The Many Dimensions of SHAPE

The image above is from www.scholastic.com/ispy. The “I Spy” books by Walter Wick and Jean Marzollo are filled with visual images and riddles requiring visual search, typically using shape, in order to solve. “I Spy” books are available from Amazon, Barnes and Noble, etc.

Outline • Motivation •Shape? •Background • 6 Experiments using shapes on different datasets •A model?

* All conjecture – nothing proven!

There are Birth Rate vs. Death Rate 1997 for 190 countries – each country assigned to a shape. 4-10 basic 30 shapes in most charts, paint 25 packages, etc. 20 te a ath r

de 15

5 Why limited to 10? 0 What if you 0 102030405060 need more birth rate than 10? Excel chart. 10 shapes, then repeats (with different color)!

• There are limitless number of pictographs. •But… – Design required – Abstract nouns, adjectives difficult to encode/decode – Ambiguity – Perceptually effectiveness?

www.aiga.org/content.cfm/symbol-signs

A. Simple geometry:

• What’s in-between these two? • Can shapes convey more than one (or two or 5) attribute(s)? • Are some shapes more perceptually effective?

B. Pictographs: 1 t⌧☯ ZH][FYEPt A#a28<:9= Limitless visual representation, typically of nouns.

Alphanumerics Symbols More Symbols •A B C D E • & ! ( ) ; : @ ? • a b c d e •€£¥₣ • 1 2 3 4 5 •+ -/ x • i ii iii iv v vi • √∞≠≤≥≈

But: • Are these shapes perceptually efficient? • Can they convey quantitative values (i.e. magnitudes), not just separate categories? • Can they convey more than one attribute?

Pictograph Hair on 1,2,3…n on Basic a Base bars, charts & Geometry Shape small multiples.

Edward Tufte: Beautiful Evidence Icons from AIGA Anymails: Visualization of Email Inbox www.aiga.org/content.cfm/symbol-signs Design & Concept: Carolin Horn Code: Florian Jenett

• Are there ways to convey multiple attributes other than just welding component shapes together?

Basic Geometry

Compound Symbols •What’s in here? Shapes Alphabets • “welded objects” • small multiples

Pictographs

I Spy books: Walter Wick and Jean Marzollo. Scholastic Sample flower shapes. From Aircraft silhouette identification –LIFE Magazine 1944, Publishing. www.scholastic.com theseedsite.co.uk/flowershapes.html Andreas Feininger. Via Google LIFE image search.

Leaf Morphology from A few of examples of more than 14,000 unique Wassily Kandinsky - Composition Example shape attributes used in bird wikimedia.org LEGO parts catalogued by fans on: peeron.com VIII - 1923 wassilykandinsky.net identification, from A Field Guide to the Birds by Roger Tory Peterson © 2009 Richard Brath except as otherwise noted. Page 9 Many Shape Techniques in InfoVis and SciVis but is there a formal list of shape attributes? Star Coordinates Sparklines Literary Organism Superquadrics

www.bonavistasystems.com/OnlineDemoReports.html

Whisker plot, Star plot, Exvis Stick

(Kandogan, 2001) (Posavec 2007) Time Wheel Genome Valence

From Colin Ware’s book. (Barr 1981) Info- Kindlmann Lotus (Fry, 2000) (Zhang (Chua & et al, Malwarez Eick, 1997) 2005) Compound Glyph authors.

Dragulescu espective r

(Stephen Rose, ???) Rohrer 1998 All i ology h c 9x) Visual Attributes ) y 6) x) 5 ( s 8 9 8 ( en ) r x n ( d as defined by visualization 7) ay (

Table of Visual Attributes h 0 l 6 in ac

and suitability for encoding a ( ptual P elan in ( K E researchers and perceptual z

data according to various ce ilkinso e

researchers. . Bert Clev Mac Mac W Maz P psychologists Attribute CQ na CQCQCQCQ P Color Hue Yx Y YYY~Y Yx Y Brightness Y Y Y Y ~ Y Y x Y Y Saturation Y Y ~ Y Y Transformation Length/Width Y Y Y x Y Y Size (Area) YY Y YYYYY x ~ Y Volume Y Y Y Orientation Y x Y Y Y ~ Y x Y Y Slope Y Y Y Form Shape x x Y x Y Y Y x Added Marks Y x Curvature x ~ Y Concavity/Convexity x ~ Closure Y Intersection Y Terminators Y Holes Y Spatial 2D position YY Y YYYY ~Y Y Grouping/Containment Y ~ x x x Y 3D Depth x x Y Sources: Connection Y Numerosity x Y Y Bertin 67: Semiology of Graphics Shadow Direction Y Cleveland 85: The Elements of Graphing Data Movement/Optics Flicker ~ x Y MacKinlay 86: Automating the Design of Graphical Presentations Motion x ~ Y MacEachren 95: How Maps Work Transparency ~ ~ Y Blur/Crispness x ~ Y Wilkinson 99: The Grammar of Graphics Shininess Y Mazza 09: Introduction to Information Visualization Texture Yx YXYYY* Perceptual Psychology: scholarpedia.org/article/Visual_search C = Categoricial/Nominal scale (Bertin's Selection) Q = Quantitative/Ordinal scale. © 2009 Richard Brath except as otherwise noted. P = Perceptually preattentive, i.e. can preattentively distinguish between two categories. Page 11 Note: Researchers are not consistent, even in terminology

Rotation/Angle/Orientation/Slope: • Wilkinson: Rotation • Cleveland: Angle • Bertin: Orientation • MacKinlay: Slope/Angle • MacEachren: Orientation

•Mazza: Orientation Vary in orientation only.

My opinion – Angle and orientation are two separate dimensions of visual attributes

Vary in angle only.

Attribute BBinaryinary CCategoryategory Order/QuantityOrder/Qty Consensus. •SSize*ize* YYYY YY But these are uniform •OrientationOrientation YYYY N - transformations on shape, not about shape ------itself. Shape•Shape ∆◊O+? YY N N Added•Ang leMarks ?Y ? N Curvature•Curvature YY NN-- •AngleAdded Marks Y N •CClosurelosure YY Incomplete •IIntenrsteecrstionection YY No consensus •TTerminatorserminators YY … •HHolesoles YY 1 2 Therefore: do a series of small experiments to 3 explore these attributes more..

GOAL: • Use curves to represent AttributeAttribute BBinaryinary CateCategorygory Order/QtyOrder/Qty •S•Sizieze** YYYY YY different categories. •• OOririentationentation YYYY ------HOW: pe Y N •S•Shhaape Y N Y N •• AAddeddded Marks Marks Y N • Gas station survey. ature Y N - •C•Cuurvrvature Y N - le 1000 people surveyed: •A•Annggle ure Y •C•Clolossure Y – Which gas station section Y •• InterIntersection Y inators Y –Age •T•Teermrminators Y •Holes Y – Fuel grade purchased •Holes Y (regular, mid-grade, premium) – Payment method –Gender –Etc.

Arco Chevron Mobil Other Shell Unocal

18-25

26-35

36-45

46-55

56-65

66-75

75+

Fuel Grade: Regular Mid-grade Premium

• Seems like curves can effectively show 3 different categories.

Experiment #2: More categories of curves

• How about more curves?

Gas station survey data set: • See both “fuel grade” and “payment method” using only curves:

Credit Branded Cash Debit Card Card

Note: there are different types of curves: e.g. conic sections vs. bezier. This bezier stands Regular out from the other half ellipses.

Mid-Grade

Premium

12 different curve shapes.

Arco Chevron Mobil Other Shell Unocal

18-25

26-35

36-45

46-55

56-65

66-75

75+

Fuel Grade: – Regular u Mid-grade U Premium Payment: Cash Debit Credit Card Branded Card

Attribute Binary Category Order/Qty 1. Curves could work for more than •Shape Y N 3 categories • Added Marks Y N •Curvature Y y- 2. Multiple attributes of curves can •Angle be utilized to create different •Closure Y • Intersection Y perceptually distinguishable •Terminators Y curve shapes: •Holes Y -amplitude -skew Attribute Binary Category Order/Qty - bulginess •Shape Y N • Added Marks Y N •Curvature Y y- 3. And, we should repeat this •Angle •Closure Y experiment for angle, hole, • Intersection Y terminators, etc •Terminators Y •Holes Y

GOAL: Replace a Treemap using quantitative shapes

Attribute Binary Category Order/Qty Shape Y N 4 hours later… Added Marks Y N Curvature Y y- Angle Closure Y Intersection Y Terminators Y Holes Y

Image src: wikipedia.org www.ucalgary.ca/~bakardji/ElectricComm/Diag%201.gif © 2009 Richard Brath except as otherwise noted. Page 21 Chappe Telegraph as applied to S&P 500 data left arm = percent change; right arm = volume relative to 30 day avg; horizontal = 0.

Up Above Average Stock Price Volume Percent change in No Change Average Today’s volume compared to stock price today 30 day average volume Down Below Average © 2009 Richard Brath except as otherwise noted. Page 22 Experiment #3: Chappe Telegraph Findings

Attribute Binary Category Order/Qty •Shape Y N Looks like angles work. • Added Marks Y N •Curvature Y y- •Angle y y •Closure Y • Intersection Y •Terminators Y •Holes Y

Experiment #4: What about more?

Which other shape attributes can be efficient at representing quantitative data?

World Demographics and Economics 2 5 0 1 1 0 8 - 1 3 9 - 5 - 8 2 1 9 - 8 5 0 5 - 8 1 Women 0 1 7 1 Examples: 0 per 100 0 3 7 1 men < > Balance of Qatar: • <70 women per 100 men trade per • > +$1000/capita balance

0 of trade capita 0 0 0 0 0 0 0 1 0 0 0 0 0 1 - 1 0 • > 4:1 birth:death (exports- 1 - 1 1 - 0 - 0 > < 0 - 0 1 0 imports) 0 - 1 0 1 0 - 1

1 : Russia: Birth to 1 < • 115-130 women per 100 1 Death : 2 - men 1 1 Ratio : : 1 4 • > +$1000/capita balance - 1 1 © 2009 Richard Brath except as otherwise noted. : : of trade Page 24 2 4 > • < 1:1 birth:death Experiment #4 Conclusions

Attribute Binary Category Order/Qty • Curve, Angle and •Shape Y N • Added Marks Y N Terminator all •Curvature Y yy potentially effectively •Angle y y •Closure Y • Intersection Y • Likely effective for •Terminators Y yy categories too. •Holes Y • And should try the other shape attributes Basic Geometry too. Compound Shapes Symbols What’s in here? Alphabets •“welded objects” • small multiples

Pictographs

Attribute Binary Category Order/Qty

•Shape Y N • Added Marks Y N •Curvature Y yy •Angle y y •Closure Y •Intersection Y •Terminators Y yy •Holes Y

Hard g n p . e l t i t _

o Jaggy n _ y Edge Type g lo ho p r Crenellated mo _ f a e L : e

g Spiky ma I / i k i w / g r o . Bubbly a i d me i k i w . s n o m m o c

Attribute Binary Category Order/Qty •Shape Y N • Added Marks Y N •Curvature Y yy •Angle y y •Closure Y • Intersection Y •Terminators Y yy •Holes Y • Edge Type y

er Type Corner Hatch n

And even more shape attributes: Cor Bulleted • Corners: hard, rounded, beveled, corner hatch, bulleted, serifed, etc. Shear • Warp: shear, bend, wobble, twist, etc. Warp Bend • External Whiskers: None, 1 (on longest side), 2 (on same side), 2 Wobble (on longest 2 sides), 1 (off of corner) (also internal whiskers, crossing whiskers). One Notch mp (longest side) • Notch/Bump: None, 1, 2, etc, One Bump • Internal Splits?: None, 1 (vertical (longest

Notch / Bu side) split into equal area), 1 (angular split 75/25), 2 splits, etc. One (longest Attribute Binary Category Order/Qty side)

Shape Y N ker Type Two Added Marks Y N (same side) Curvature Y yy Angle y y Two Closure Y (longest two Intersection Y sides) Terminators Y yy External Whis Holes Y 50/50 Edge Type y vertical? Corner Type Warp 25/75 Split Type © 2009Not cRichardh Bum Brathp except as otherwise noted. angular? Page 28 And even more attributes

Solid Closed Open Fork More

Each of these attributes may have e

r None multiple sub-dimensions of T richness. Consider: V • Terminator Type: Serif (full) - V, serif, dot, arrow, drop… Serif (½) - solid, closed, open, fork… ½Circle • Holes Dot - 1, 2, 3… End Type vs. Fill/Closu Arrow - square, circle, diamond… Diamond Drop Hook Heart Spade Club 1 Square Pin Branch 2 Circles Half Branch Serrated 3 Diamonds Hole Shape & # Loop

• ~80 very brief stories (5-15 sentences) – Multiple authors, editors, revisions over time • What similarities exist between stories? – In vocabulary – In sentence structure –In dialogue • Inspiration: Stephanie Posavec’s Sentence Drawing visualizations; but with more shape attributes

Example:

The Fox and the Mask

A Fox had by some means got into the store-room of a theatre.

Suddenly he observed a face glaring down on him and began to be very frightened; but looking more closely he found it was only a Mask such as actors use to put over their face.

"Ah," said the Fox, "you look very fine; it is a pity you have not got any brains."

Outside show is a poor substitute for inner worth.

A story is a Each word Punctuation angles the line: Dialog differs in line style: line between is an a start and alternating end: curve: Short Med. Long Comma Semi-Colon Colon Period Normal Dialogue in quotes

A story is a Each word Punctuation angles the line: Dialog differs in line style: line between is an a start and alternating end:© 2009 Richard Brath except as curve:otherwise noted. Page 32 Short Med. Long Comma Semi-Colon Colon Period Normal Dialogue in quotes Experiment #5: Further Work

• Yet more attributes to consider

Attribute Binary Category Order/Qty Shape Y N Added Marks Y N Curvature Y yy Angle y y Closure Y Intersection Y Terminators Y yy Holes Y Edge Type y Corner Type Warp Notch/Bump

Sub-attributes? •Curve: – 2 control points, each with direction and amplitude •Terminator: – Shape and filled/closed/open/forked •Holes – Shape and number

Could sub-attributes make a star/radar glyph more effective?

Problems with radars and stars:

Var 1 1.2 1 0.8 Var 6 0.6 Var 2 0.4 Series1 Series2 Series3 0.2 0

Var 5 Var 3

Series4 Series5 Series6 Series7 Var 4 Series1 Series2 Series3 1. Many overlapping lines: Spaghetti difficult to visually Series4 Series5 Series6 separate and decipher. Series7 2. Can be solved by separation. But shape without a reference difficult to decode. 3. Can add a reference (star) but some shapes are still ambiguous. 4. Can add reference and axes. 5. Not just about shape anymore.

Whisker instead of stars: + Ambiguity from radar resolved. - Can the technique scale up to 8, 16, 24, 32, 100 attributes? - How can one refer to which axis? - Doesn’t it just become noise with Series1 Series2 Series3 real data each axis of a different length? - Possibly solvable with interactive filtering. But interaction limits potential in collaboration and hardcopy.

Series4 Series5 Series6 Series7

Bulginess

Twistiness

Amplitude

Legend:

3mo T-Bill Twist: Correlation (clockwise + / counter - ) 2yr Treasury Oil Bulge: Trend (thick = increasing, thin = decreasing) Corn 30yr Treasury Amplitude: Volatility (further = more volatile)

• Yet more attributes to consider

Attribute Binary Category Order/Qty Sub-Attributes . Shape Y N square/circle/triangle/dash/star/kite/etc Added Marks Y N whiskers/etc, amplitude, density Curvature Y yy amplitude, bulge Angle y y angle Closure Y degree of closure? Intersection Y number of branches, tree attributes Terminators Y yy width, depth, none/serif/circle/square Holes Y shape, size, number Edge Type yy shape, amplitude, frequency Corner Type shape, amplitude, frequency Warp bulge/pinch, amplitude, twist, shear Notch/Bump semi-circle/v/square, amplitude, width, number

© 2009 Richard Brath except as otherwise noted. Page 39 The Many Dimensions of Shape Shape has many attributes and sub-attributes, worth much more exploration, experimentation and evaluation. Here’s a possible framework for shape attributes and sub-attributes:

Shape Attribute Categoric Quantitative 1. Closure closed/open degree of closure? 2. Curvature curved a bit/alot/not amplitude, skew, bulge 3. Corner Angle obtuse/right/acute degree of angle 4. Edge Type straight/spiky/etc amplitude, frequency 5. Corner Type sharp/round/serif/etc size 6. End Type none/serif/dot/etc width, depth 7. Notch/Bump v/half-round/etc width, depth 8. Whiskers (?) on/not/slope/etc density, length 9. Holes shape size, number 10. Intersection three/four/five number of spokes 11. Local Warp shear, twist, bulge factor

Fuel Purchases at Fuel Grade Payment Gender Income Mobil by people Regular Cash Male Low ages 36-45: Mid-grade Debit Female Lower-Middle Premium CreditCard Middle-High BrandCard High