NDIST 2012NDIST 2012

Shape Representation

Carlo H. Séquin

University of California, Berkeley

Focus of TalkFocus of Talk

Shape representation issuesat the start and conclusion

of designing RP models

Focus on HCI difficulties and CAD problems,at the start and end of a design / modeling project:

How to get started? How to get your ideas into the CAD system.

How to finish? How to get your model properly 3D printed.

A designer for 30 years…A designer for 30 years…

CCD TV Camera Soda Hall

RISC 1 Computer Chip Octa-Gear (Cyberbuild)

Recent Designs and ModelsRecent Designs and Models

Talk OutlineTalk Outline

Start: Concept Input

“Sculpture Generator I”

“Viae Globi” Sculptures

Interactive Inverse 3D Modeling

Finish: Obtaining Tangible Output

Construction of “Pax Mundi”

Slicing Imperfect .STL files

Brent CollinsBrent Collins

“Hyperbolic Hexagon II”

Brent Collins: Stacked SaddlesBrent Collins: Stacked Saddles

All photos by Phillip Geller

ScherkScherk’’s 2nd Minimal Surfaces 2nd Minimal Surface

Isolated core

““ScherkScherk Towers” Towers” (2nd and 3d order)(2nd and 3d order)

Normal“biped”saddles

Generalization to higher-order saddles(“monkey saddles”)“Scherk Tower”

““Hyperbolic HexagonHyperbolic Hexagon”” by B. Collins by B. Collins

6 saddles in a ring

= “wound up” 6-story Scherk tower

6 holes passing through symmetry plane at ±45º

Discussion: What if …

we added more stories ?

or introduced a twist before closing the ring ?

Closing the LoopClosing the Loop

straight

or

twisted

“Scherk Tower” “Scherk-Collins Toroids”

““Hyperbolic HeptagonHyperbolic Heptagon” - ” - Paper Skeleton Paper Skeleton

Brent CollinsBrent Collins’’ Prototyping Process Prototyping Process

Armature for the Hyperbolic Heptagon

Mockup for the Saddle Trefoil

Time-consuming ! (1-3 weeks)

Sculpture Generator ISculpture Generator I, GUI , GUI

Some of the Parameters in Some of the Parameters in ““SC1SC1””

Base Geometry: One Scherk StoryBase Geometry: One Scherk Story

Hyperbolic Slices ==> Triangle Strips

Pre-computed -- then warped into toroid

Generated Scherk-Collins ShapesGenerated Scherk-Collins Shapes

Shapes from Shapes from Sculpture Generator ISculpture Generator I

A Simple Scherk-Collins ToroidA Simple Scherk-Collins Toroid

Parameters:(genome)

branches = 2 stories = 1 height = 5.00 flange = 1.00 thickness = 0.10 rim_bulge = 1.00 warp = 360.00 twist = 90 azimuth = 90 textr_tiles = 3 detail = 8

A Scherk Tower A Scherk Tower (on its side)(on its side)

branches = 7 stories = 3 height = 0.2 flange = 1.00 thickness = 0.04 rim_bulge = 0 warp = 0 twist = 0 azimuth = 0 textr_tiles = 2 detail = 6

V-artV-art

VirtualGlassScherkTowerwithMonkeySaddles

(Radiance 40 hours)

Jane Yen

CollinsCollins’’ Fabrication Process Fabrication Process

Example: Vox Solis

Layered laminated main shapeWood master pattern

for sculpture

““Vox SolisVox Solis”” by Brent Collins by Brent Collins

Slices through Slices through ““Minimal TrefoilMinimal Trefoil””

50% 10%23%30%

45% 5%20%27%

35% 2%15%25%

SSL Contours from QuickSliceSSL Contours from QuickSliceShaded STL-file SSL-slices

SSL Contours from QuickSliceSSL Contours from QuickSliceShaded STL-file SSL-slices

SML-roads in one of the central slices

One thick slicethru sculpture,from which Brent can cut boards and assemble a rough shape.

Traces represent: top and bottom,as well as cuts at 1/4, 1/2, 3/4of one board.

Profiled Slice through Profiled Slice through ““HeptoroidHeptoroid””

Emergence of the Emergence of the Heptoroid Heptoroid (1)(1)

Assembly of the precut boards

Emergence of the Emergence of the HeptoroidHeptoroid (2) (2)

Forming a continuous smooth edge

Emergence of the Emergence of the HeptoroidHeptoroid (3) (3)

Smoothing the whole surface

The Finished The Finished HeptoroidHeptoroid

at Fermi Lab Art Gallery (1998).

Part 1b: VIAE GLOBIPart 1b: VIAE GLOBI

A completely different paradigm . . .

Brent CollinsBrent Collins’’ ““Pax MundiPax Mundi””

1997: wood, 301997: wood, 30””diam.diam.

2006: Commission from H&R Block, Kansas Cityto make a 70”diameter version in bronze.

My task: to define the master geometry.

How to Model “How to Model “Pax MundiPax Mundi”...”...

Already addressed that question in 1998:

Pax Mundi could not be done with Sculpture Generator I

Needed a more general program !

Used the Berkeley SLIDE environment.

First: Needed to find the basic paradigm

Sculptures by Naum GaboSculptures by Naum Gabo

Pathway on a sphere:

Edge of surface is like seam of tennis- or base-ball;

2-period Gabo curve.

2-period 2-period ““Gabo CurveGabo Curve””

Approximation with quartic B-splinewith 8 control points per period;but only 3 DOF are used (symmetry!).

4-period 4-period ““Gabo CurveGabo Curve””

Same construction as for as for 2-period curve

Pax MundiPax Mundi Revisited Revisited Can be seen as:

Amplitude modulated, 4-period Gabo curve

SLIDE-GUI for SLIDE-GUI for ““Pax MundiPax Mundi”” Shapes ShapesGood combination of interactive 3D graphicsand parameterizable procedural constructs.

Many Different Many Different Viae GlobiViae Globi Models Models

1c: Interactive Inverse 3D Modeling1c: Interactive Inverse 3D Modeling

How to generalize this approach.

Important: Include the designer in the reverse-engineering loop!

Example Design ScenarioExample Design Scenario

Kitchen appliances “With a Heart”

Modular Reverse EngineeringModular Reverse Engineering

Extract parameterized descriptions, module by module.

In each case choose a representation that best enables the intended re-design.

Use plausible, commonly used CAD constructs: CSG

Quadrics

Extrusions

Rotational Sweeps

Progressive Sweeps

Interactive Inverse 3D Modeling Interactive Inverse 3D Modeling ( Jimmy Andrews( Jimmy Andrews’’ PhD thesis) PhD thesis)

Let the user select a high-level model structurethat is most useful for immediate re-design.

Initial artifact Redesigns enabled by different imposed structure

Option 1: Varying Rotational SymmetryOption 1: Varying Rotational Symmetry

3 fold 4 fold 20 fold

Extract one sector; collapse/expand in polar coordinates.

Opt.2: Editing as Surface of RevolutionOpt.2: Editing as Surface of Revolution

Mesh is rotationally collapsed to yielda compound “cross-section”;

This cross-sectioncan then be edited,and this will affectthe whole mesh.

Opt.3: Extraction as Opt.3: Extraction as a Progressive Sweepa Progressive Sweep

20-story Scherk chain

Revised trefoil sweep path

User-Guided Fitting ModulesUser-Guided Fitting Modules Stationary sweeps:

(Surfaces of revolution, helices, etc)

Progressive sweeps:

Quadrics:

Freeform surfaces:

CSG modules: …

… then assume point 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

Fitting Algorithm:Fitting Algorithm: Find velocity field that fits marked data points:

Minimize (subject to constraint):

Grow the region by adding more fitting points

Repeat (typically converges in 2-3 iterations)

[ Pottmann, Lee, and Randrup, 98 ]

Interactive Surface EditingInteractive 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 and cheeks area is enlarged;• (b) only the nose is stretched.

(a) (b)

Progressive SweepsProgressive Sweeps More parameters: Make incremental local adjustments

Allow more complex cross-section transformations(translation, rotation, scaling)

User stroke provides initial guess

Fit by iteratively extending and optimizing

Progressive Sweep FittingProgressive Sweep Fitting

Starting from user stroke, optimize cross section

Iteratively extend and re-optimize

Stop when best further extension would have high error

[Andrews, Joshi, Sequin 2011]

Flexibility of Progressive SweepsFlexibility of Progressive Sweeps

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 2nd stroke extends or restricts the sweep range.

Versatility of Progressive SweepsVersatility 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.

Preserving Surface DetailsPreserving Surface Details

• Modifying the sweep path & scaling,while preserving surface details:

Freeform Surfaces:Freeform Surfaces:Laplacian Surface EditingLaplacian Surface Editing

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

System PipelineSystem Pipeline

Unstructured mesh

Unstructured mesh

PhotosPhotos

3D scans3D scans

Input Data

Editable Model

Editable Model

ModelHierarchy

& Re-fitting

Clean

User-guided fitting

modules

Nice rendering

Nice rendering

STL for RPSTL for RP

OBJ for CAD

OBJ for CAD

Redesigned output

PART II: Output EndPART II: Output End

Fabrication of Fabrication of Pax MundiPax Mundi

Target GeometryTarget Geometry

Constraints:• Bronze; 70” diameter• Less than 1500 pounds• Less than $50’000• Maintain beauty, strength• Minimize master geometry

Emulation; Define Master PatternEmulation; Define Master Pattern

Use 4 copies.

Master to make a mold from.

Alignment tab

Model of Master Part Made with FDMModel of Master Part Made with FDM

4 pieces make the whole sculpture

Joe ValasekJoe Valasek’’s CNC Milling Machines CNC Milling Machine

Styrofoam milling machine

Design of Two-Part MasterDesign of Two-Part Master

Alignment tabs for easy assembly

Subdivide into Subdivide into TwoTwo Master Segments Master Segments

Machined Master Pattern #2Machined Master Pattern #2

(Cut) Master (Cut) Master Silicone Rubber MoldSilicone Rubber Mold

MoldMold Several (4) Wax Copies Several (4) Wax Copies

SpruingSpruing the the Wax PartsWax Parts for Casting for Casting

Ceramic Slurry ShellCeramic Slurry Shell Around Wax Part Around Wax Part

Taking the Taking the ShellShell out of the out of the KilnKiln

ShellShell Ready Ready for Castingfor Casting

Pouring Liquid BronzePouring Liquid Bronze

Casting with Casting with Liquid BronzeLiquid Bronze

Freeing the Freeing the Bronze CastBronze Cast

Assembling the SegmentsAssembling the Segments

The The ““GrowingGrowing”” Ribbon Ribbon

The Assembly is Too Squat !!The Assembly is Too Squat !!

Changing the CurvatureChanging the Curvature

PHYSICS is important too ...PHYSICS is important too ...

not just Geometry !not just Geometry !

Grinding the Welded Seams,Grinding the Welded Seams,Polishing the SurfacePolishing the Surface

Applying PatinaApplying Patina

Front Door of the ...Front Door of the ...

H&R Block Building

Making Plastic RP ModelsMaking Plastic RP Models

3D model of the regular 4-dimensional 120-Cell

Acceptable Model FilesAcceptable Model Files

The STL file should be a proper watertight 2-manifold, with no cracks or intersecting faces.

All faces should have their normals point outwards, i.e., away form material.

In this boundary mesh every edge should be used exactly twice, once each in opposite directions.

An Actual Model of the 120-CellAn Actual Model of the 120-Cell

Based on the way it is constructed, such a model may look quite differently.

My model was formed by projecting all edges from 4D to 3D, and then replacing each edge with a prism of reasonable diameter, so that a robust model results.

But then we do not get a manifold B-Rep !At every vertex there are 4 intersecting prisms, plus, perhaps, an additional sphere!

(And for the 600-Cell there would be 12 cylinders!)

How does an RP machine handle such a file ?

And Things Can Get Much Worse!And Things Can Get Much Worse!

Slicing the gridded “TetraBoy” surface:

The .STL file displayed by QuickSlice

The .SSL slicesgenerated by QuickSlice:

Lots of stuff missing!

One of Many Bad LayersOne of Many Bad Layers

many missing struts

incomplete features

““Tetra-Boy SurfaceTetra-Boy Surface””

A single-sided, non-orientable surface of genus 4

Model Clean-upModel Clean-up

Ideally all models should be cleaned up …

But general 3D Model Clean-up is very hard !!!

I don’t know of any program than can do this, even for only moderately “flawed” models.

QuickSliceQuickSlice Idiosyncrasies IdiosyncrasiesWhat happens at overlapping / intersecting contours?

Slices every facet individually, ignoring orientation.

Re-constructs contours by joining line segments.

In general, uses an XOR “in/out” definition.

Flips contour orientation “if it seems to help”. . .

On concentric circles the inner contour is flipped.

On overlapping circles no flip is introduced;but a void then occurs in overlap area.

But: Slicing programs could do a better job, with a quite simple approach . . .

““BadBad”” .STL Files .STL Files

If they come from a CAD tool, errors are not random:

NOT: randomly missing triangles

NOT: randomly mis-oriented faces

More likely: overlapping “legal” parts:

Unexecuted Booleans: mostly unions ,since this works fine for graphics displays.

Possibly self-intersecting sweeps, e.g. in tight knots or in Klein bottles.

Very likely, the facet orientation is trustworthy . . .

Let’s use it properly!

2D Model Interpretation2D Model Interpretation

Intelligent 2D model clean-up is easy:

Use The Winding Number Paradigm !

Slice all triangles;

Use facet normals to produce oriented line segments (CCW contours around inside material.)

Define “inside” with positive winding numbers.

Overlapping parts produce winding numbers > 1.

Review of Winding NumberReview of Winding Number Defined only for closed curves (in the plane).

Defined with respect to a (sample) point.

Evaluation along scan-line with up-down counter.

Why Is This a Good Thing?Why Is This a Good Thing?

Implicit assumption is that designer wants Boolean union or (simple = 1 level) difference.

Positive winding numbers

means: inside.

Negativewinding numbers

get ignored.

Simple overlapping parts will be union-ed together!

Works Even with Negative Inside ContoursWorks Even with Negative Inside Contours

OK to have hollow parts with clockwise contours inside;This guarantees proper subtraction of winding number.

Final Plea . . . Final Plea . . .

Please use your influence to promote the

Winding Number Paradigm!

A lot of headaches with slicing software will then disappear!

Questions ?Questions ?