How to normalize a position in 3d game?
Assuming each coordinate axis has a fixed max and min value, and $|min_{x}| = max_{x}$, $|min_{y}| = max_{y}$, $|min_{z}| = max_{z}$, the standard normalisation procedure would be:

$$ (x,y,z) \mapsto (\frac{x}{max_{x}},\frac{y}{max_{y}},\frac{z}{max_{z}})$$

I.e. mapping the values to within the range $(-1,-1,-1)$ to $(1,1,1)$.



E.g. if your corrdinate system was fixed between $-100$ and $100$ for each axis, the coordinate $(10,-52,-8)$ would normalise to:

$$ (10,-52,-8) \mapsto (\frac{10}{100},\frac{-52}{100},\frac{-8}{100}) = (0.1, -0.52, -0.08)$$