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# sknano.core.geometric_regions.Ellipsoid¶

class sknano.core.geometric_regions.Ellipsoid(center=None, rx=1, ry=1, rz=1)[source][source]

Geometric3DRegion for an ellipsoid.

New in version 0.3.0.

Represents an axis-aligned ellipsoid centered at the point $$(c_x, c_y, c_z)$$ with semi-axes lengths $$r_x, r_y, r_z$$.

Parameters: center : array_like or Point 3-tuple of floats or an instance of the Point class specifying the center point coordinates $$(x,y,z)$$ of the axis-aligned Ellipsoid with semi-axes lengths rx, ry, rz. rx, ry, rz : float, optional Semi-axes lengths $$r_x, r_y, r_z$$ of axis-aligned Ellipsoid centered at center.

Notes

Ellipsoid represents the axis-aligned ellipsoid:

$\left\{\{x, y, z\}\in R^3| \left(\frac{x-c_x}{r_x}\right)^2 + \left(\frac{y-c_y}{r_y}\right)^2 + \left(\frac{z-c_z}{r_z}\right)^2\le 1\right\}$

Calling Ellipsoid with no parameters is equivalent to Ellipsoid(center=[0, 0, 0], rx=1, ry=1, rz=1).

Attributes

 center Ellipsoid center point $$(c_x, c_y, c_z)$$. centroid Alias for center. fmtstr Format string. measure Alias for volume, which is the measure of a 3D geometric region. rx Length of semi-axis $$r_x$$. ry Length of semi-axis $$r_y$$. rz Length of semi-axis $$r_z$$. volume Ellipsoid volume, $$V=\frac{4}{3}\pi r_x r_y r_z$$.

Methods

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