Computational design of cold bent glass façades

Cold bent glass is a promising and cost-efficient method for realizing doubly curved glass façades. They are produced by attaching planar glass sheets to curved frames and must keep the occurring stress within safe limits. However, it is very challenging to navigate the design space of cold bent glass panels because of the fragility of the material, which impedes the form finding for practically feasible and aesthetically pleasing cold bent glass façades. We propose an interactive, data-driven approach for designing cold bent glass façades that can be seamlessly integrated into a typical architectural design pipeline. Our method allows non-expert users to interactively edit a parametric surface while providing real-time feedback on the deformed shape and maximum stress of cold bent glass panels. The designs are automatically refined to minimize several fairness criteria, while maximal stresses are kept within glass limits. We achieve interactive frame rates by using a differentiable Mixture Density Network trained from more than a million simulations. Given a curved boundary, our regression model is capable of handling multistable configurations and accurately predicting the equilibrium shape of the panel and its corresponding maximal stress. We show that the predictions are highly accurate and validate our results with a physical realization of a cold bent glass surface.

[1]  Yin Yang,et al.  Stress‐Constrained Thickness Optimization for Shell Object Fabrication , 2017, Comput. Graph. Forum.

[2]  Olga Sorkine-Hornung,et al.  Wallpaper pattern alignment along garment seams , 2019, ACM Trans. Graph..

[3]  Markus H. Gross,et al.  Interactive design of 3D-printable robotic creatures , 2015, ACM Trans. Graph..

[4]  Eder Miguel,et al.  FlexMaps: computational design of flat flexible shells for shaping 3D objects , 2019, ACM Trans. Graph..

[5]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[6]  Martin Kilian,et al.  Paneling architectural freeform surfaces , 2010, SIGGRAPH 2010.

[7]  M. Kilian,et al.  Paneling architectural freeform surfaces , 2010, ACM Trans. Graph..

[8]  C. Weischedel A discrete geometric view on shear-deformable shell models , 2012 .

[9]  Markus H. Gross,et al.  Stenciling: Designing Structurally‐Sound Surfaces with Decorative Patterns , 2016, Comput. Graph. Forum.

[10]  Bernd Bickel,et al.  State of the Art on Stylized Fabrication , 2018, Comput. Graph. Forum.

[11]  Jan Belis,et al.  Cold bending of laminated glass panels , 2007 .

[12]  Eitan Grinspun,et al.  Computing discrete shape operators on general meshes , 2006, Comput. Graph. Forum.

[13]  Johannes Wallner,et al.  Geometric Modeling with Conical Meshes and Developable Surfaces , 2006, ACM Trans. Graph..

[14]  David I. W. Levin,et al.  Latent‐space Dynamics for Reduced Deformable Simulation , 2019, Comput. Graph. Forum.

[15]  Harry Giles,et al.  Quadrilateral panelization of freeform surface structures , 2017 .

[16]  Mark Pauly,et al.  X-Shells , 2019, ACM Trans. Graph..

[17]  Huamin Wang,et al.  NNWarp: Neural Network-Based Nonlinear Deformation , 2020, IEEE Transactions on Visualization and Computer Graphics.

[18]  Iasonas Kokkinos,et al.  CreativeAI: deep learning for graphics , 2018, SIGGRAPH 2018.

[19]  Denis Zorin,et al.  Structurally optimized shells , 2019, ArXiv.

[20]  Jie Xu,et al.  Interactive design space exploration and optimization for CAD models , 2017, ACM Trans. Graph..

[21]  Hujun Bao,et al.  Numerical coarsening using discontinuous shape functions , 2018, ACM Trans. Graph..

[22]  Baining Guo,et al.  General planar quadrilateral mesh design using conjugate direction field , 2011, ACM Trans. Graph..

[23]  Radomír Mech,et al.  Stress relief , 2012, ACM Trans. Graph..

[24]  Johannes Wallner,et al.  Freeform surfaces from single curved panels , 2008, SIGGRAPH 2008.

[25]  Eitan Grinspun,et al.  A Discrete Model for Inelastic Deformation of Thin Shells , 2004 .

[26]  Olivier Baverel,et al.  Marionette Meshes: Modelling free-form architecture with planar facets , 2017 .

[27]  Jernej Barbic,et al.  Real-Time subspace integration for St. Venant-Kirchhoff deformable models , 2005, ACM Trans. Graph..

[28]  Kyriaki Corinna Datsiou Design and Performance of Cold Bent Glass , 2017 .

[29]  Wojciech Matusik,et al.  Data-driven finite elements for geometry and material design , 2015, ACM Trans. Graph..

[30]  Michael Wimmer,et al.  Reduced-order shape optimization using offset surfaces , 2015, ACM Trans. Graph..

[31]  Niloy J. Mitra,et al.  Learning an intrinsic garment space for interactive authoring of garment animation , 2019, ACM Trans. Graph..

[32]  Dennis R. Shelden,et al.  A Parametric Strategy for Freeform Glass Structures Using Quadrilateral Planar Facets , 2004, ACADIA proceedings.

[33]  Alex Pentland,et al.  Good vibrations: modal dynamics for graphics and animation , 1989, SIGGRAPH.

[34]  Nobuyuki Umetani,et al.  Learning three-dimensional flow for interactive aerodynamic design , 2018, ACM Trans. Graph..

[35]  James F. O'Brien,et al.  Adaptive tearing and cracking of thin sheets , 2014, ACM Trans. Graph..

[36]  Geoffrey E. Hinton,et al.  Layer Normalization , 2016, ArXiv.

[37]  Miguel A. Otaduy,et al.  Tactile rendering based on skin stress optimization , 2020, ACM Trans. Graph..

[38]  Eike Schling,et al.  Low-Cost Double Curvature: Geometrical and Structural Potentials of Rectangular, Cold-Bent Glass Construction , 2016 .

[39]  Jun-Hai Yong,et al.  Geometric Hermite curves with minimum strain energy , 2004, Comput. Aided Geom. Des..

[40]  Takeo Igarashi,et al.  Guided exploration of physically valid shapes for furniture design , 2012, ACM Trans. Graph..

[41]  Johannes Wallner,et al.  Architectural geometry , 2007, Comput. Graph..

[42]  Martin Kilian,et al.  Visual smoothness of polyhedral surfaces , 2019, ACM Trans. Graph..

[43]  Jian Sun,et al.  Deep Residual Learning for Image Recognition , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[44]  Eder Miguel,et al.  CurveUps , 2017, ACM Trans. Graph..

[45]  Keenan Crane,et al.  Rapid deployment of curved surfaces via programmable auxetics , 2018, ACM Trans. Graph..

[46]  Angelika Foerster,et al.  An Introduction To Structural Optimization , 2016 .

[47]  Jonas Zehnder,et al.  Set-in-stone , 2018, ACM Trans. Graph..

[48]  Sepp Hochreiter,et al.  Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs) , 2015, ICLR.

[49]  Olivier Baverel,et al.  From shape to shell: a design tool to materialize freeform shapes using gridshell structures , 2013 .

[50]  Philippe Block,et al.  Shell Structures for Architecture - Form Finding and Optimization , 2014, Shell Structures for Architecture.

[51]  Anders Klarbring,et al.  An Introduction to Structural Optimization , 2008 .

[52]  Johannes Wallner,et al.  Freeform surfaces from single curved panels , 2008, ACM Trans. Graph..

[53]  Jan Knippers,et al.  Geometrie und Tragverhalten von doppelt gekrümmten Ganzglasschalen aus kalt verformten Glaslaminaten , 2011 .

[54]  Szymon Rusinkiewicz,et al.  State of the Art in Methods and Representations for Fabrication‐Aware Design , 2017, Comput. Graph. Forum.

[55]  Levent Burak Kara,et al.  Lightweight structure design under force location uncertainty , 2017, ACM Trans. Graph..