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# sknano.core.geometric_regions.Parallelepiped¶

class sknano.core.geometric_regions.Parallelepiped(o=None, u=None, v=None, w=None)[source][source]

Geometric3DRegion for a parallelepiped.

New in version 0.3.0.

Represents a parallelepiped with origin $$(o_x, o_y, o_z)$$ and direction vectors $$\mathbf{u}=(u_x, u_y, u_z)$$, $$\mathbf{v}=(v_x, v_y, v_z)$$, and $$\mathbf{w}=(w_x, w_y, w_z)$$.

Parameters: o : array_like, optional Parallelepiped origin. If None, it defaults to o=[0, 0, 0]. u, v, w : array_like, optional Parallelepiped direction vectors stemming from origin o. If None, then the default values are u=[1, 0, 0], v=[1, 1, 0], and w=[0, 1, 1].

Notes

Parallelepiped represents the bounded region $$\left\{o+\lambda_1\mathbf{u}+\lambda_2\mathbf{v}+ \lambda_3\mathbf{w}\in R^3|0\le\lambda_i\le 1\right\}$$, where $$\mathbf{u}$$, $$\mathbf{v}$$, and $$\mathbf{w}$$ have to be linearly independent.

Calling Parallelepiped with no parameters is equivalent to Parallelepiped(o=[0, 0, 0], u=[1, 0, 0], v=[1, 1, 0], w=[0, 1, 1]).

Attributes

 center Alias for centroid. centroid Parallelepiped centroid, $$(c_x, c_y, c_z)$$. fmtstr Format string. measure Alias for volume, which is the measure of a 3D geometric region. o 3D point coordinates $$(o_x, o_y, o_z)$$ of origin. u 3D direction vector $$\mathbf{u}=(u_x, u_y, u_z)$$, with origin o v 3D direction vector $$\mathbf{v}=(v_x, v_y, v_z)$$, with origin o volume Parallelepiped volume, $$V$$. w 3D direction vector $$\mathbf{w}=(w_x, w_y, w_z)$$, with origin o

Methods

 center_centroid() Center centroid on origin. contains(point) Test region membership of point in Parallelepiped. rotate([angle, axis, anchor_point, ...]) Rotate GeometricRegion points and vectors. todict() Returns a dict of the Parallelepiped constructor parameters. translate(t[, fix_anchor_points]) Translate GeometricRegion points and vectors by Vector t.