Square

class sknano.core.geometric_regions.Square(center=None, a=1)

Bases: sknano.core.geometric_regions.Geometric2DRegion

Geometric2DRegion for a square.

New in version 0.3.0.

Represents the axis-aligned bounded region with center \((c_x, c_y)\) and side length \(a\).

Parameters:

• center (array_like, optional) – The center point coordinate \((c_x, c_y)\) of the axis-aligned square.
• a (float, optional) – The side length \(a\) of the axis-aligned square.

Notes

Square represents the region \(\left\{\{c_i\pm\frac{a}{2}\}|a>0\forall i\in\{x,y\}\right\}\).

Calling Square with no parameters is equivalent to Square(center=[0, 0], a=1).

Attributes

a	Side length \(a\) of the axis-aligned square.
area	Square area, \(A=a^2\).
bounding_box	Bounding Cuboid.
center	Center point \((c_x, c_y)\) of axis-aligned square.
centroid	Alias for center.
fmtstr	Format string.
measure	Alias for area, which is the measure of a 2D geometric region.
ndim	Return the dimensions.
pmax	Point at maximum extent.
pmin	Point at minimum extent.

Methods

center_centroid()	Center centroid on origin.
contains(point)	Test region membership of point in Square.
get_points()	Return list of points from GeometricRegion.points and GeometricRegion.vectors
rotate(**kwargs)	Rotate GeometricRegion points and vectors.
todict()	Returns a dict of the Square constructor parameters.
translate(t[, fix_anchor_points])	Translate GeometricRegion points and vectors by Vector t.

Attributes Summary

a	Side length \(a\) of the axis-aligned square.
area	Square area, \(A=a^2\).
center	Center point \((c_x, c_y)\) of axis-aligned square.
centroid	Alias for center.

Methods Summary

contains(point)	Test region membership of point in Square.
todict()	Returns a dict of the Square constructor parameters.

Attributes Documentation

a

Side length \(a\) of the axis-aligned square.

area

Square area, \(A=a^2\).

center

Center point \((c_x, c_y)\) of axis-aligned square.

centroid

Alias for center.

Methods Documentation

contains(point)

Test region membership of point in Square.

Parameters:point (array_like) – Returns:True if point is within Square, False otherwise. Return type:bool

Notes

A point \((p_x, p_y)\) is within the bounded region of a square with center \((c_x, c_y)\) and side length \(a\) if the following is true:

\[c_i - \frac{a}{2}\le p_i\le c_i + \frac{a}{2}\forall i\in \{x, y\}\]

todict()

Returns a dict of the Square constructor parameters.