sknano.core.geometric_regions.Cone

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

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:

p1, p2 : array_like, optional

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 \(\boldsymbol{\ell}=p_2 - p_1\)
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.
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

center_centroid()	Center centroid on origin.
contains(point)	Test region membership of point in Cone.
rotate([angle, axis, anchor_point, ...])	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.