Forward and Inverse D-Form Modelling based on Optimisation

D-Form is a special piece-wise developable surface formed by aligning the boundaries of two planar domains. It has been widely used in different design scenarios. In this paper, we study how to computationally and intuitively model D-Forms. We present an optimisation-based framework that can efficiently generate D-Form shapes. Our framework can model D-Forms with two approaches based on two different user inputs, including the forward modelling from two given planar domains and, more importantly, the inverse modelling from a given space curve where the planar domains are no longer needed. Our optimisation is devised based on two critical characteristics of D-Forms. Firstly, the constituent developable surfaces of a D-Form are isometrically deformed from planar domains. Secondly, there is a close relationship between a D-Form and the convex hull of its seam. Through extensive evaluation, we demonstrate that our approach can model plausible D-Forms efficiently from various inputs with different geometric properties.