1. EECS Computer Sciences, U.C.Berkeley
Granada 2003
Thank You !
Fun with geometric designs . . .
Dear Pere, dear colleagues,
I am deeply honored to be counted among the Solid Modeling Pioneers. Geometry has been in my blood-stream since high-school; and for the last 60 years I have had a lot of fun with geometric designs.
In the following, I offer some thoughts, stimulated by the questions I was asked.
Carlo H. Séquin
EECS Computer Sciences, U.C.Berkeley

2. Granada 2003
2D Geometry
The large, fairly regular layouts of the CCD chip that resulted in the first all-solid-state TV camera at Bell Labs and of the RISC chips at UC Berkeley made me focus early in my career on parametrized, procedural design descriptions – You would not want to place a few hundred thousand electrodes by hand!
CCD TV Camera RISC I MicroChip Bell Labs (1973) U.C. Berkeley (1981)

3. UNIX + Graphics  “Berkeley UniGrafiX” (1983)
Granada 2003
Early Contributions
UNIX + Graphics  “Berkeley UniGrafiX” (1983)
In 1983 carried this approach from 2D circuit layouts to 3D geometric shapes. The resulting “Berkeley UniGrafiX” system then allowed me to make images like the “Granny Knot Lattice” or the “3D projection of the regular 4-dimensional 120-Cell.”
Granny-Knot Lattice Regular 4D 120-Cell

4. Solid Modeling Instruction
Granada 2003
Solid Modeling Instruction
CS 184 “Introduction to Computer Graphics”
Perhaps most rewarding in the long run are the results of my instructional activities.
At the undergraduate level, when teaching the basic computer graphics course, I devoted more then 50% of the time to modeling, rather than just rendering techniques.
Some of my focal points were to give students a good understanding, how to create well-structured, hierarchical descriptions for complex, static or dynamic scenes, and how to focus on the key issues of a design task: What are hard constraints? What are goals that should be optimized? What are all available degrees of freedom? I still think that the world needs many more well-trained modelers than it needs computer graphics rendering experts.
Final Project: “Steerable Cyclist on a Klein Bottle”

5. “Star” Graduate Students
Granada 2003
“Star” Graduate Students
Manolis Katevenis: RISC, 1984 Eric A. Bier: Snap-Dragging, 1988 Leon A. Shirman: UniCubiX, 1990 Seth J. Teller: Building Walk-Throughs, 1992 Henry P. Moreton: Min.Variation Surfaces, 1992 Tom Funkhouser: Architectural Models, 1993 Sara McMains: Solid Modeling, 2000 Richard Bukowski: Indoor Fire Simulations, 2001 Jordan Smith: Berkeley SLIDE, 2004 Pushkar P. Joshi: Aesthetic Surface Design, 2008 Raph Levien: Euler Spirals, 2009 James Andrews: Inverse 3D Modeling, 2013 Three special topics > > >
The best contributions to this field have been made by some of my star PhD students. A dozen of them who have made contributions to modeling and design are listed here.
There are also others, who have made key contributions to circuit and layout optimizations. In the following I will mention three topics that I feel particularly good about …

6. Aesthetic Functionals for Surfaces
Granada 2003
Aesthetic Functionals for Surfaces
Henry P. Moreton: “Minimum Curvature Variation Curves, Networks, and Surfaces for Fair Free-Form Shape Design” Dec. 18, 1992.
One of the classical ways to make a nice smooth surface was to minimize the bending energy of a thin-plate surface; the left figure shows a result of using this functional.
Henry Moreton showed that minimizing instead the CHANGE of curvature gives nicer results, with more evenly balanced tunnels and handles, and with nice toroidal arms.
This whole domain of investigation was eventually rounded out and completed by also looking at higher-order curvature components. By doing a cylindrical Fourier decomposition around the surface normal, Pushkar Joshi could clarify the individual contributions of higher-order terms.
Min.Bend.Energy Min.Curv.Variation rd order Patch
Pushkar P. Joshi: “Minimizing Curvature Variation for Aesthetic Surface Design” October 2, 2008

7. Building Walk-Throughs
Granada 2003
Building Walk-Throughs
Soda Hall th-floor cells Walkthru in Atrium
Walk-through programs can provide efficient interactive rendering for large, complex scenes by splitting them into cells and then pre-computing a visibility graph that tells what other cells can be seen from inside each individual cell. Depending on where the virtual observer is at any one time, only a small number of cells have to be sent through the rendering pipeline. Seth Teller used a clever stab-line algorithm to make the computation of the visibility graph fast and robust. Tom Funkhouser used this visibility graph to load from disk into memory those cells that could possibly become visible in the near future.
Seth J. Teller: “Visibility Computations in Densely Occluded Polyhedral Environments” Oct. 20, Tom Funkhouser: “Database and Display Algorithms for Interactive Visualization of Architectural Models” Sep., 1993.

8. Design and Fabrication of Solid Models
Granada 2003
Design and Fabrication of Solid Models
Sara McMains: “Data Representations and Algorithms for Solid Free-form Fabrication” June 29, 2000.
In the mid 1990s, 3D printers came along. Sara McMains developed robust and efficient methods to slice complex geometries into hundreds of horizontal slabs for layered manufacturing.
But soon, it was clear that the real bottleneck was the design of those 3D objects. Sara and her students looked for better “3D-ways” to design such geometries – exploring the use of a virtual reality (VR) environment.
A mechanical boom provided haptic feedback so that one could feel the surface of the object when one wanted to draw on it. This was a bit ahead of its time. I think the VR environments are still not good enough that I would feel comfortable to use them for several hours a day to design 3D geometries.
Youngung Shon, “Development and Evaluation of a Haptic Rendering System for Virtual Design Environments”, 2006.

9. Desirable Developments
Granada 2003
Desirable Developments
Ever more sophisticated CAD tools . . .
But not enough people that can use them.
 We need better modeling education!
There are many sophisticated solid modelers: SolidWorks, Rhino3D, CATIA, AutoCAD, Autodesk Maya, AutoCAD ... Most of them are difficult to use for novices, when it comes to making non-technical, aesthetically pleasing, free-form shapes: Just observe a novice trying to make a smooth, triply twisted Möbius band or a Klein bottle! Most users probably use only a few percent of the capabilities of these programs (just like users of Photoshop!).
Conferences like SPM2017 now focus on sophisticated extensions to these programs. -- But how many people will be able to use these new features? To make a disputable analogy: It seems that we are building ever better “Formula-1 race-cars,” but we have no plans to also train drivers for such cars.
Perhaps this conferences and the supporting journals may want to publish more papers that show how to use these programs and their existing capabilities in an effective way for novel applications, -- for instance, for making a non-orientable, single-sided surface of some specified genus.
Formula-1 Race-Car Non-orientable Surface

10. A Desirable CAD Environment
Granada 2003
A Desirable CAD Environment
Parameterized Procedural Design Initiation + Interactive adjustment of parameter values.
The designer/user interface for most CAD programs still has lots of room for improvement!
For some objects that have inherent regularity and symmetry, a high-level, procedural description is the preferred way to get the design started. Such a description likely contains some adjustable parameters, perhaps an integer, n, that generalizes this description for objects with n-fold rotational symmetry. It may also contain parameters that control the rounding or filleting of some final geometry, or the distance of two offset surfaces around a mathematical 2-manifold to make physical objects on different 3D printers.
-- Ideally, most of these parameters would be set and fine-tuned, while a designer looks at an interactive display of the object in its final form (i.e., while looking at the right-hand image rather than the left one. -- In addition, we would also like to do some interactive graphical editing of the geometry >>>
Keep all parameters active and functional through subdivision smoothing and offsetting!

11. Granada 2003
A Technical Challenge
bank pb #A bank of parameter definitions: set rad ; #Define radius parameter set sep ; #Define separation parameter endbank point p0 ( {pb.rad} 0 0 ); #Define some points: point p1 ( {-0.5*pb.rad} {0.866*pb.rad} 0 ); #forming equilateral triangle point p2 ( {-0.5*pb.rad} {0.866*pb.rad} 0 ); #third triangle point face triangle ( p0 p1 p2 ); #face spanned by these points group triapair #A group of transformed faces: instance tn triangle translate( {-pb.sep} 0 0 ); #shifted negative instance tp triangle translate( { pb.sep} 0 0 ); #shifted positive endgroup instance gview triapair; #Geometry to be displayed
Here is a trivial example of a parameterized procedural description. Two instances of an equilateral triangle with adjustable size are placed with an adjustable separation between them.
It would be highly desirable, for such a system to also allow making changes in the graphics domain:
>>>next>>> Here we just add one more triangle by clicking on the 3 vertices defining the yellow triangle.
Most 3D modelers allow the user to do such editing to some degree, but typically the result is then captured in a low-level, non-hierarchical manner that may no longer respond to the parameterization introduced in the original procedural description.
The technical challenge is to find a way to integrate such interactively made changes into the original, high-level, hierarchical description, so that these edits follow the geometry changes resulting from any changes in the parameter values. It is not immediately clear, how this can be done in a "generic" manner for complex hierarchical scenes.
Interactively added face, defined by hierarchical point-names, persists as a connected rubber sheet as parameters are changed:
face glue ( gview.tn.p0 gview.tp.p3 gview.tp.p2 );

12. Granada 2003
CAVEAT
Perhaps some 3D modelers already do most of this … If this is the case, -- then this just emphasizes my point made above: We need better “modeler education”!
CAVEAT: Perhaps some 3D modelers already do most of this – If this is the case, then this just emphasizes my point made above: We need better “modeler education”!