approximates a rectangle with a set of circles. These circles are spaced uniformly along the long axis of the rectangle with distance x1 between them.

Example

For a rectangle with length=2.5, width=1, and x1=0.3, the approximation would look like Fig. 29.

Fig. 29 Circular approximation of rectangle.

Parameters:x1 (float or None) – (optional) Spacing between the circles. If not specified, the spacing is 0.25x the length of the shortest side. Returns:An Nx3 array, where each row is a circle and the columns are x, y, and r. Return type:numpy.ndarray

classmethod area_expectation(**kwargs)

Expected area of rectangle

This method computes the expected area of a rectangle. There are two main ways to define the size of a rectangle: by the length and width and by the bounds. If the input rectangle is defined by length and width, the expected area is:

\[\mathbb{E}[A] = \mathbb{E}[L W] = \mu_L \mu_W\]

For the case where it is defined by upper and lower bounds:

\[\mathbb{E}[A] = \mathbb{E}[(X_U - X_L) (Y_U - Y_L)]\]

\[\mathbb{E}[A] = \mu_{X_U}\mu_{Y_U} - \mu_{X_U} \mu_{Y_L} - \mu_{X_L}\mu_{Y_U} + \mu_{X_L}\mu_{Y_L}\]

Example

>>> import scipy.stats
>>> import microstructpy as msp
>>> L = scipy.stats.uniform(loc=1, scale=2)
>>> W = scipy.stats.norm(loc=3.2, scale=5.1)
>>> L.mean() * W.mean()
6.4
>>> msp.geometry.Rectangle.area_expectation(length=L, width=W)
6.4

Parameters:**kwargs – Keyword arguments, same as Rectangle but the inputs can be from the scipy.stats module. Returns:Expected/average area of rectangle. Return type:float

best_fit(points)

Find rectangle of best fit for points

Parameters:points (list) – List of points to fit. Returns:an instance of the class that best fits the points. Return type:Rectangle

plot(**kwargs)

Plot the rectangle.

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

Parameters:**kwargs (dict) – Keyword arguments for the patch.

within(points)

Test if points are within n-box.

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

Parameters:points (list or numpy.ndarray) – Point or list of points. Returns:Flags set to True for points in geometry. Return type:bool or numpy.ndarray

angle

Rotation angle of rectangle - degrees

Type:float

angle_deg

Rotation angle of rectangle - degrees

Type:float

angle_rad

Rotation angle of rectangle - radians

Type:float

area

Area of rectangle

Type:float

bounds

(lower, upper) bounds of the box

Type:list

corner

bottom-left corner

Type:list

length

Length of rectangle, side length along 1st axis

Type:float

limits

(lower, upper) bounds of the box

Type:list

n_dim

Number of dimensions, 2

Type:int

n_vol

area, volume of n-box

Type:float

sample_limits

(lower, upper) bounds of the sampling region of the box

Type:list

width

Width of rectangle, side length along 2nd axis

Type:float