Projective Geometry Perspective Cartography

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Projective Geometry PerspectiveCartography

• Katie Allen

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Projective Geometry

• The study of the projection of objects in a plane
  is called projective geometry
• The axioms of projective geometry are
• 1. If A and B are distinct points on a plane,
  there is at least one line containing both A and
  B.
• 2. If A and B are distinct points on a plane,
  there is not more than one line containing both A
  and B.
• 3. Any two lines in a plane have at least one
  point of the plane (which may be the point at
  infinity) in common.
• 4. There is at least one line on a plane.
• 5. Every line contains at least three points of
  the plane.
• 6. All the points of the plane do not belong to
  the same line.

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Information on Perspective

• Perspective is the art and mathematics of
  realistically depicting three-dimensional objects
  in a two-dimensional plane.
• Rules of perspective
• 1. The horizon appears as a line.
• 2. Straight lines in space appear as straight
  lines in the image.
• 3. Sets of parallel lines meet at a vanishing
  point.
• 4. Lines parallel to the picture plane appear
  parallel and therefore have no vanishing point.

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Scholar Artists

• Filippo Brunelleschi
• Born in Florence, Italy, 1377
• Died in Florence, Italy, 1446
• Leon Battista Alberti
• Born in Genoa, Italy, 1404
• Died in Roam, Italy, 1472
• Piero della Francesca
• Born in Sepolero (now Sansepolc), Italy, 1412
• Died in Borgo San Sepolero, Italy, 1492

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Piero della Francesca

• The Flagellation

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Albrecht Dürer

• The Adoration of the Magi

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Leonardo da Vinci

• The Virgin of the Rocks

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Leonardo da Vinci

• The Last Supper

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Raphael of Urbino
Marriage of the Virgin
Ansidei Madonna
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Michelangelo Buonarroti

• The Last Judgement,

Pieta St. Peters, Rome 1500
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Cartography

• Pedro Nunez
• Gerardus Mercator

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Mercator Projections