Interactive Procedural Modeling for Abstract Geometrical Sculptures

1. SMI-FASE 2019, Vancouver Procedural Modeling & Interactive Graphical Editing for the Design of Abstract Geometrical Sculptures Carlo H. Séquin and Toby Chen EECS Computer Science Division University of California, Berkeley

2. 2-Manifolds Defined by Their Borders Modeling tools tried: Maya, Blender, Solidworks, 3DS-Max, . . . Soap film Naum Gabo Eva Hild Charles Perry

3. SLIDE-GUI for “Pax Mundi” Shapes Parameterized procedural constructs.

4. One of My Heroes: Charles O. Perry (1929-2011) “Star Cinder” – 18” sand cast.

5. “Orderly Tangles” by Alan Holden

6. “Orderly Tangle” of 10 Triangles Rounded triangle corners Icosahedral symmetry

7. Perry’s “Star Cinder ” “Orderly Tangle” of ten Sand-cast “Star Cinder” smoothed triangular loops

8. Development Models for “Four Orbits” Pictures supplied by Paul Perry

9. NOME Non-Orientable Manifold Editor: Add interactive graphics capabilitiesto define surface elements between borders. Must handle single-sided surfaces,such as Möbius bands and Klein bottles. Keep the parameterized, procedural specificationfully functional through the whole design process. Integrate the interactive graphical editsinto the initial procedural specification file.

10. 10 Interlinked Triangles And suspended 2-manifold surfaces

11. Parameterized Specification MODULE instance ID_0 MODULE yellow end_instance instance ID_1 MODULE orange rotate(0 0 1)(72) end_instance instance ID_2 MODULE red rotate(0 0 1)(144) end_instance instance ID_3 MODULE purple rotate(0 0 1)(216) end_instance instance ID_4 MODULE green rotate(0 0 1)(288) end_instance NOME: modular, parameterized, procedural description

12. NOME Workflow Example z Rpo Rc Rpi +z Num=100 Sep Parameterized definition of the border curves. Incremental construction of the suspended 2-manifold.

13. NOME Workflow Example Orthogonal view Oblique view (Fairly flat geometry) (Thickened in Z) Incremental construction of a 2-manifold suspended by the two border curves ( circle & cinquefoil ).

14. “Soap-film-like” Surfaces 2 levels of subdivision 3 levels of subdivision( + normal vectors ) Smoothing by Catmull-Clark subdivision:

15. Making the Surface “Physical” Geometrical fine-tuning Offset surface generation

16. Substantial Geometry Changes OK: Topology change due to a reduced rim radius. BAD: Excessive enlargement of central hole. Parameter change causes topological change:

17. Back to the Hierarchical View Hierarchical view of the new topology.More geometrical changes: narrowing the cinquefoil lobes.

18. More Challenging Designs Volume-filling “Star Cinders” Design on the left only fills outer 20% of sphere. Want a single 2-manifold that fills sphere more fully. Need border curves that dive closer to the center.

19. More Complex Border Curves (3,4)-Torus-knot. (3,3)-Torus-knot: Triple-Loop. Replace the rounded triangle loops = (3,1)-Torus-knot . . .

20. Complex Tangle of Border Curves Now, just add the faces . . . 10 Triple-Loops Sampled NOME curves

21. Starting to Fill In the Surface Sampled NOME curves Some first outer facets + added symmetry markers

22. Construction of a 3-level Star Cinder The 30 outer lobes. Connecting the outermost shell.

23. Continue Process to the Inside The innermost shell Complete CAD model+ one radial connector

24. 3-level Star Cinder 3D ABS print.

25. A Different Approach… Construct individual single-layer shells; nest them concentrically; connect them radially. Let’s build a shell based on the cuboctahedron:Start with a few rudimentary surface elements

26. Twisted Cuboctahedron Frame This is one of the shells in a nested assembly . . . Edge-ribbons  Twisted 180  3D-print

27. Scaling and Nesting such Shells Three nested cuboctahedron shells: not very interesting! Nested dual frames with skewed edge crossings. Concentrically place a smaller copy inside; Connect radially at the red mid-edge squares.

28. Twisted Rhombic-Dodecahedron Frame NOME skeleton -- smoothed model -- 3D-print To be nested with the cuboctahedron frame . . . The dual of the cuboctahedron

29. Cuboctahedron Frame with Rhombic-Dodecahedron Inside Smooth CAD Model -- 3D-Print

30. Three Nested Shells Cuboctahedron Rhombic Dodecahedron Cuboctahedron

31. 4 Nested Tetrahedral Shells The tetrahedron is its own dual. Only one shell needs to bedesigned. Nesting is doneby scaling andby rotation. Radial connecting ribbon-elements remain the same.

32. Comparison of the Two Approaches Approach #1:Offers: nice, smooth, well-controlled border curves;Difficult to create an intersection-free 2-manifold using all those border curves. Approach #2:Offers: well-defined ribbon-frame shells;Difficult to predict what border curves may look like;typically, they form crazy, curly-cue loops. In both approaches, NOME is very helpful in defining the needed surface elements in one representative sector of the whole symmetrical assembly.

33. Nested Genus-1 Surfaces Torus with 12 x 6 quad grid -- Twisted ribbon frame Approach is not limited to nested spherical shells!

34. Two Nested Toroidal Frames Properly rotated (before any radial connections)

35. Fused Dual Toroidal Frames Smoothed and thickened CAD model

36. Two Nested Toroidal Frames 3D-Print (PLA)

37. NOME Development Status Version #3 under active development. Good enough for me to produce these designs that were on my mind. Not yet ready to be exposed to a large group of users.

38. 5-level “Super Star-Cinder” 3D ABS print.

39. EXTRA

40. Charles O. Perry’s Studio, Norwalk, CT “Star Cinder”

41. Charles O. Perry: “Star Cinder” Photo provided byPaul Perry Provides the inspiration for the following!

42. Smooth Borders, “Minimal” Surfaces Cables for smooth edges; panty hose for surfaces, approximating a minimal surface Perry’s design method is very physical !