Some math to explore 3D rotation, find the center point of the orbit.

rotate.js

axie = k1 * (x*i + y*j + z*k)
point = a*i + b*j + c*k

distance = (k1*x - a)*i + (k1*y - b)*j + (k1*z - c)*k

0 = axie * distance = k1 * (x*i + y*j + z*k) * ((k1*x - a)*i + (k1*y - b)*i + (k1*z - c)k)

0 = (x*i + y*j + z*k) * ((k1*x - a)*i + (k1*y - b)*i + (k1*z - c)k)
  = (x*i) * ((k1*x - a)*i + (k1*y - b)*j + (k1*z - c)k)
    + y*j * ((k1*x - a)*i + (k1*y - b)*j + (k1*z - c)k)
    + z*k * ((k1*x - a)*i + (k1*y - b)*j + (k1*z - c)k)
  = ((k1*x - a)*x*i + (k1*y - b)*x*j + (k1*z - c)*x*k)i
    + ((k1*x - a)*y*i + (k1*y - b)*y*j + (k1*z - c)*y*k)j
    + ((k1*x - a)*z*i + (k1*y - b)*z*j + (k1*z - c)*z*k)k
  = (-(k1*x - a)*x - (k1*y - b)*x*k + (k1*z - c)*x*j)
    + ((k1*x - a)*y*k - (k1*y - b)*y - (k1*z - c)*y*i)
    + (-(k1*x - a)*z*j + (k1*y - b)*z*i - (k1*z - c)*z)
  = - (k1*x - a)*x - (k1*y - b)*y - (k1*z - c)*z
    + (k1*y - b)*z*i - (k1*z - c)*y*i
    + (k1*z - c)*x*j - (k1*x - a)*z*j
    + (k1*x - a)*y*k - (k1*y - b)*x*k


0 = - (k1*x - a)*x - (k1*y - b)*y - (k1*z - c)*z
  = - k1*x^2 + a*x - k1*y^2 + b*y - k1*z^2 + c*z
  = k1(- x^2 - y^2 - z^2) + a*x + b*y + c*z

k1 = (a*x + b*y + c*z)/(x^2 + y^2 + z^2)