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Optimized Quad Gridshell from Stress Field and Curvature Field

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Presented at IASS 2018 @ MIT

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Optimized Quad Gridshell from Stress Field and Curvature Field

  1. 1. Optimized Quad Gridshell from Stress Field and Curvature Field Lorenzo Greco, www.parametricism.co.uk, AKT II Paper number 204 lorenzogreco@gmail.com
  2. 2. Lorenzo Greco, parametricism.co.uk, lorenzogreco@gmail.com 2 Court Queen Elizabeth II - British Museum, London Yas Marina Hotel - Abu Dhabi Cour Visconti – Louvre, Paris Neumünster Abbey – Luxemburg
  3. 3. Lorenzo Greco, parametricism.co.uk, lorenzogreco@gmail.com 3 In architecture there might be more constraints compared with computer graphics, for example: ● Dictated position for some nodes ● Positioning of irregular vertices ● Strict boundary conditions for aesthetic and structural reasons ● Localized anisotropy to enhance details or sharp features ● Regular quad shape reduces glass cut-offs and is generally more aesthetically pleasant ● Planarity or single curvature at most, greatly reduces costs
  4. 4. Lorenzo Greco, parametricism.co.uk, lorenzogreco@gmail.com 4 Top-down quadrangulation It becomes hard when it puts restraints to the quality and size of individual quads and to the overall mesh topology, whilst minimizing the deviation from it. Bottom-up quadrangulation The bottom-up approach is the easiest to achieve. It consists of recreating the given surface using translational, rotational, and scaled surfaces, or any combination of them. ● Developable ● Planar quad ● Hard to match the initial surface ● The quad topology is strictly linked to how the mesh has been rationalized.
  5. 5. Lorenzo Greco, parametricism.co.uk, lorenzogreco@gmail.com 5 Workflow showing the steps to generate a planar quad mesh
  6. 6. Lorenzo Greco, parametricism.co.uk, lorenzogreco@gmail.com 6 Initial surface
  7. 7. Lorenzo Greco, parametricism.co.uk, lorenzogreco@gmail.com 7 Principal stress directions (black) principal curvature (red) directions of the freeform continuous shell
  8. 8. Lorenzo Greco, parametricism.co.uk, lorenzogreco@gmail.com 8 Selecting a subset of vectors to be used to generate a global smooth vector field
  9. 9. Lorenzo Greco, parametricism.co.uk, lorenzogreco@gmail.com 9 Comparison between fields: (black) principal stress, (red) principal curvature, (white) smooth vector field from n- PolyVector field
  10. 10. Lorenzo Greco, parametricism.co.uk, lorenzogreco@gmail.com 10 Comparison between fields: (black) principal stress, (red) principal curvature, (green) naïf point-wise interpolation, and (white) smooth vector field from n-PolyVector field
  11. 11. Lorenzo Greco, parametricism.co.uk, lorenzogreco@gmail.com 11 Conjugated vector field from principal stress and curvature fields
  12. 12. Lorenzo Greco, parametricism.co.uk, lorenzogreco@gmail.com 12 Orthogonal map derived from frame field global parameterization
  13. 13. Lorenzo Greco, parametricism.co.uk, lorenzogreco@gmail.com 13 The vectors chosen to inform the grid directionality are in the black rectangles. The resulting gridshell (red and green) follows those directions with good accuracy whilst still being smooth across the whole domain.
  14. 14. Lorenzo Greco, parametricism.co.uk, lorenzogreco@gmail.com 14 Capybara Dodo

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