Easily Dealing with Any-Dimensional Planes

4 months ago

A plane is an n-1 dimensional sub-space of an n-dimensional space that is flat.
A plane can be fully specified using a normal vector (`n`) and any point within the plane (`o`).
The condition for a point `p` to lie on the plane is `dot(p - o, n) = 0`.
The plane can be represented using the normal vector and the scalar value `dot(o, n)`, which is the distance from the origin to the plane along the normal.
A hyperplane representation is suggested using a template `hyperplane = vec<ScalarT, N+1>`.
Operations like finding the distance from a point to the plane or checking if two planes are parallel are simplified with this representation.
The logic generalizes to higher dimensions as well as to lower dimensions, such as lines in 2D space.

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