We propose a novel and automatic method to model shapes using a small set of discrete developable patches. Central to our approach is using implicit neural shape representation that makes our algorithm independent of tessellation and allows us to obtain the Gaussian curvature of each point analytically. With this powerful representation, we first deform the input shape to be an almost developable shape with clear and sparse salient feature curves. Then, we convert the deformed implicit field to a triangle mesh, which is further cut to disk topology along parts of the sparse feature curves. Finally, we achieve the resulting piecewise developable mesh by alternatingly optimizing discrete developability, enforcing manufacturability constraints, and merging patches. The feasibility and practicability of our method are demonstrated over various shapes. Compared to the state-of-the-art methods, our method achieves a better tradeoff between the number of developable patches and the approximation error.