To treat an object with an arbitrary geometry using PO, the object is first decomposed into many small elementary patches or cells, which have a simple geometry such as a rectangle or triangle. Then, using the tangent plane approximation, the equivalent electric and magnetic surface currents, '''J(r)''' and '''M(r)''', on the lit region of the scatterer are approximated by:
:<math> \mathbf{J(r)} = (\mathbf{\hat{n}\times} \begin{bmatrix} 1+-\alphaGamma_{||} & 0 \\ 0 & 1-\Gamma_{\perp}} \end{bmatrix} \cdot \begin{bmatrix} I^{(J) } \\ V^{(M)} \end{bmatrix} \mathbf{\hat{n} \times H(r)} </math>
:<math> \mathbf{M(r)} = -(1-\alpha) \mathbf{\hat{n} \times E(r)} </math>
:<math> \begin{bmatrix} Z^{(EJ)} & T^{(EM)} \\ U^{(HJ)} & Y^{(HM)} \end{bmatrix} \cdot \begin{bmatrix} I^{(J)} \\ V^{(M)} \end{bmatrix} = \begin{bmatrix} V^{(E)} \\ I^{(M)} \end{bmatrix} </math>