Developable surfaces are generated by interactively evolving curves on a 2D surface embedded in 3D space using an iterative process to produce a model for the construction of a stylized three dimensional sculpture. Each iteration includes tessellating loops formed by the curves on the surface and unfolding the resulting tessellated strips onto a 2D plane. Collisions between the unfolded tessellated strips in 2D and between the loops in 3D are resolved, and the rendered evolved curve in 3D and tessellated strips in 2D are displayed simultaneously during the evolution. A graphical user interface allows the curve network, tessellated strips, and curve evolution parameters to be modified by a user. 2D textures may be mapped to the unfolded tessellated strips, and a set of tool paths may be output for cutting a 2D material.