From Bézier to NURBS: Integrating Material and Digital Techniques through a Plywood Shell

The development of digital fabrication has reintroduced material processes with digital processes. There has been much discussion about the tool and the objects of the tool, but little discussion of the implication of the material process on the digital process. A brief historical review on the development of computer numerical control and the origins of the Bezier curve reveals an instrumental fact: computer numerical controlled tools necessitated advancements in computational surfaces which eventually led to NURBS (Non-Uniform Rational B-Splines) surfaces. In other words, the origins of NURBS surfaces resides in its relation to material processes, rather than many current approaches that develop free form surfaces and then force the tool onto the material without regard to the material properties. From this historical and mathematical review, this project develops toward more intelligent construction methods based on the integration of NURBS differential geometry paired with material qualities and processes. Specifically, a digital technique of developing conceptual NURBS geometry into piecewise surface patches are then flattened based on the material thickness and density. From these flattened patches, a material technique is developed to intelligently remove material to allow the rigid flat material to re-develop into physical surface patches. The goal of this research is to develop digital and material techniques toward intelligent construction based on the correspondence between digitally driven surface and digitally driven material processes. The application of this technique as a rational and flexible system is to support the dynamic response of form and material toward such performative aspects as structure, daylight, ventilation, and thermal properties. “Each idea must be related to the principle of a material system, simple and primitive though it may look, on which a variable solution could be based.” Gerald Farin, Curves and Surfaces for Computer Aided Geometric Design