Bending-active structures are curved structures created using initially planar components that have been elastically bent so that they take on a three-dimensional shape. The 3D shape that the structure assumes depends not only on the applied external forces, but also on the elastic properties of the physical material used. By altering the fine-scale structure of this material, we are able to locally control its macroscopic elastic properties. We introduce a computational framework for the inverse design of custom 3D surfaces using bending-active structures. We optimize the internal structure of laser-cut planar surface strips, so that they approximate a desired 3D freeform surface when being clamped at both extremities. The specific orthotropic design of the structure of the strips allows us to locally control their bending behavior. In contrast to past work the planar surface strips can be of arbitrary shape, not necessarily rectangular, and when deformed, they form a piecewise continuous surface.