The topic of this paper is the connection of digital modelling with generative programming and rapid prototyping, to produce physical sketch surface models. The physical surface models are assembled out of developable strips connected through a puzzle-like detail. The use of programming as a design approach allows the generation of connection details that corresponds to the rules of flat sheet rapid prototyping techniques of laser cutting and water jet cutting. With numerically controlled cutting, there is no need to keep the joint detail related to manually achievable forms or to apply a standardized dimension. This paper demonstrates the possibilities of programming to generate cutting geometries that adapt to the local surface properties. The larger perspective of the research approach is the question of how to formulate and capture design intention through programming. What influence does the use of generative modelling in combination with rapid prototyping have on the design language of physical objects?