We propose a novel way of computing surface folding maps via solving a linear PDE.This framework is a generalization to the existing quasiconformal methods and allows manipulation of the geometry of folding. Moreover, the crucial quantity that characterizes the geometry occurs as the coefficient of the equation, namely the Alternating Beltrami Coefficient (ABC). This allows us to solve an inverse problem of parametrizing the folded surface given only partial data but with known folding topology. Various interesting applications such as fold sculpting on 3D models and self-occlusion reasoning are demonstrated to show the effectiveness of our method. This is a joint work with Qiu DI. This work is supported by HKRGC GRF.