Question

I have planes in 3D space defined by a normal vector and a center point. I’d like to determine whether these planes are horizontal or perpendicular to the ground floor, or neither. Usually, this can be found by is how it can be found:

a.b = |a||b|cos(t)

where a and b are two 3D vectors.

If a.b = 0, then they are perpendicular to each other; If a.b is equal to the product of lengths of a and b, the cosine of t is 1 and t is 0, so they are parallel

But I don’t have a ground plane!!!!

Many thanks

Answer 1

You will need to identify what you’re calling a ground plane. A couple ways of determining this plane are:

1. Pick a reference ground plane. For instance if you’re interested in
   using the X-Y plane as your ground plane, the normal you would use
   is just <0, 0, 1>.

2. If your situations doesn’t permit easy use of an axially aligned reference
   plane, pick three non-colinear points on your reference ground plane, T,
   U, V. Then the normal to the plane containing the three points
   is given by N = +/-[ (U-T) x (V-T) ] where x is the cross product
   operator.