Module geometry 

Vectors of the three-dimensional Euclidean space, as [f64; 3]: the scalar product, the difference, the norm and the direction of a vector, and the unit vector of spherical angles.

The geometry of the antenna arrays of the CDL channel and of the indoor optical channel (positions, directions, orientations) is written with these.

Examples

use comnum_math::geometry::{difference, dot, norm, unit};
let (a, b) = ([1.0, 2.0, 2.0], [1.0, 0.0, 0.0]);
assert_eq!(dot(a, b), 1.0);
assert_eq!(norm(a), 3.0);
assert_eq!(difference(a, b), [0.0, 2.0, 2.0]);
assert_eq!(unit([0.0, 0.0, -2.0]), Some([0.0, 0.0, -1.0]));

Spherical angles

from_spherical takes the zenith (polar) angle $\theta$ from $+z$ and the azimuth $\phi$ from $+x$ towards $+y$, in radians (ISO 80000-2; the angles of 3GPP TR 38.901, (7.5-23)):

$$ \hat{r}(\theta, \phi) = (\sin\theta \cos\phi,\ \sin\theta \sin\phi,\ \cos\theta)^{T}. $$

An elevation $\epsilon$ above the $xy$ plane is the zenith $\theta = \pi/2 - \epsilon$.

Functions

difference

The difference $a - b$.

dot

The scalar product $a \cdot b = a_{0} b_{0} + a_{1} b_{1} + a_{2} b_{2}$.

from_spherical

The unit vector $\hat{r}(\theta, \phi) = (\sin\theta \cos\phi, \sin\theta \sin\phi, \cos\theta)$ of the zenith zenith_rad (from $+z$) and the azimuth azimuth_rad (from $+x$ towards $+y$), see the module.

norm

The Euclidean norm $\lVert a \rVert = \sqrt{a \cdot a}$.

unit

The direction $a / \lVert a \rVert$ of a; None for a zero or non-finite norm.

Type Aliases

Vec3

A vector of the three-dimensional space.