Forward and inverse D-Form modelling based on optimisation

Abstract

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 generates 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 sometrically deformed from planar domains. Secondly, there is a close relationship between a D-Form and the convex hull of its seam. We also add other constraints to make the algorithm robust and generalised. Through extensive evaluation, we demonstrate that our approach can model plausible D-Forms efficiently from various inputs with different geometric properties.several cases and evaluated through numerical studies. Our algorithm is the first completed tool for modelling D-Forms. And we hope it enables new investigations into piece-wise developable surfaces.