- #1

sqljunkey

- 175

- 7

So if this was in one dimension, and at p1 I had 90 degrees and p2 I had 80 degrees and I would get that the change in temperature is -10. telling me that if I go in the direction of p2 my temperature will decrease.

Someone helped me out for the case of 3d, But I don't quite understand it.

if p_1, ..., p_8 are your points and

w_1, ..., w_8 are your weights (or temperatures) and p is

the point in the middle, calculate T := Sum w_i * (p_i - p)

* (p_i - p)^T for 1 <= i <= 8, and then calculate the

eigenvectors v_1, v_2, v_3 and according eigenvalues l_1,

l_2, l_3 of T, and then pick the v_k where abs(l_k) is > 0

and the greatest or smallest of all abs(l_j) [for 1 <= j,k

<= 3]

if the point p in the middle has a temperature (w)

as well, you should to use (w_i - w) instead of w_i of course

You could also "normalize" your tensor T by multiplying with

1 / Sum w_i (or 1 / Sum (w_i - w) if you have w), but that

makes no difference for the eigenvectors

Can anybody help me?