(49g 50g) Shoelace algorithm

[Albert Chan]

Is this a valid RPL program ?

\(A=\frac{1}{2}|\sum_{i=1}^{n}(x_{i+1}+x_{i})(y_{i+1}-y_{i})|\)

where \(x_{n+1}=x_{1}\) and \(y_{n+1}=y_{1}\).

(xs ys -- area)

Code:

« DUP HEAD + ΔLIST               @ do y diff
  SWAP DUP DUP HEAD + TAIL ADD   @ do x sums
  * ∑LIST ABS 2 /                @ do area
»