projections - algorithmic botany
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Orthographic projection is very simple...
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x
y
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n!
xn
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Oblique projection
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Parallel
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Perspective
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Parallel
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Perspective
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Geometric perspective
16th century copy of Leonardo da Vinci’s The Last Supper (1498)Convent of Santa Maria delle Grazie (Refectory), Milan
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Geometric perspective
Christ Handing the Keys to St. Peter by Pietro Perugino (1481-82) Fresco, 335 x 550 cm Cappella Sistina, Vatican
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Albrecht Dürer: The Painter's Manual, 1525. Another perspective device.
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Perspective transformation
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Camera obscura (Mo-Ti, China, 470-390 BC); Aristotle, Euclid (~350-300BC)
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Argument 1: sudden increase of realism (incl. shading) between 1425 and 1430
Masolino da Panicale 1425 Robert Campin 1430
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Argument 2: geometry of textures
Masolino da Panicale ~1425
Antonio and Piero del Pollaiuolo 1467-8
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Agnolo Bronzino 1545
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Argument 3: curved mirrors (and lenses) were known
Arnolfini Weddingvan Eyck 1434
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Hans Holbein The Ambassadors 1533
Argument 4: precision and distortions
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Hans Holbein The Ambassadors 1533
Argument 4: precision and distortions
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Hans Holbein The Ambassadors 1533
Argument 4: precision and distortions
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Argument 5: reflections and refractions
Frans Hals 1626-8
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Argument 6: drawing speed
Still life, Cotan 1602
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Another use of perspective:Piazza del Popolo (Rome) : Bernini, 2nd half of 17th century
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Another use of perspective:Piazza del Popolo (Rome) : Bernini, 2nd half of 17th century
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Non-linear perspective
See also:http://people.csail.mit.edu/fredo/Depiction/15_Drawing/nonlinear.pdf