Forward and Inverse D-Form Modelling based on Optimisation

Avery Huang, Caigui Jiang, Tony Wills, Yongliang Yang

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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.

Original languageEnglish
Article number103467
JournalComputer-Aided Design
Early online date7 Jan 2023
Publication statusPublished - 30 Apr 2023


  • D-Form
  • Developable surfaces
  • Isometric deformation
  • Optimisation

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering

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