Function nearest_point_from_point_to_line

pub fn nearest_point_from_point_to_line<F, const D: usize>(
    point: &Matrix<F, Const<D>, Const<1>, ArrayStorage<F, D, 1>>,
    line: &(Matrix<F, Const<D>, Const<1>, ArrayStorage<F, D, 1>>, Matrix<F, Const<D>, Const<1>, ArrayStorage<F, D, 1>>),
) -> (F, Matrix<F, Const<D>, Const<1>, ArrayStorage<F, D, 1>>, F)
where
    F: Copy + RealField,

Calculate the point on a line which is closest to an external given point.

This function takes an external point $\vec{p}$ and a line segment described by two points $\vec{p}_1,\vec{p}_2$. It returns a tuple $(d, \vec{x}, q)$ which contains the distance $d$ between the calculated nearest point and the external point, the calculated point $\vec{x}$ and a fractional value $0\leq q\leq 1$ which is the relative length of the calculated nearest point between the points of the given line segment given by: $$\vec{x} = (1-q)\vec{p}_1 + q\vec{p}_2$$

use nalgebra::Vector2;

let external_point = Vector2::from([0f64; 2]);
let line_segment = (
    Vector2::from([1.0, 0.0]),
    Vector2::from([-1.0, 2.0]),
);
let (dist, point, rel_length) = nearest_point_from_point_to_line(
    &external_point,
    &line_segment,
);

assert!((dist - 1.0/2f64.sqrt()).abs() < 1e-10);
assert!((rel_length - 0.25).abs() < 1e-10);
assert!((point.x - 0.5).abs() < 1e-10);
assert!((point.y - 0.5).abs() < 1e-10);