Cylinder

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

Bases: sknano.core.geometric_regions.Geometric3DRegion

Geometric3DRegion for a cylinder.

New in version 0.3.10.

Represents a cylinder of radius $r$ around the line from $(x_1, y_1, z_1)$ to $(x_2, y_2, z_2)$.

Parameters:

• p2 (p1,) – 3-tuples or Point class instances specifying the Cylinder axis from point $p_1=(x_1,y_1,z_1)$ to $p_2=(x_2,y_2,z_2)$.
• r (float, optional) – Cylinder radius $r$

Notes

Cylinder represents a cylinder region $\left\{p_1+\rho\cos(\theta)\mathbf{v}_1 + \rho\sin(\theta)\mathbf{v}_2 + \mathbf{v}_3 z| 0\le\theta\le 2\pi\land 0\le\rho\le 1\land 0\le z\le 1\right\}$ where $\mathbf{v}_3=p_2 - p_1$ and the 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 Cylinder with no parameters is equivalent to Cylinder(p1=[0, 0, -1], p2=[0, 0, 1], r=1).

Attributes

axis	Cylinder axis Vector $\boldsymbol{\ell}=p_2 - p_1$.
bounding_box	Bounding Cuboid.
center	Alias for centroid.
centroid	Cylinder 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	Cylinder axis point $p_1=(x_1, y_1, z_1)$.
p2	Cylinder axis point $p_2=(x_2, y_2, z_2)$.
pmax	Point at maximum extent.
pmin	Point at minimum extent.
r	Cylinder radius $r$.
volume	Cylinder volume, $V=\pi r^2 \ell$.

Methods

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

Attributes Summary

axis	Cylinder axis Vector $\boldsymbol{\ell}=p_2 - p_1$.
centroid	Cylinder centroid, $(c_x, c_y, c_z)$.
p1	Cylinder axis point $p_1=(x_1, y_1, z_1)$.
p2	Cylinder axis point $p_2=(x_2, y_2, z_2)$.
r	Cylinder radius $r$.
volume	Cylinder volume, $V=\pi r^2 \ell$.

Methods Summary

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

Attributes Documentation

axis

Cylinder axis Vector $\boldsymbol{\ell}=p_2 - p_1$.

Returns:3D Vector along Cylinder axis from Point $p_1=(x_1, y_1, z_1)$ to Point $p_2=(x_2, y_2, z_2)$. Return type:Vector

centroid

Cylinder centroid, $(c_x, c_y, c_z)$.

Computed as:

$$c_x = \frac{x_1 + x_2}{2}$$ $$c_y = \frac{y_1 + y_2}{2}$$ $$c_z = \frac{z_1 + z_2}{2}$$

p1

Cylinder axis point $p_1=(x_1, y_1, z_1)$.

p2

Cylinder axis point $p_2=(x_2, y_2, z_2)$.

r

Cylinder radius $r$.

volume

Cylinder volume, $V=\pi r^2 \ell$.

Methods Documentation

contains(point)

Test region membership of point in Cylinder.

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

Notes

A point $(p_x, p_y, p_z)$ is within the bounded region of a cylinder with radius $r$ around the line from $p_1=(x_1, y_1, z_1)$ to $p_2 = (x_2, y_2, z_2)$ if the following is true:

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

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 Cylinder constructor parameters.