Cone

class sknano.core.geometric_regions.Cone(p1=None, p2=None, r=1)

Bases: sknano.core.geometric_regions.Geometric3DRegion

Geometric3DRegion for a cone.

New in version 0.3.10.

Represents a cone with a base of radius \(r\) centered at \(p_1=(x_1,y_1,z_1)\) and a tip at \(p_2=(x_2, y_2, z_2)\).

Parameters:

• p2 (p1,) – 3-tuples or Point class instances for a Cone with a base of radius r centered at \(p_1=(x_1,y_1,z_1)\) and a tip at \(p_2=(x_2,y_2,z_2)\).
• r (float, optional) – Radius \(r\) of Cone base

Notes

Cone represents a bounded cone region \(\left\{p_1+\rho(1-z)\cos(\theta)\mathbf{v}_1 + \rho(1-z)\sin(\theta)\mathbf{v}_2+\mathbf{v}_3 z| 0\le\theta\le 2\pi\land 0\le\rho\le 1\land 0\le z\le 1\right\}\) where \(\mathbf{v}_3=p_2-p_1\) and vectors \((\mathbf{v}_1,\mathbf{v}_2,\mathbf{v}_3)\) are orthogonal with \(|\mathbf{v}_1|=|\mathbf{v}_2|=1\) and \(p_1=(x_1,y_1,z_1)\) and \(p_2=(x_2, y_2, z_2)\).

Calling Cone with no parameters is equivalent to Cone(p1=[0, 0, 0], p2=[0, 0, 2], r=1).

Attributes

axis	Cone axis Vector from \(\boldsymbol{\ell}=p_2 - p_1\)
bounding_box	Bounding Cuboid.
center	Alias for centroid.
centroid	Cone centroid, \((c_x, c_y, c_z)\).
fmtstr	Format string.
measure	Alias for volume, which is the measure of a 3D geometric region.
ndim	Return the dimensions.
p1	Center point \((x_1, y_1, z_1)\) of Cone base.
p2	Point \((x_2, y_2, z_2)\) of Cone tip.
pmax	Point at maximum extent.
pmin	Point at minimum extent.
r	Radius \(r\) of Cone base.
volume	Cone volume, \(V=\frac{1}{3}\pi r^2 \ell\).

Methods

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

Attributes Summary

axis	Cone axis Vector from \(\boldsymbol{\ell}=p_2 - p_1\)
centroid	Cone centroid, \((c_x, c_y, c_z)\).
p1	Center point \((x_1, y_1, z_1)\) of Cone base.
p2	Point \((x_2, y_2, z_2)\) of Cone tip.
r	Radius \(r\) of Cone base.
volume	Cone volume, \(V=\frac{1}{3}\pi r^2 \ell\).

Methods Summary

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

Attributes Documentation

axis

Cone axis Vector from \(\boldsymbol{\ell}=p_2 - p_1\)

Returns: Return type:Vector

centroid

Cone centroid, \((c_x, c_y, c_z)\).

Computed as:

\[c_x = \frac{3 x_1 + x_2}{4}\]\[c_y = \frac{3 y_1 + y_2}{4}\]\[c_z = \frac{3 z_1 + z_2}{4}\]

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

p1

Center point \((x_1, y_1, z_1)\) of Cone base.

p2

Point \((x_2, y_2, z_2)\) of Cone tip.

r

Radius \(r\) of Cone base.

volume

Cone volume, \(V=\frac{1}{3}\pi r^2 \ell\).

Methods Documentation

contains(point)

Test region membership of point in Cone.

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

Notes

A point \((p_x, p_y, p_z)\) is within the bounded region of a cone with a base of radius \(r\) centered at \(p_1=(x_1, y_1, z_1)\) and tip at \(p_2 = (x_2, y_2, z_2)\) if the following is true:

\[0\le q\le 1\land (x_1 - p_x + (x_2 - x_1) q)^2 + (y_1 - p_y + (y_2 - y_1) q)^2 + (z_1 - p_z + (z_2 - z_1) q)^2 \le r^2 q^2\]

where \(q\) is:

\[q = \frac{(p_x - x_1)(x_2 - x_1) + (p_y - y_1)(y_2 - y_1) + (p_z - z_1)(z_2 - z_1)}{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}\]

todict()

Returns a dict of the Cone constructor parameters.