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History of
Perspective
Projective Geometry
May 2008
Optics
    The science that describes the behavior

    and properties of light and the interaction
    of light with mat...
History of Optics
    ~300 BC: Euclid (Alexandria) In his Optica he noted that light travels

    in straight lines and d...
History of Optics
    ~1000 AD: Ibn al-Haytham gave the first correct explanation of

    vision, showing that light is r...
History of Optics
    ~1278: Witelo wrote Perspectiva, which became the standard text

    for optics for the next few ce...
Early Perspective
    ~1000 AD: Master of the Sophien Cathedral of Ohrid, Fresco

Early Perspective
    1290: Giotto, L'hommage d'un homme simple

Early Perspective
    ~1333: Simone Martini's

    Passion (or Orsini) Polyptych
Renaissance Perspective
    Filippo Brunelleschi (1377-1446)

      Inventor of linear perspective
    
     Architect ...
Renaissance Perspective
    1425: Masaccio, Holy Trinity

Renaissance Perspective
    1435: Alberti wrote De Pictura

    De pictura is in three parts, the first of which gives th...
Renaissance Perspective
     1410-1492: Piero Della Francesca
 
     Artist and mathematician, painted famous work as wel...
Renaissance Perspective
~1460, Piero Della Francesca, Flagellation of Christ
Renaissance Perspective
    ~1470: Piero Della Francesca, Ideal City

Renaissance Perspective
    ~1498: Leonardo da Vinci, The Last Supper

Historical context
    ~1439: Gutenberg invented moveable type printing

    ~1480: Beginning of Renaissance Humanism, a ...
Renaissance Perspective
    1518: Raphael, The School of Athens

2-Point Perspective
    1505: Pélérin, first known diagrams of 2-point perspective in his

    book, De Artificiali Persp...
2-Point Perspective
    1517: Raphael, Coronation of Charlemagne

2-Point Perspective
    1517: Raphael, Coronation of Charlemagne

2-Point Perspective




http://visualeditors.ning.com/video/video/show?id=1985197%3AVideo%3A9529
3-Point Perspective
    1960: M.C. Escher, Ascending and Descending

Camera Obscura, Anamorphism
    David Hockney (1937- ) believes that the Old Masters, including

    Caravaggio, Vermeer,...
Renaissance Perspective
    1525: Albrecht Dürer, Instruction How to Measure with Compass

    and Straight Edge
Camera Obscura, Anamorphism
    1533: Hans Holbein the Younger, The Ambassadors





                                   H...
Camera Obscura, Anamorphism
    1533: Hans Holbein the Younger, The Ambassadors

Play on Perspective
    1754: William Hogarth, False Perspective

Play on Perspective
    1914: Giorgio di Chirico, Melancholy and Mystery of a Street

Play on Perspective
    1955: Rene Magritte, Promenades of Euclid

Multiple Viewpoints
    1986: David Hockney, Pearblossom Highway

Multiple Viewpoints
    1432: Jan van Eyck, Ghent Altarpiece

one point perspective
How to draw a house and fence




    Draw the front of the house.

How to draw a house and fence




    Indicate a vanishing point, draw the side of the house.

How to draw a house and fence




    Find the center of the wall by drawing an X, draw roof.

    How do we draw the roo...
How to draw a house and fence




    Follow the side of the roof to a point directly above v0.

How to draw a house and fence




    That is the second vanishing point for the other roof.

How to draw a house and fence




    Nice house!

How to draw a house and fence




    The house is on the side of the road. Draw the road.

How to draw a house and fence




    To make a fence along the road, draw a second

    vanishing point using diagonals....
How to draw a house and fence




    Nice fence posts!

How to draw a house and fence




    What a lovely house and fence in perspective.

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History Of Perspective

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History Of Perspective

  1. 1. History of Perspective Projective Geometry May 2008
  2. 2. Optics The science that describes the behavior  and properties of light and the interaction of light with matter.
  3. 3. History of Optics ~300 BC: Euclid (Alexandria) In his Optica he noted that light travels  in straight lines and described the law of reflection.  believed that vision involves rays going from the eyes to the object seen.  studied the relationship between the apparent sizes of objects and the angles that they subtend at the eye.
  4. 4. History of Optics ~1000 AD: Ibn al-Haytham gave the first correct explanation of  vision, showing that light is reflected from an object into the eye. Wrote 7 volume work on Optics, Kitab al-Manazir. Translated into Latin  in 1270, Opticae thesaurus Alhazeni.
  5. 5. History of Optics ~1278: Witelo wrote Perspectiva, which became the standard text  for optics for the next few centuries Largely taken from al-Haytham’s work, recently translated  Greatly influenced Kepler (of the Laws of Planetary Motion fame) and  Leonardo da Vinci Witelo had a moon crater named after him, Vitello 
  6. 6. Early Perspective ~1000 AD: Master of the Sophien Cathedral of Ohrid, Fresco 
  7. 7. Early Perspective 1290: Giotto, L'hommage d'un homme simple 
  8. 8. Early Perspective ~1333: Simone Martini's  Passion (or Orsini) Polyptych
  9. 9. Renaissance Perspective Filippo Brunelleschi (1377-1446)  Inventor of linear perspective   Architect of dome on Florence Cathedral  understood that there should be a single vanishing point to which all parallel lines in a plane converge.  correctly computed the relation between the actual length of an object and its length in the picture depending on its distance behind the plane of the canvas.
  10. 10. Renaissance Perspective 1425: Masaccio, Holy Trinity 
  11. 11. Renaissance Perspective 1435: Alberti wrote De Pictura  De pictura is in three parts, the first of which gives the mathematical  description of perspective which Alberti considers necessary to a proper understanding of painting.
  12. 12. Renaissance Perspective 1410-1492: Piero Della Francesca  Artist and mathematician, painted famous work as well as write  mathematics texts icosahedron inscribed in a cube, ~1460 Flagellation of Christ from text: Libellus De Quinque Corporibus Regularibus,
  13. 13. Renaissance Perspective ~1460, Piero Della Francesca, Flagellation of Christ
  14. 14. Renaissance Perspective ~1470: Piero Della Francesca, Ideal City 
  15. 15. Renaissance Perspective ~1498: Leonardo da Vinci, The Last Supper 
  16. 16. Historical context ~1439: Gutenberg invented moveable type printing  ~1480: Beginning of Renaissance Humanism, a return to  primary sources, study of Latin and Greek texts ~1492: Age of Exploration: de Gama and Columbus go  exploring ~1517: Protestant Reformation: Luther challenges the  Pope’s authority ~1543: Scientific Revolution: Copernicus displaced earth  as the center of the universe
  17. 17. Renaissance Perspective 1518: Raphael, The School of Athens 
  18. 18. 2-Point Perspective 1505: Pélérin, first known diagrams of 2-point perspective in his  book, De Artificiali Perspectiva
  19. 19. 2-Point Perspective 1517: Raphael, Coronation of Charlemagne 
  20. 20. 2-Point Perspective 1517: Raphael, Coronation of Charlemagne 
  21. 21. 2-Point Perspective http://visualeditors.ning.com/video/video/show?id=1985197%3AVideo%3A9529
  22. 22. 3-Point Perspective 1960: M.C. Escher, Ascending and Descending 
  23. 23. Camera Obscura, Anamorphism David Hockney (1937- ) believes that the Old Masters, including  Caravaggio, Vermeer, Holbein, Ingres, etc. used the camera obscura to paint with perfect accuracy.
  24. 24. Renaissance Perspective 1525: Albrecht Dürer, Instruction How to Measure with Compass  and Straight Edge
  25. 25. Camera Obscura, Anamorphism 1533: Hans Holbein the Younger, The Ambassadors  Hockney believes Hans Holbein the Younger may have used camera obscura to paint certain objects in the room, including • the lute • the globe • the music written in the books •the drapery
  26. 26. Camera Obscura, Anamorphism 1533: Hans Holbein the Younger, The Ambassadors 
  27. 27. Play on Perspective 1754: William Hogarth, False Perspective 
  28. 28. Play on Perspective 1914: Giorgio di Chirico, Melancholy and Mystery of a Street 
  29. 29. Play on Perspective 1955: Rene Magritte, Promenades of Euclid 
  30. 30. Multiple Viewpoints 1986: David Hockney, Pearblossom Highway 
  31. 31. Multiple Viewpoints 1432: Jan van Eyck, Ghent Altarpiece 
  32. 32. one point perspective
  33. 33. How to draw a house and fence Draw the front of the house. 
  34. 34. How to draw a house and fence Indicate a vanishing point, draw the side of the house. 
  35. 35. How to draw a house and fence Find the center of the wall by drawing an X, draw roof.  How do we draw the roof on the other side? 
  36. 36. How to draw a house and fence Follow the side of the roof to a point directly above v0. 
  37. 37. How to draw a house and fence That is the second vanishing point for the other roof. 
  38. 38. How to draw a house and fence Nice house! 
  39. 39. How to draw a house and fence The house is on the side of the road. Draw the road. 
  40. 40. How to draw a house and fence To make a fence along the road, draw a second  vanishing point using diagonals. Draw the other fence posts. 
  41. 41. How to draw a house and fence Nice fence posts! 
  42. 42. How to draw a house and fence What a lovely house and fence in perspective. 

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