What is the equation of a pyramid with a square base?

Question

Which algebraic description can be found for a pyramid, defined as a scalar function $$f:\mathbb{R}^2 \rightarrow \mathbb{R}$$ $$(x,y)\rightarrow z$$

Particular assumptions: Square base $z=0 \iff x=(0,t) \lor (t,0)$ $\forall K \ge t \ge 0 $

Answer 1

Given the center of a square pyramid of area $L^2$, $(x_c,y_c)$, and its height $z_{max}$ a mapping is given by: $$ z(x,y)=z_{max}(1- \frac{max(\lvert x-x_c \rvert ,\lvert y-y_c \rvert)}{L}) $$

This should be enough to compute the pyramid. Other operations might benefit from the formulation as an optimization problem and then re-formulation to a non linear equations system.