Flow of the lens model: Dashed line is the primary curve ξ whose parametrization is shown in Eq. (4). Given a primary curve the function ζ (shown in Eq. (9)) is a coordinate system that labels the points on the image plane with coordinates t,s. The transitive lensing function $\tilde{y}$ (defined in Eq. (10)) maps the points on the t−s plane onto the source plane. Combining $\tilde{y}$ with the inverse function ζ⁻¹ gives us the lensing function y that maps the image plane to the source plane.