Cuboid

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

Bases: sknano.core.geometric_regions.Geometric3DRegion

Geometric3DRegion for a cuboid.

New in version 0.3.0.

Represents an axis-aligned cuboid with lower corner $p_{\mathrm{min}}= (x_{\mathrm{min}},y_{\mathrm{min}},z_{\mathrm{min}})$ and upper corner $p_{\mathrm{max}}= (x_{\mathrm{max}},y_{\mathrm{max}},z_{\mathrm{max}})$.

Parameters:

• pmax (pmin,) – The minimum and maximum 3D point coordinates of the axis-aligned cuboid from pmin=[xmin, ymin, zmin] to pmax=[xmax, ymax, zmax].
• ymin, zmin (xmin,) – The minimum $(x, y, z)$ coordinates of the axis-aligned cuboid.
• ymax, zmax (xmax,) – The maximum $(x, y, z)$ coordinates of the axis-aligned cuboid.

Notes

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

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

Attributes

a	Alias for Cuboid.lx.
abc	Alias for Cuboid.lengths.
b	Alias for Cuboid.ly.
bounding_box	Bounding Cuboid.
c	Alias for Cuboid.lz.
center	Alias for centroid.
centroid	Cuboid centroid, $(c_x, c_y, c_z)$.
fmtstr	Format string.
lengths	tuple of side lengths
lx	Distance between $x_{\mathrm{max}}-x_{\mathrm{min}}$.
ly	Distance between $y_{\mathrm{max}}-y_{\mathrm{min}}$.
lz	Distance between $z_{\mathrm{max}}-z_{\mathrm{min}}$.
measure	Alias for volume, which is the measure of a 3D geometric region.
ndim	Return the dimensions.
pmax	Point at maximum extent.
pmin	Point at minimum extent.
volume	Cuboid volume, $V=\ell_x\ell_y\ell_z$.
xmax	$x_{\mathrm{max}}$ coordinate.
xmin	$x_{\mathrm{min}}$ coordinate.
ymax	$y_{\mathrm{max}}$ coordinate.
ymin	$y_{\mathrm{min}}$ coordinate.
zmax	$z_{\mathrm{max}}$ coordinate.
zmin	$z_{\mathrm{min}}$ coordinate.

Methods

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

Attributes Summary

a	Alias for Cuboid.lx.
abc	Alias for Cuboid.lengths.
b	Alias for Cuboid.ly.
c	Alias for Cuboid.lz.
centroid	Cuboid centroid, $(c_x, c_y, c_z)$.
lengths	tuple of side lengths
lx	Distance between $x_{\mathrm{max}}-x_{\mathrm{min}}$.
ly	Distance between $y_{\mathrm{max}}-y_{\mathrm{min}}$.
lz	Distance between $z_{\mathrm{max}}-z_{\mathrm{min}}$.
pmax	Point at maximum extent.
pmin	Point at minimum extent.
volume	Cuboid volume, $V=\ell_x\ell_y\ell_z$.
xmax	$x_{\mathrm{max}}$ coordinate.
xmin	$x_{\mathrm{min}}$ coordinate.
ymax	$y_{\mathrm{max}}$ coordinate.
ymin	$y_{\mathrm{min}}$ coordinate.
zmax	$z_{\mathrm{max}}$ coordinate.
zmin	$z_{\mathrm{min}}$ coordinate.

Methods Summary

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

Attributes Documentation

a

Alias for Cuboid.lx.

abc

Alias for Cuboid.lengths.

b

Alias for Cuboid.ly.

c

Alias for Cuboid.lz.

centroid

Cuboid centroid, $(c_x, c_y, c_z)$.

Computed as the 3D Point $(c_x, c_y, c_z)$ with coordinates:

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

Returns:3D Point of centroid. Return type:Point

lengths

tuple of side lengths

lx

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

ly

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

lz

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

pmax

Point at maximum extent.

pmin

Point at minimum extent.

volume

Cuboid volume, $V=\ell_x\ell_y\ell_z$.

xmax

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

xmin

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

ymax

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

ymin

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

zmax

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

zmin

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

Methods Documentation

contains(point)

Test region membership of point in Cuboid.

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

Notes

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

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

todict()

Returns a dict of the Cuboid constructor parameters.