Function triangle_3d_area_squared 

pub fn triangle_3d_area_squared<S>(
    a: Point3<S>,
    b: Point3<S>,
    c: Point3<S>,
) -> NonNegative<S>
where
    S: OrderedField + Sqrt + AbsDiffEq<Epsilon = S>,

Square area of three points in 3D space.

Uses a numerically stable Heron’s formula: https://en.wikipedia.org/wiki/Heron%27s_formula#Numerical_stability

assert_relative_eq!(
  3.0/4.0,
  *triangle_3d_area_squared (
    [-1.0,  0.0,  0.0].into(),
    [ 0.0,  0.0,  1.0].into(),
    [ 0.0,  1.0,  0.0].into())
);

If the area squared is zero then the points are colinear:

assert_eq!(
  0.0,
  *triangle_3d_area_squared (
    [-1.0, -1.0, -1.0].into(),
    [ 0.0,  0.0,  0.0].into(),
    [ 1.0,  1.0,  1.0].into())
);