We consider planar liquid crystal elastomers: two-dimensional objects made of anisotropic responsive materials that remain flat when stimulated, however change their planar shape. We derive a closed form, analytical solution based on the implicit linearity featured by this subclass of deformations. Our solution provides the nematic director field on an arbitrary domain starting with two initial director curves. We discuss the different gauge choices for this problem and the inclusion of disclinations in the nematic order. Finally, we propose several applications and useful design principles based on this theoretical framework.