1. Schloss Dagstuhl, September 2014 Shape Representation Carlo H. Séquin University of California, Berkeley User-Guided Inverse 3D Modeling

2. Dagstuhl Discussion Points: Shape representation issues at the start and conclusion of designing RP models u Focus on HCI difficulties and CAD problems, at the start and end of a design / modeling project: u How to get started?  How to get your ideas into the CAD system.  I like to obtain a high-level parameterized procedural description.

3. Background: 40 Years of Design CCD TV Camera (1973) Soda Hall (1992) RISC 1 Computer Chip (1984) Octa-Gear (CyberBuild,1999)

4. Recent Designs and Models “Evolving Trefoil” Double-Boy Klein Bottle 4-dimensional 120-Cell “Inverted double-sock” Klein bottle

5. Brent Collins “Hyperbolic Hexagon II”

6. “Hyperbolic Hexagon” by B. Collins u 6 saddles in a ring u = “wound up” 6-story Scherk tower u 6 holes passing through symmetry plane at ±45º u Discussion: What if … l we added more stories ? l or introduced a twist before closing the ring ?

7. Brent Collins’ Prototyping Process Armature for the Hyperbolic Heptagon Mockup for the Saddle Trefoil Time-consuming ! (1-3 weeks)

8. Sculpture Generator I, GUI

9. Captured Concept straight or twisted “Scherk Tower”“Scherk-Collins Toroids” Scherk’s 2 nd minimal surface

10. Base Geometry: One Scherk Story u Hyperbolic Slices ==> Triangle Strips u Pre-computed -- then warped into toroid

11. Shapes from Sculpture Generator I

12. A Simple Scherk-Collins Toroid Parameters: (genome) u branches = 2 u stories = 1 u height = 5.00 u flange = 1.00 u thickness = 0.10 u rim_bulge = 1.00 u warp = 360.00 u twist = 90 u azimuth = 90 u textr_tiles = 3 u detail = 8

13. Generalizing the Above Approach  “User-guided Inverse 3D Modeling” u Start from some previously defined artifact that might be reverse engineered. u Create a high-level description with suitable parameterization. u Important: Include the designer in the reverse-engineering loop!

14. Possible Starting Points u A (re-)design rarely starts in a vacuum! u There may be available: l a physical artifact to be 3D-scanned, l a set of photographs of an inspirational object, l a wire-mesh (.STL file) of a previous design. u We want to obtain a high-level description, l suitably modularized (handles, body, feet…), l and parameterized (handle diameter; body profile).

15. Modular Reverse Engineering u Extract parameterized descriptions, module by module. u In each case choose a representation that best enables the intended re-design. u Use plausible, commonly used CAD constructs: l CSG l Quadrics l Extrusions l Rotational Sweeps l Progressive Sweeps

16. User-guided Inverse 3D Modeling ( Jimmy Andrews’ PhD thesis) u Let the user select a high-level model structure that is most useful for immediate re-design. Initial artifact Redesigns enabled by different imposed structure

17. Option 1: Varying Rotational Symmetry 3 fold4 fold20 fold Extract one sector; collapse/expand in polar coordinates.

18. Opt.2: Editing as Surface of Revolution Mesh is rotationally collapsed to yield a compound “cross-section”; This cross-section can then be edited, and this will affect the whole mesh.

19. Opt.3: Extraction as a Progressive Sweep 20-story Scherk chain Revised trefoil sweep path

20. User-Guided Fitting Modules (Andrews) u Stationary sweeps: (Surfaces of revolution, helices, etc) u Progressive sweeps: u Quadrics: u Freeform surfaces: u CSG modules: …

21. … then assume point or facet belongs to sweep. If normal is perpendicular to velocity field: (simple motion)(simple velocity field) Defined by a simple sweep motion, with a fixed axis (e.g. revolution, helix, spiral) Stationary Sweeps

22. Fitting Algorithm: u Find velocity field that fits marked data points: Minimize (subject to constraint): u Grow the region by adding more fitting points u Repeat (typically converges in 2-3 iterations) [ Pottmann, Lee, and Randrup, 98 ]

23. Interactive Surface Editing A rotational sweep around the z-axis is specified. A “thick profile” is extracted by collapsing φ-component. Portions of the “thick profile” can be selected and moved; the corresponding surface elements move radially: (a) the whole nose & cheeks area is enlarged; (b) only the nose tips are stretched. (a) (b)

24. Progressive Sweeps u More parameters: Make incremental local adjustments u Allow more complex cross-section transformations (translation, rotation, scaling) u User stroke provides initial guess u Fit by iteratively extending and optimizing

25. Progressive Sweep Fitting u Starting from user stroke, optimize cross section u Iteratively extend and re-optimize u Stop when best further extension would have high error [Andrews, Joshi, Sequin 2011]

26. Flexibility of Progressive Sweeps u Capture the parameterized procedural description that best fits the users re-design plans. Yellow strokes (#1) defines the start of a progressive sweep. An optional 2 nd stroke extends or restricts the sweep range.

27. Versatility of Progressive Sweeps Different starting strokes and different error tolerances result in a wide variety of possible extracted sweeps. Sweep path and profiles can be edited independently. Surface details with respect to the extracted sweep can be conserved and reapplied after any editing moves, or they can be ignored or smoothed out.

28. Preserving Surface Details Modifying the sweep path & scaling, while preserving surface details:

29. Freeform Surfaces: Laplacian Surface Editing This is the workhorse to handle “everything else”: - Smoothing out unwanted details (ear). - Keeping model elements smoothly connected (leg).

30. System Pipeline Unstructured mesh Photos 3D scans Input Data Editable Model Model Hierarchy & Re-fitting Clean User- guided fitting modules Nice rendering STL for RP OBJ for CAD Redesigned output

31. Salient Points u Designer knows best in what direction she wants to push a particular design. u That knowledge determines preferred representation. u Use a GUI where the designer can easily convey that information to the extraction system. u See results immediately and try to make desired modification (if it does not work as intended do a somewhat different extraction)  Instant feedback.  Your ideas and comments ??