Ellipse

class sknano.core.geometric_regions.Ellipse(center=None, rx=1, ry=1)

Bases: sknano.core.geometric_regions.Geometric2DRegion

Geometric2DRegion for an ellipse.

New in version 0.3.0.

Represents an axis-aligned ellipse centered at \((c_x, c_y)\) with semi-axes lengths \(r_x, r_y\).

Parameters:

• center (array_like, optional) – Center of axis-aligned ellipse with semi-axes lengths \(r_x, r_y\)
• ry (rx,) – Lengths of semi-axes \(r_x, r_y\)

Notes

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

Attributes

area	Ellipse area, \(A=\pi r_x r_y\).
bounding_box	Bounding Cuboid.
center	Ellipse center point \((c_x, c_y)\).
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.
rx	Length of semi-axis \(r_x\).
ry	Length of semi-axis \(r_y\).

Methods

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

Attributes Summary

area	Ellipse area, \(A=\pi r_x r_y\).
center	Ellipse center point \((c_x, c_y)\).
centroid	Alias for center.
rx	Length of semi-axis \(r_x\).
ry	Length of semi-axis \(r_y\).

Methods Summary

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

Attributes Documentation

area

Ellipse area, \(A=\pi r_x r_y\).

center

Ellipse center point \((c_x, c_y)\).

centroid

Alias for center.

rx

Length of semi-axis \(r_x\).

ry

Length of semi-axis \(r_y\).

Methods Documentation

contains(point)

Test region membership of point in Ellipse.

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

Notes

A point \((p_x, p_y)\) is within the bounded region of an ellipse with center \((c_x, c_y)\) and semi-axes lengths \(r_x, r_y\) if the following is true:

\[\left(\frac{p_x - c_x}{r_x}\right)^2 + \left(\frac{p_y - c_y}{r_y}\right)^2\le 1\]

todict()

Returns a dict of the Ellipse constructor parameters.