Non-linear drawing systems
The Art and Science of Depiction
Non-linear
Drawing systems
Fredo Durand
MIT- Lab for Computer Science
Drawing systems
Munch exhibition
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Munch
• Boston College
• Until May 21.
• Birth of expressionism
Drawing systems
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Munch
Drawing systems
Drawing systems
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Munch
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Drawing systems
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1
Munch
Drawing systems
Munch
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Munch
Drawing systems
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Munch
9
Green flash
Drawing systems
Drawing systems
Drawing systems
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Green flash
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Drawing systems
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2
Green flash
Drawing systems
Green flash
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Green flash
Drawing systems
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Anamorphosis
• Gregoire Huret
1670
Drawing systems
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Drawing systems
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Plan
Classification of drawing systems
• Drawing and projection
• Linear
• Non Linear
– Parallel
– Linear perspective & the Renaissance
– Drawing systems
• Orthogonal
• Fold-out oblique
– Horizontal oblique
– Vertical oblique
Catalogue of “all” drawing systems
Advantage/disadvantages
• Orthographic
– Isometric
– Others
– Distortion and constraints
• Non orthogonal
– Oblique
– Axonometric
• Denotation
• Tone & color
– Linear perspective
• One point
• Two points
• Three points
– Quasi linear
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Naïve perspective
Expressionist perspective
Importance-driven
Cell panorama
– Curved projections
• Panorama
• Fish-eye
– Topological
– Split views, fold-out
– Multiple viewpoints
– Divergent perspective
Drawing systems
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Drawing systems
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Linear projections
Classification of drawing systems
• Straight lines and alignments are preserved
• Can be expressed in primary geometry
• Linear
– Parallel
– Linear perspective
– Divergent perspective
– Ray-image intersections
– A matrix
• Non Linear
• Parallel
– Quasi linear
– Curved projections
– Topological
– Split views, fold-out
– Multiple viewpoints
• Linear perspective
• Divergent perspective
Drawing systems
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Drawing systems
Non Linear
Non Linear
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Does not preserve straight lines
Can get rid of some distortions
More freedom
Dramatic effects
Drawing systems
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Quasi linear
Curved projections
Topological
Split views, fold-out
Multiple viewpoints
Drawing systems
Quasi linear
Quasi linear
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Locally linear
Preserves the drawn straight lines
No “accurate” space
Unified space
Drawing systems
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Naïve perspective
“Expressionist” perspective
Importance-driven
Locally linear
Cell panorama
Drawing systems
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4
Naïve perspective
Naïve perspective
• Attempt to depict scene 3 dimensionally
• Often lack of skill
• More or less formal secondary geometry rules
• Pompeii
Drawing systems
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Drawing systems
Naïve perspective
Naïve perspective
• Giotto
• 18th century
Drawing systems
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Drawing systems
Locally linear
Locally linear
• Linear for objects or parts of the scene
• Choose the best system for each part
• Allows different scales, provide context
• Folk
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• In fact, this is the most common system!
Drawing systems
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Drawing systems
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Locally linear
Locally linear
• Egyptian
• Best view
for each
object
Drawing systems
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Locally linear
Drawing systems
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Locally linear
• Persian miniature, 1494
• Oblique+vertical oblique
Drawing systems
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Drawing systems
Locally linear
Locally linear
• Plan of Manhattan
• Llibre Dels Feus
1162-1199
Drawing systems
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Drawing systems
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Locally linear
Locally linear
• St John the Baptist Retiring to the Desert
Giovanni di Paolo 1454
• Raphael, The School of Athens
Drawing systems
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Importance-driven
Drawing systems
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Importance-driven
• Size depends on importance, symbol
Drawing systems
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Drawing systems
Importance-driven
Comparison
• Piero de la Francesca
Mercy
• Piero de la Francesca , Flagellation, 1460
Drawing systems
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Drawing systems
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Importance-driven
Data-driven
• Scientific American
Drawing systems
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Drawing systems
Cell multiperspective panorama
Multiperspective panorama
• Pinocchio, Walt Disney
• [Wood et al. 98]
Drawing systems
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Drawing systems
Multiperspective panorama
Multiperspective panorama
• [Wood et al. 98]
• [Wood et al. 98]
Drawing systems
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Drawing systems
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“Impressionist” perspective
“Expressionist” perspective
• Pissaro
• Munch,
the Scream
Drawing systems
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Drawing systems
“Expressionist” perspective
Cézanne
• Van Gogh
• Still life with basket, composition rule
Drawing systems
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Drawing systems
Cézanne
Cézanne
• Montagne Ste Victoire
• Montagne Ste Victoire
Drawing systems
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Drawing systems
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“Expressionist” perspective
“Expressionist” perspective
• Max Beckman Family Picture 1920
• Umberto
Boccioni
The Street
Enters
The House
1911
Drawing systems
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Drawing systems
Quasi linear
Classification of drawing systems
• Modigliani
Femme au Chapeau
• Linear
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– Parallel
– Linear perspective
– Divergent perspective
• Non Linear
– Quasi linear
– Curved projections
– Topological
– Split views, fold-out
– Multiple viewpoints
Drawing systems
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Drawing systems
Leonardo & contradictions
Leonardo & contradictions
• Wide angle vision
• Wide angle vision
• Lateral recession
Drawing systems
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Drawing systems
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60
10
Curved perspective
Curved perspective
• Panorama
– Preserve verticals
• Fish eye
Drawing systems
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Drawing systems
Curved perspective
Curved perspective
• Jean Fouquet, 15th century
• A View of Delft Carel Fabritius (follower of
Rembrandt) 1652
Drawing systems
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Drawing systems
Curved perspective
Curved perspective
• Turner Petworth Park Tillington, Church in the
Distance 1828
• Panoramic camera
Drawing systems
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Drawing systems
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“Expressionist” perspective
“Expressionist” perspective
• Van Gogh, Bedroom in Arles
• Van Gogh, Bedroom in Arles
Drawing systems
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Curved perspective
Drawing systems
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Fish-eye
• Panorama
– Preserve verticals
• Fish eye
Drawing systems
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Fish-eye vs. wide angle
Drawing systems
Drawing systems
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Fish-eye vs. wide angle
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Drawing systems
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Bird’s eye attachment
Drawing systems
Fish-eye
73
Drawing systems
Fish-eye
Fish-eye
• MC Escher,
Hand with
Reflecting Globe
• MC Escher,
Balcony
Drawing systems
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Drawing systems
Fish-eye
Fish-eye
• London from
St Paul's
cathedral
1845
• Anthony Green The 30th Wedding Anniversary
Drawing systems
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Drawing systems
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Projection surface
Projection
• Panorama, Imax
• “Good viewpoint”
• Pavilion in the
Colosseum
Regent's Park
1829
– Primary geometry and viewing conditions match
Drawing systems
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Drawing systems
Classification of drawing systems
Topological
• Linear
• Paul Klee,
Another Camel
– Parallel
– Linear perspective
– Divergent perspective
80
• Non Linear
– Quasi linear
– Curved projections
– Topological
– Split views, fold-out
– Multiple viewpoints
Drawing systems
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Drawing systems
Topological
Topological
• London Underground, Beck, 1931
• Children drawing
Drawing systems
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Drawing systems
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84
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Topological
Classification of drawing systems
• Comics
• Linear
– Parallel
– Linear perspective
– Divergent perspective
• Non Linear
– Quasi linear
– Curved projections
– Topological
– Split views, fold-out
– Multiple viewpoints
Drawing systems
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Split views, fold-out
Drawing systems
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Split views, fold-out
• Can be seen as a smooth viewpoint change
• Can represent an object from all sides
• Continuity, preserves topology
Drawing systems
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Split views, fold-out
Drawing systems
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Split views, fold-out
• Picasso,
Portrait of a woman
Drawing systems
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Drawing systems
90
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Split views, fold-out
Split views, fold-out
• Northwest Indian
Double Profile Bear
Drawing systems
91
Drawing systems
Split views, fold-out
Split views, fold-out
• Multiple-center of projection images, Paul
Rademacher
• Multiple-center of projection images, Paul
Rademacher
Drawing systems
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Drawing systems
Split views, fold-out
Split views, fold-out
• Multicultural
study
• Interactive caricature (Fred Vernier)
Drawing systems
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Drawing systems
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96
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Split views, fold-out
Split views, fold-out
• Interactive caricature (Fred Vernier)
• Interactive caricature (Fred Vernier)
Drawing systems
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Drawing systems
Split views, fold-out
Cinema
• Interactive caricature (Fred Vernier)
• Robert Wiene The cabinet of Dr Caligari 19191920
Drawing systems
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Drawing systems
Classification of drawing systems
Multiple viewpoints
• Linear
• No more unity of pictorial space
• Represents objects from different viewpoints
• Less continuity, no topology
– Parallel
– Linear perspective
– Divergent perspective
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• Non Linear
– Quasi linear
– Curved projections
– Topological
– Split views, fold-out
– Multiple viewpoints
Drawing systems
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Drawing systems
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Cubism
Cubism
• Candlestick
George Braque
1911
• Boats
George Braque
Drawing systems
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Hockney
Drawing systems
Drawing systems
Hockney
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Drawing systems
Escher
Mirrors, lenses
• Other World 1947
• Freddie Francis
The Skull
Drawing systems
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Drawing systems
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108
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Mirrors, lenses
Mirrors, lenses
• Hedgecoe
• Casas Abarca
Le Salon
1875-1958
Drawing systems
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Drawing systems
Mirrors, lenses
Discussion
• Manet, Le Bar Des Folies Bergeres
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Drawing systems
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No universal solution
Secondary geometry
Invariants
Property mapping or translation
Drawing systems
112
Drawing and cinema
• Characters too close
• Trenching
• Etc.
Drawing systems
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