Optimizing contact-based assemblies

Davi Colli Tozoni, Yunfan Zhou, Denis Zorin

Research output: Contribution to journalArticlepeer-review


Modern fabrication methods have greatly simplified manufacturing of complex free-form shapes at an affordable cost, and opened up new possibilities for improving functionality and customization through automatic optimization, shape optimization in particular. However, most existing shape optimization methods focus on single parts. In this work, we focus on supporting shape optimization for assemblies, more specifically, assemblies that are held together by contact and friction. Examples of which include furniture joints, construction set assemblies, certain types of prosthetic devices and many other. To enable this optimization, we present a framework supporting robust and accurate optimization of a number of important functionals, while enforcing constraints essential for assembly functionality: weight, stress, difficulty of putting the assembly together, and how reliably it stays together. Our framework is based on smoothed formulation of elasticity equations with contact, analytically derived shape derivatives, and robust remeshing to enable large changes of shape, and at the same time, maintain accuracy. We demonstrate the improvements it can achieve for a number of computational and experimental examples.

Original languageEnglish (US)
Article number269
JournalACM Transactions on Graphics
Issue number6
StatePublished - Dec 10 2021


  • additive fabrication
  • deformable objects
  • shape optimization

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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