the anamorphic imagerhammack/math490/adrian.pdfsidewalk drawings by julian beever. floor drawings by...
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The Anamorphic Image
Richard Hammack
MATH 490February 4, 2015
www.people.vcu.edu/∼rhammack
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Why do the tracks converge?
Answer Involves Two Facts
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Why do the tracks converge?Answer Involves Two Facts
![Page 7: The Anamorphic Imagerhammack/Math490/Adrian.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Shigeo Fukuda (1936{2009) Shigeo Fukuda (1936{2009) Shigeo Fukuda](https://reader034.vdocument.in/reader034/viewer/2022042708/5f38a27525684e337d08b3df/html5/thumbnails/7.jpg)
1. If you look at a line straight on, you see...
...a point:
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1. If you look at a line straight on, you see...
...a point:
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1. If you look at a line straight on, you see...
...a point:
2. If you look at a plane straight on, you see...
...a line:
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1. If you look at a line straight on, you see...
...a point:
2. If you look at a plane straight on, you see...
...a line:
![Page 11: The Anamorphic Imagerhammack/Math490/Adrian.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Shigeo Fukuda (1936{2009) Shigeo Fukuda (1936{2009) Shigeo Fukuda](https://reader034.vdocument.in/reader034/viewer/2022042708/5f38a27525684e337d08b3df/html5/thumbnails/11.jpg)
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P
P′
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P
P′
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Frescoed wall of the shrine of Hathor from Deir el-BahriNew Kingdom 1570-1070 BCE
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Spanish, c. 1180 Lippo Memmi (Italian, Sienese) c. 1340 English, c. 1270
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Giotto di Bondone
Homage of a Simple Man Meeting at the Golden Gate
(detail) 1295–1300 1304–1306
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Giotto di Bondone
Homage of a Simple Man Meeting at the Golden Gate
(detail) 1295–1300 1304–1306
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Duccio di Buoninsegna, c. 1310
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Duccio di Buoninsegna, c. 1310
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Duccio di Buoninsegna, c. 1310
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Fra Angelico
Annunciation, c. 1450
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Fra Angelico
Annunciation, c. 1450
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The Inventors of Perspective
Filippo Brunelleschi1377–1446
Leone Battista Alberti1404–1472
Piero della Francesca1412–1492
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From Peiro della Francesca’s book On Perspective for Painting, c. 1475
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Piero della Francesca, Federigo da Montefeltro and his wife Battista Sforza
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Piero della Francesca, The Flagellation of Christ, 1460
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Piero della Francesca, The Flagellation of Christ, 1460
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Piero della Francesca, 1473Virgin and Child with Saints, Angels, and Federigo da Montefeltro
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Piero della Francesca, 1473Virgin and Child with Saints, Angels, and Federigo da Montefeltro
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Hans Holbein the Younger, The Ambassadors, 1533
Anamorphosis
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Hans Holbein the Younger, The Ambassadors, 1533
Anamorphosis
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How to make an anamorphosis
A
B C
D A′
B′
V
D′
C ′
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How to make an anamorphosis
A
B C
D
A′
B′
V
D′
C ′
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How to make an anamorphosis
A
B C
D A′
B′
V
D′
C ′
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How to make an anamorphosis
A
B C
D A′
B′
V
D′
C ′
![Page 36: The Anamorphic Imagerhammack/Math490/Adrian.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Shigeo Fukuda (1936{2009) Shigeo Fukuda (1936{2009) Shigeo Fukuda](https://reader034.vdocument.in/reader034/viewer/2022042708/5f38a27525684e337d08b3df/html5/thumbnails/36.jpg)
How to make an anamorphosis
A
B C
D A′
B′
V
D′
C ′
![Page 37: The Anamorphic Imagerhammack/Math490/Adrian.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Shigeo Fukuda (1936{2009) Shigeo Fukuda (1936{2009) Shigeo Fukuda](https://reader034.vdocument.in/reader034/viewer/2022042708/5f38a27525684e337d08b3df/html5/thumbnails/37.jpg)
How to make an anamorphosis
A
B C
D A′
B′
V
D′
C ′
![Page 38: The Anamorphic Imagerhammack/Math490/Adrian.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Shigeo Fukuda (1936{2009) Shigeo Fukuda (1936{2009) Shigeo Fukuda](https://reader034.vdocument.in/reader034/viewer/2022042708/5f38a27525684e337d08b3df/html5/thumbnails/38.jpg)
How to make an anamorphosis
A
B C
D A′
B′
V
D′
C ′
![Page 39: The Anamorphic Imagerhammack/Math490/Adrian.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Shigeo Fukuda (1936{2009) Shigeo Fukuda (1936{2009) Shigeo Fukuda](https://reader034.vdocument.in/reader034/viewer/2022042708/5f38a27525684e337d08b3df/html5/thumbnails/39.jpg)
How to make an anamorphosis
A
B C
D A′
B′
V
D′
C ′
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How to make an anamorphosis
A
B C
D A′
B′
V
D′
C ′
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How to make an anamorphosis
A
B C
D A′
B′
V
D′
C ′
![Page 42: The Anamorphic Imagerhammack/Math490/Adrian.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Shigeo Fukuda (1936{2009) Shigeo Fukuda (1936{2009) Shigeo Fukuda](https://reader034.vdocument.in/reader034/viewer/2022042708/5f38a27525684e337d08b3df/html5/thumbnails/42.jpg)
How to make an anamorphosis
A
B C
D A′
B′
V
D′
C ′
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How to make an anamorphosis
A
B C
D A′
B′
V
D′
C ′
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How to make an anamorphosis
A
B C
D A′
B′
V
D′
C ′
![Page 45: The Anamorphic Imagerhammack/Math490/Adrian.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Shigeo Fukuda (1936{2009) Shigeo Fukuda (1936{2009) Shigeo Fukuda](https://reader034.vdocument.in/reader034/viewer/2022042708/5f38a27525684e337d08b3df/html5/thumbnails/45.jpg)
How to make an anamorphosis
A
B C
D A′
B′
V
D′
C ′
![Page 46: The Anamorphic Imagerhammack/Math490/Adrian.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Shigeo Fukuda (1936{2009) Shigeo Fukuda (1936{2009) Shigeo Fukuda](https://reader034.vdocument.in/reader034/viewer/2022042708/5f38a27525684e337d08b3df/html5/thumbnails/46.jpg)
How to make an anamorphosis
A
B C
D A′
B′
V
D′
C ′
![Page 47: The Anamorphic Imagerhammack/Math490/Adrian.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Shigeo Fukuda (1936{2009) Shigeo Fukuda (1936{2009) Shigeo Fukuda](https://reader034.vdocument.in/reader034/viewer/2022042708/5f38a27525684e337d08b3df/html5/thumbnails/47.jpg)
How to make an anamorphosis
A
B C
D A′
B′
V
D′
C ′
![Page 48: The Anamorphic Imagerhammack/Math490/Adrian.pdfSidewalk Drawings by Julian Beever. Floor Drawings by Kurt Wenner. Shigeo Fukuda (1936{2009) Shigeo Fukuda (1936{2009) Shigeo Fukuda](https://reader034.vdocument.in/reader034/viewer/2022042708/5f38a27525684e337d08b3df/html5/thumbnails/48.jpg)
Leonardo da Vinci, c. 1505
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Erhard Schon, c.1531-4
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Istvan Orosz
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Istvan Orosz
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Istvan Orosz (1981)
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Istvan Orosz (1981)
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Istvan Orosz (1997)
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Istvan Orosz (1997)
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Istvan Orosz (1997)
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Sidewalk Drawings by Julian Beever
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Floor Drawings by Kurt Wenner
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Shigeo Fukuda (1936–2009)
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Shigeo Fukuda (1936–2009)
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Shigeo Fukuda (1936–2009)
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Shigeo Fukuda (1936–2009)
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Shigeo Fukuda (1936–2009)
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Tim Noble and Sue Webster
Real Life is Rubbish
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