Rectangle

class sknano.core.geometric_regions.Rectangle(pmin=None, pmax=None, xmin=0, ymin=0, xmax=1, ymax=1)

Bases: sknano.core.geometric_regions.Geometric2DRegion

Geometric2DRegion for a rectangle.

New in version 0.3.0.

Represents an axis-aligned bounded region from $p_{\mathrm{min}}=(x_{\mathrm{min}},y_{\mathrm{min}})$ to $p_{\mathrm{max}}=(x_{\mathrm{max}},y_{\mathrm{max}})$.

Parameters:

• pmax (pmin,) – The minimum and maximum 2D point coordinates of the axis-aligned rectangle from pmin=[xmin, ymin] to pmax=[xmax, ymax].
• ymin (xmin,) – The minimum $(x, y)$ point of the axis-aligned rectangle.
• ymax (xmax,) – The maximum $(x, y)$ point of the axis-aligned rectangle.

Notes

Rectangle represents the region $\left\{\{x, y\}|x_{\mathrm{min}}\le x\le x_{\mathrm{max}} \land y_{\mathrm{min}}\le y\le y_{\mathrm{max}}\right\}$

Calling Rectangle with no parameters is equivalent to Rectangle(pmin=[0, 0], pmax=[1, 1]).

Attributes

a	Alias for Rectangle.lx.
area	Rectangle area, $A=\ell_x\ell_y$
b	Alias for Rectangle.ly.
bounding_box	Bounding Cuboid.
center	Alias for centroid.
centroid	Rectangle centroid, $(c_x, c_y)$.
fmtstr	Format string.
lengths	tuple of side lengths
lx	Distance between $x_{\mathrm{max}}-x_{\mathrm{min}}$.
ly	Distance between $y_{\mathrm{max}}-y_{\mathrm{min}}$.
measure	Alias for area, which is the measure of a 2D geometric region.
ndim	Return the dimensions.
pmax	2D Point at (xmax, ymax).
pmin	2D Point at (xmin, ymin).
xmax	$x_{\mathrm{max}}$ coordinate.
xmin	$x_{\mathrm{min}}$ coordinate.
ymax	$y_{\mathrm{max}}$ coordinate.
ymin	$y_{\mathrm{min}}$ coordinate.

Methods

center_centroid()	Center centroid on origin.
contains(point)	Test region membership of point in Rectangle.
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 Rectangle constructor parameters.
translate(t[, fix_anchor_points])	Translate GeometricRegion points and vectors by Vector t.

Attributes Summary

a	Alias for Rectangle.lx.
area	Rectangle area, $A=\ell_x\ell_y$
b	Alias for Rectangle.ly.
centroid	Rectangle centroid, $(c_x, c_y)$.
lengths	tuple of side lengths
lx	Distance between $x_{\mathrm{max}}-x_{\mathrm{min}}$.
ly	Distance between $y_{\mathrm{max}}-y_{\mathrm{min}}$.
pmax	2D Point at (xmax, ymax).
pmin	2D Point at (xmin, ymin).
xmax	$x_{\mathrm{max}}$ coordinate.
xmin	$x_{\mathrm{min}}$ coordinate.
ymax	$y_{\mathrm{max}}$ coordinate.
ymin	$y_{\mathrm{min}}$ coordinate.

Methods Summary

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

Attributes Documentation

a

Alias for Rectangle.lx.

area

Rectangle area, $A=\ell_x\ell_y$

b

Alias for Rectangle.ly.

centroid

Rectangle centroid, $(c_x, c_y)$.

Computed as the 2D Point $(c_x, c_y)$ with coordinates:

$$c_x = \frac{x_{\mathrm{min}}+x_{\mathrm{max}}}{2}$$ $$c_y = \frac{y_{\mathrm{min}}+y_{\mathrm{max}}}{2}$$

Returns:2D Point of centroid. Return type:Point

lengths

tuple of side lengths

lx

Distance between $x_{\mathrm{max}}-x_{\mathrm{min}}$.

ly

Distance between $y_{\mathrm{max}}-y_{\mathrm{min}}$.

pmax

2D Point at (xmax, ymax).

pmin

2D Point at (xmin, ymin).

xmax

$x_{\mathrm{max}}$ coordinate.

xmin

$x_{\mathrm{min}}$ coordinate.

ymax

$y_{\mathrm{max}}$ coordinate.

ymin

$y_{\mathrm{min}}$ coordinate.

Methods Documentation

contains(point)

Test region membership of point in Rectangle.

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

Notes

A point $(p_x, p_y)$ is within the bounded region of a rectangle with lower corner at $p_{\mathrm{min}}= (x_{\mathrm{min}}, y_{\mathrm{min}})$ and upper corner at $p_{\mathrm{max}}= (x_{\mathrm{max}}, y_{\mathrm{max}})$ if the following is true:

$$x_{\mathrm{min}}\le x\le x_{\mathrm{max}}\land$$ $$y_{\mathrm{min}}\le y\le y_{\mathrm{max}}$$

todict()

Returns a dict of the Rectangle constructor parameters.