Question

If you have an equilateral triangle in 3D space, where all the sides are of length 1, there are two points that you could use to form a tetrahedron. One floating out in front of the triangle, and one behind it. Given the coordinates of the three known vertices, how would you calculate either of the possible fourth vertices?

I would really appreciate it if you can show how to do it with the Processing vector class definition

Answer 1

Average your three points to get the center of the triangle:

center = (a + b + c) / 3

Calculate the normal vector by taking the cross product of two of the sides:

normal = (c - a) x (b - a)

Normalize the normal vector (make it of unit length):

unit_normal = normal / |normal|

Scale the normal by the height of regular tetrahedron:

scaled_normal = unit_normal * sqrt(2/3)

Now, your two points are:

top = center + scaled_normal
bottom = center - scaled_normal