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.