How do you get 3D gradient direction and magnitude ?

Hi all,

I know that we can get the magnitude and direction from 2D gradient ?

1) mag(Gx,Gy)  = sqrt ( Gx^2 + Gy^2 )
2) angle(Gx, Gy) = tan^-1 (Gy/Gx)

What about in 3D?

1) mag(Gx,Gy,Gz)  = sqrt ( Gx^2 + Gy^2 + Gz^2 )
2) angle(Gx,Gy,Gz) = ???

I seriously need your help. Many, many thanks, Gary

Answer 1

[Matt J]

I'd probably define direction this way

 angle(Gx,Gy,Gz) = [Gx,Gy,Gz]/mag(Gx,Gy,Gz)

[Gary Tsui]

Hi Matt, thanks, would you please further elaborate on the definition of [Gx,Gy,Gz]?

[Youssef Khmou]

Gi, is the ith matrix