Fooling The Eye: Brunelleschi, Alberti, & Linear Perspective

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Fooling The Eye: Brunelleschi, Alberti, & Linear Perspective

  1. 1. Fooling The Eye Brunelleschi, Alberti & Linear Perspective Professor Will Adams Valencia CollegeTuesday, February 26, 13
  2. 2. THE INVENTION OF LINEAR PERSPECTIVETuesday, February 26, 13
  3. 3. WHAT IS LINEAR PERSPECTIVE?Tuesday, February 26, 13
  4. 4. WHAT IS LINEAR PERSPECTIVE?  Linear perspective is a system for creating the illusion of a three- dimensional space on a two- dimensional, flat surface.Tuesday, February 26, 13
  5. 5. WHAT IS LINEAR PERSPECTIVE?  Linear perspective is a system for creating the illusion of a three- dimensional space on a two- dimensional, flat surface.  It was discovered in Florence, Italy in the early 15th century by Filippo Brunelleschi & Leon Batista Alberti.Tuesday, February 26, 13
  6. 6. DEVELOPING LINEAR PERSPECTIVE  Filippo Brunelleschi (1377-1446 CE) was the Italian sculptor and architect who demonstrated the principles of perspective through optics.  In 1415 CE, Brunelleschi painted a picture of the Florentine Baptistery on the surface of a small mirror, right on top of its own reflection.Tuesday, February 26, 13
  7. 7. DEVELOPING LINEAR PERSPECTIVETuesday, February 26, 13
  8. 8. DEVELOPING LINEAR PERSPECTIVE  To demonstrate the fact that his painting was indeed an exact replica that could fool the eye, Brunelleschi drilled a small hole in the mirror and then stood directly in front of the Baptistery, looking through the peephole to see the real building. Tuesday, February 26, 13
  9. 9. DEVELOPING LINEAR PERSPECTIVE  To demonstrate the fact that his painting was indeed an exact replica that could fool the eye, Brunelleschi drilled a small hole in the mirror and then stood directly in front of the Baptistery, looking through the peephole to see the real building.   He then held up a second, clean mirror in front of his painted panel.  The second mirror blocked the view of the real building, but now reflected his painted version on the original mirror.Tuesday, February 26, 13
  10. 10. DEVELOPING LINEAR PERSPECTIVETuesday, February 26, 13
  11. 11. DEVELOPING LINEAR PERSPECTIVETuesday, February 26, 13
  12. 12. DEVELOPING LINEAR PERSPECTIVE  By holding up the panel and pressing the hole to one eye while holding a mirror with the other hand, the viewer could see the painting’s reflection.Tuesday, February 26, 13
  13. 13. DEVELOPING LINEAR PERSPECTIVE  By holding up the panel and pressing the hole to one eye while holding a mirror with the other hand, the viewer could see the painting’s reflection.  A viewer standing in the cathedral doorway could check the painted illusion against the real view.Tuesday, February 26, 13
  14. 14. LEON BATTISTA ALBERTITuesday, February 26, 13
  15. 15. LEON BATTISTA ALBERTI  Alberti (1404-1472) was an architect and writer who first formulates rules that artists could follow to create perspectival work.Tuesday, February 26, 13
  16. 16. LEON BATTISTA ALBERTI  Alberti (1404-1472) was an architect and writer who first formulates rules that artists could follow to create perspectival work.  He imagined the picture surface as an “open window” through which a painted world is seen.Tuesday, February 26, 13
  17. 17. LEON BATTISTA ALBERTI  Alberti (1404-1472) was an architect and writer who first formulates rules that artists could follow to create perspectival work.  He imagined the picture surface as an “open window” through which a painted world is seen.  Showed how a perspective “checkerboard pavement” is created within the picture space - in which the receding parallel lines represent the visual rays connecting the spectator’s eye to a spot in the distance.Tuesday, February 26, 13
  18. 18. LEON BATTISTA ALBERTI  Based his system on the height of the human figure, being 3 braccia tall  Drew a rectangular picture plane, imagined as an open window  Divided the ground line into 6 scaled braccia  Fixed the central vanishing point by drawing a vertical line three braccia high from the center of the ground line  Drew diagonals – orthogonals - joining the ground line to the vanishing pointTuesday, February 26, 13
  19. 19. USING LINEAR PERSPECTIVETuesday, February 26, 13
  20. 20. USING LINEAR PERSPECTIVE  Brunelleschi used the knowledge of perspective for architectural purposes.Tuesday, February 26, 13
  21. 21. USING LINEAR PERSPECTIVE  Brunelleschi used the knowledge of perspective for architectural purposes.  He is said to have made a ground plan for the Church of Santo Spirito on the basis of which he produced a perspective drawing to show his clients how it would look after it was built.Tuesday, February 26, 13
  22. 22. USING LINEAR PERSPECTIVE  Brunelleschi used the knowledge of perspective for architectural purposes.  He is said to have made a ground plan for the Church of Santo Spirito on the basis of which he produced a perspective drawing to show his clients how it would look after it was built.  We can compare this drawing with a modern photo of the actual church.Tuesday, February 26, 13
  23. 23. USING LINEAR PERSPECTIVE Brunelleschi’s proposal drawing of A photograph of the interior of Santo Santo Spirito, dated 1543 Spirito as it looks today.Tuesday, February 26, 13
  24. 24. USING LINEAR PERSPECTIVE Brunelleschi’s proposal drawing of A photograph of the interior of Santo Santo Spirito, dated 1543 Spirito as it looks today.Tuesday, February 26, 13
  25. 25. ONE-POINT PERSPECTIVETuesday, February 26, 13
  26. 26. ONE-POINT PERSPECTIVETuesday, February 26, 13
  27. 27. ONE-POINT PERSPECTIVE LINEAR PERSPECTIVETuesday, February 26, 13
  28. 28. ONE-POINT PERSPECTIVE LINEAR PERSPECTIVE  Based on the way the human eye sees the world.Tuesday, February 26, 13
  29. 29. ONE-POINT PERSPECTIVE LINEAR PERSPECTIVE  Based on the way the human eye sees the world.  Objects that are closer appear larger, more distant objects appear smaller.Tuesday, February 26, 13
  30. 30. ONE-POINT PERSPECTIVE LINEAR PERSPECTIVE  Based on the way the human eye sees the world.  Objects that are closer appear larger, more distant objects appear smaller.  To create the illusion of space the artist creates a vanishing point on the horizon line.Tuesday, February 26, 13
  31. 31. ONE-POINT PERSPECTIVE LINEAR PERSPECTIVE  Based on the way the human eye sees the world.  Objects that are closer appear larger, more distant objects appear smaller.  To create the illusion of space the artist creates a vanishing point on the horizon line.  Objects are drawn using orthogonal lines, which lead to the vanishing point.Tuesday, February 26, 13
  32. 32. ONE-POINT PERSPECTIVE  Horizon Line: The place where the land and the sky meet.  Vanishing Point: The single point on the horizon where all the lines on the ground level seem to come together.  Orthogonals: Lines that connect to the vanishing point.Tuesday, February 26, 13
  33. 33. ONE-POINT PERSPECTIVE  Horizon Line: The place where the land and the sky meet.  Vanishing Point: The single point on the horizon where all the lines on the ground level seem to come together.  Orthogonals: Lines that connect to the vanishing point.Tuesday, February 26, 13
  34. 34. ONE-POINT PERSPECTIVE  Horizon Line: The place where the land and the sky meet.  Vanishing Point: The single point on the horizon where all the lines on the ground level seem to come together.  Orthogonals: Lines that connect to the vanishing point.Tuesday, February 26, 13
  35. 35. ONE-POINT PERSPECTIVE  Horizon Line: The place where the land and the sky meet.  Vanishing Point: The single point on the horizon where all the lines on the ground level seem to come together.  Orthogonals: Lines that connect to the vanishing point.Tuesday, February 26, 13
  36. 36. ONE-POINT PERSPECTIVE  Horizon Line: The place where the land and the sky meet.  Vanishing Point: The single point on the horizon where all the lines on the ground level seem to come together.  Orthogonals: Lines that connect to the vanishing point.Tuesday, February 26, 13
  37. 37. ONE-POINT PERSPECTIVE  Horizon Line: The place where the land and the sky meet.  Vanishing Point: The single point on the horizon where all the lines on the ground level seem to come together.  Orthogonals: Lines that connect to the vanishing point.Tuesday, February 26, 13
  38. 38. ONE-POINT PERSPECTIVE  Horizon Line: The place where the land and the sky meet.  Vanishing Point: The single point on the horizon where all the lines on the ground level seem to come together.  Orthogonals: Lines that connect to the vanishing point.Tuesday, February 26, 13
  39. 39. ONE-POINT PERSPECTIVE In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  40. 40. ONE-POINT PERSPECTIVE In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  41. 41. ONE-POINT PERSPECTIVE Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  42. 42. ONE-POINT PERSPECTIVE Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  43. 43. ONE-POINT PERSPECTIVE Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  44. 44. ONE-POINT PERSPECTIVE Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  45. 45. ONE-POINT PERSPECTIVE Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  46. 46. ONE-POINT PERSPECTIVE Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  47. 47. ONE-POINT PERSPECTIVE Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  48. 48. ONE-POINT PERSPECTIVE Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  49. 49. ONE-POINT PERSPECTIVE Orthogonals Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  50. 50. ONE-POINT PERSPECTIVE Orthogonals Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  51. 51. ONE-POINT PERSPECTIVE Orthogonals Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  52. 52. ONE-POINT PERSPECTIVE Orthogonals Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  53. 53. ONE-POINT PERSPECTIVE Orthogonals Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  54. 54. ONE-POINT PERSPECTIVE Orthogonals Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  55. 55. ONE-POINT PERSPECTIVE Orthogonals Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  56. 56. ONE-POINT PERSPECTIVE Vanishing point! Orthogonals Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  57. 57. ONE-POINT PERSPECTIVE Vanishing point! Orthogonals Horizon Line In one-point perspective, the vanishing point can be at any location along the horizon line; where is the vanishing point in this example?Tuesday, February 26, 13
  58. 58. ONE-POINT PERSPECTIVE In this painting, Little Street, by Vermeer, the vanishing point is hidden by the building itself; can you locate it?Tuesday, February 26, 13
  59. 59. ONE-POINT PERSPECTIVE In this painting, Little Street, by Vermeer, the vanishing point is hidden by the building itself; can you locate it?Tuesday, February 26, 13
  60. 60. ONE-POINT PERSPECTIVE Horizon Line In this painting, Little Street, by Vermeer, the vanishing point is hidden by the building itself; can you locate it?Tuesday, February 26, 13
  61. 61. ONE-POINT PERSPECTIVE Horizon Line In this painting, Little Street, by Vermeer, the vanishing point is hidden by the building itself; can you locate it?Tuesday, February 26, 13
  62. 62. ONE-POINT PERSPECTIVE Horizon Line In this painting, Little Street, by Vermeer, the vanishing point is hidden by the building itself; can you locate it?Tuesday, February 26, 13
  63. 63. ONE-POINT PERSPECTIVE Horizon Line In this painting, Little Street, by Vermeer, the vanishing point is hidden by the building itself; can you locate it?Tuesday, February 26, 13
  64. 64. ONE-POINT PERSPECTIVE Horizon Line In this painting, Little Street, by Vermeer, the vanishing point is hidden by the building itself; can you locate it?Tuesday, February 26, 13
  65. 65. ONE-POINT PERSPECTIVE Horizon Line In this painting, Little Street, by Vermeer, the vanishing point is hidden by the building itself; can you locate it?Tuesday, February 26, 13
  66. 66. ONE-POINT PERSPECTIVE Horizon Line Orthogonals In this painting, Little Street, by Vermeer, the vanishing point is hidden by the building itself; can you locate it?Tuesday, February 26, 13
  67. 67. ONE-POINT PERSPECTIVE Horizon Line Orthogonals In this painting, Little Street, by Vermeer, the vanishing point is hidden by the building itself; can you locate it?Tuesday, February 26, 13
  68. 68. ONE-POINT PERSPECTIVE Horizon Line Orthogonals In this painting, Little Street, by Vermeer, the vanishing point is hidden by the building itself; can you locate it?Tuesday, February 26, 13
  69. 69. ONE-POINT PERSPECTIVE Horizon Line Orthogonals In this painting, Little Street, by Vermeer, the vanishing point is hidden by the building itself; can you locate it?Tuesday, February 26, 13
  70. 70. ONE-POINT PERSPECTIVE Horizon Line Orthogonals In this painting, Little Street, by Vermeer, the vanishing point is hidden by the building itself; can you locate it?Tuesday, February 26, 13
  71. 71. ONE-POINT PERSPECTIVE Horizon Line Orthogonals In this painting, Little Street, by Vermeer, the vanishing point is hidden by the building itself; can you locate it?Tuesday, February 26, 13
  72. 72. ONE-POINT PERSPECTIVE Vanishing Point! Horizon Line Orthogonals In this painting, Little Street, by Vermeer, the vanishing point is hidden by the building itself; can you locate it?Tuesday, February 26, 13
  73. 73. ONE-POINT PERSPECTIVE Vanishing Point! Horizon Line Orthogonals In this painting, Little Street, by Vermeer, the vanishing point is hidden by the building itself; can you locate it?Tuesday, February 26, 13
  74. 74. ONE-POINT PERSPECTIVE Sometimes the vanishing point can be obscured by subjects within the composition or placed outside the picture plane itself; where is it in da Vinci’s The Last Supper?Tuesday, February 26, 13
  75. 75. ONE-POINT PERSPECTIVE Sometimes the vanishing point can be obscured by subjects within the composition or placed outside the picture plane itself; where is it in da Vinci’s The Last Supper?Tuesday, February 26, 13
  76. 76. ONE-POINT PERSPECTIVE Horizon Line Sometimes the vanishing point can be obscured by subjects within the composition or placed outside the picture plane itself; where is it in da Vinci’s The Last Supper?Tuesday, February 26, 13
  77. 77. ONE-POINT PERSPECTIVE Horizon Line Sometimes the vanishing point can be obscured by subjects within the composition or placed outside the picture plane itself; where is it in da Vinci’s The Last Supper?Tuesday, February 26, 13
  78. 78. ONE-POINT PERSPECTIVE Horizon Line Sometimes the vanishing point can be obscured by subjects within the composition or placed outside the picture plane itself; where is it in da Vinci’s The Last Supper?Tuesday, February 26, 13
  79. 79. ONE-POINT PERSPECTIVE Horizon Line Sometimes the vanishing point can be obscured by subjects within the composition or placed outside the picture plane itself; where is it in da Vinci’s The Last Supper?Tuesday, February 26, 13
  80. 80. ONE-POINT PERSPECTIVE Horizon Line Sometimes the vanishing point can be obscured by subjects within the composition or placed outside the picture plane itself; where is it in da Vinci’s The Last Supper?Tuesday, February 26, 13
  81. 81. ONE-POINT PERSPECTIVE Orthogonals Horizon Line Sometimes the vanishing point can be obscured by subjects within the composition or placed outside the picture plane itself; where is it in da Vinci’s The Last Supper?Tuesday, February 26, 13
  82. 82. ONE-POINT PERSPECTIVE Orthogonals Horizon Line Sometimes the vanishing point can be obscured by subjects within the composition or placed outside the picture plane itself; where is it in da Vinci’s The Last Supper?Tuesday, February 26, 13
  83. 83. ONE-POINT PERSPECTIVE Orthogonals Horizon Line Sometimes the vanishing point can be obscured by subjects within the composition or placed outside the picture plane itself; where is it in da Vinci’s The Last Supper?Tuesday, February 26, 13
  84. 84. ONE-POINT PERSPECTIVE Orthogonals Horizon Line Sometimes the vanishing point can be obscured by subjects within the composition or placed outside the picture plane itself; where is it in da Vinci’s The Last Supper?Tuesday, February 26, 13
  85. 85. ONE-POINT PERSPECTIVE Orthogonals Horizon Line Sometimes the vanishing point can be obscured by subjects within the composition or placed outside the picture plane itself; where is it in da Vinci’s The Last Supper?Tuesday, February 26, 13
  86. 86. ONE-POINT PERSPECTIVE Orthogonals Horizon Line Sometimes the vanishing point can be obscured by subjects within the composition or placed outside the picture plane itself; where is it in da Vinci’s The Last Supper?Tuesday, February 26, 13
  87. 87. ONE-POINT PERSPECTIVE Vanishing Point! Orthogonals Horizon Line Sometimes the vanishing point can be obscured by subjects within the composition or placed outside the picture plane itself; where is it in da Vinci’s The Last Supper?Tuesday, February 26, 13
  88. 88. ONE-POINT PERSPECTIVE Vanishing Point! Orthogonals Horizon Line Sometimes the vanishing point can be obscured by subjects within the composition or placed outside the picture plane itself; where is it in da Vinci’s The Last Supper?Tuesday, February 26, 13
  89. 89. TWO-POINT PERSPECTIVETuesday, February 26, 13
  90. 90. TWO-POINT PERSPECTIVE  In two-point perspective, there are two vanishing points located along the horizon line.  This allows an artist to create a three-quarter view of a structure, as if you are standing at the corner of a city block.  Horizon Line  Front edge (corner)  Orthogonals  Vanishing pointsTuesday, February 26, 13
  91. 91. TWO-POINT PERSPECTIVE  In two-point perspective, there are two vanishing points located along the horizon line.  This allows an artist to create a three-quarter view of a structure, as if you are standing at the corner of a city block.  Horizon Line  Front edge (corner)  Orthogonals  Vanishing pointsTuesday, February 26, 13
  92. 92. TWO-POINT PERSPECTIVE  In two-point perspective, there are two vanishing points located along the horizon line.  This allows an artist to create a three-quarter view of a structure, as if you are standing at the corner of a city block.  Horizon Line  Front edge (corner)  Orthogonals  Vanishing pointsTuesday, February 26, 13
  93. 93. TWO-POINT PERSPECTIVE  In two-point perspective, there are two vanishing points located along the horizon line.  This allows an artist to create a three-quarter view of a structure, as if you are standing at the corner of a city block.  Horizon Line  Front edge (corner)  Orthogonals  Vanishing pointsTuesday, February 26, 13
  94. 94. TWO-POINT PERSPECTIVE  In two-point perspective, there are two vanishing points located along the horizon line.  This allows an artist to create a three-quarter view of a structure, as if you are standing at the corner of a city block.  Horizon Line  Front edge (corner)  Orthogonals  Vanishing pointsTuesday, February 26, 13
  95. 95. TWO-POINT PERSPECTIVE  In two-point perspective, there are two vanishing points located along the horizon line.  This allows an artist to create a three-quarter view of a structure, as if you are standing at the corner of a city block.  Horizon Line  Front edge (corner)  Orthogonals  Vanishing pointsTuesday, February 26, 13
  96. 96. TWO-POINT PERSPECTIVE  In two-point perspective, there are two vanishing points located along the horizon line.  This allows an artist to create a three-quarter view of a structure, as if you are standing at the corner of a city block.  Horizon Line  Front edge (corner)  Orthogonals  Vanishing pointsTuesday, February 26, 13
  97. 97. TWO-POINT PERSPECTIVE  In two-point perspective, there are two vanishing points located along the horizon line.  This allows an artist to create a three-quarter view of a structure, as if you are standing at the corner of a city block.  Horizon Line  Front edge (corner)  Orthogonals  Vanishing pointsTuesday, February 26, 13
  98. 98. TWO-POINT PERSPECTIVE  In two-point perspective, there are two vanishing points located along the horizon line.  This allows an artist to create a three-quarter view of a structure, as if you are standing at the corner of a city block.  Horizon Line  Front edge (corner)  Orthogonals  Vanishing pointsTuesday, February 26, 13
  99. 99. TWO-POINT PERSPECTIVE  In two-point perspective, there are two vanishing points located along the horizon line.  This allows an artist to create a three-quarter view of a structure, as if you are standing at the corner of a city block.  Horizon Line  Front edge (corner)  Orthogonals  Vanishing pointsTuesday, February 26, 13
  100. 100. TWO-POINT PERSPECTIVE  In two-point perspective, there are two vanishing points located along the horizon line.  This allows an artist to create a three-quarter view of a structure, as if you are standing at the corner of a city block.  Horizon Line  Front edge (corner)  Orthogonals  Vanishing pointsTuesday, February 26, 13
  101. 101. TWO-POINT PERSPECTIVE  In two-point perspective, there are two vanishing points located along the horizon line.  This allows an artist to create a three-quarter view of a structure, as if you are standing at the corner of a city block.  Horizon Line  Front edge (corner)  Orthogonals  Vanishing pointsTuesday, February 26, 13
  102. 102. TWO-POINT PERSPECTIVE  In two-point perspective, there are two vanishing points located along the horizon line.  This allows an artist to create a three-quarter view of a structure, as if you are standing at the corner of a city block.  Horizon Line  Front edge (corner)  Orthogonals  Vanishing pointsTuesday, February 26, 13
  103. 103. TWO-POINT PERSPECTIVE  In two-point perspective, there are two vanishing points located along the horizon line.  This allows an artist to create a three-quarter view of a structure, as if you are standing at the corner of a city block.  Horizon Line  Front edge (corner)  Orthogonals  Vanishing pointsTuesday, February 26, 13
  104. 104. TWO-POINT PERSPECTIVE  In two-point perspective, there are two vanishing points located along the horizon line.  This allows an artist to create a three-quarter view of a structure, as if you are standing at the corner of a city block.  Horizon Line  Front edge (corner)  Orthogonals  Vanishing pointsTuesday, February 26, 13
  105. 105. TWO-POINT PERSPECTIVETuesday, February 26, 13
  106. 106. TWO-POINT PERSPECTIVE  Notice how the corner of the building is facing the viewer.  This is a simple example of two-point perspective.  Where are the vanishing points?  Sometimes vanishing points are not on the picture plane at all!Tuesday, February 26, 13
  107. 107. TWO-POINT PERSPECTIVE How To Create A Basic Image In Two-Point Perspective  Draw in the horizon line across the picture plane and place a vanishing point at either end of it.  Draw a vertical front edge line toward the center of the picture plane between the ground line & horizon line.  Draw orthogonals from the top & bottom ends of the front edge line to the left & right vanishing points, respectively.  Within each of the triangles the orthogonals create on either side of the front edge, draw in a vertical back edge line.  The, from the top, outside corners of each back edge, draw orthogonal lines connecting them to the opposite vanishing points.  Voila! A box rendered in two-point perspective!Tuesday, February 26, 13
  108. 108. TWO-POINT PERSPECTIVE Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  109. 109. TWO-POINT PERSPECTIVE Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  110. 110. TWO-POINT PERSPECTIVE Horizon line Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  111. 111. TWO-POINT PERSPECTIVE Horizon line Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  112. 112. TWO-POINT PERSPECTIVE Horizon line Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  113. 113. TWO-POINT PERSPECTIVE Vanishing points Horizon line Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  114. 114. TWO-POINT PERSPECTIVE Vanishing points Horizon line Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  115. 115. TWO-POINT PERSPECTIVE Vanishing points Horizon line Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  116. 116. TWO-POINT PERSPECTIVE Vanishing points Horizon line Front edge Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  117. 117. TWO-POINT PERSPECTIVE Vanishing points Horizon line Front edge Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  118. 118. TWO-POINT PERSPECTIVE Vanishing points Horizon line Front edge Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  119. 119. TWO-POINT PERSPECTIVE Vanishing points Horizon line Front edge Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  120. 120. TWO-POINT PERSPECTIVE Vanishing points Horizon line Front edge Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  121. 121. TWO-POINT PERSPECTIVE Vanishing points Horizon line Front edge Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  122. 122. TWO-POINT PERSPECTIVE Vanishing points Horizon line Orthogonals Orthogonals Front edge Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  123. 123. TWO-POINT PERSPECTIVE Vanishing points Horizon line Orthogonals Orthogonals Front edge Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  124. 124. TWO-POINT PERSPECTIVE Vanishing points Horizon line Orthogonals Orthogonals Front edge Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  125. 125. TWO-POINT PERSPECTIVE Vanishing points Horizon line Orthogonals Orthogonals Front edge Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  126. 126. TWO-POINT PERSPECTIVE Vanishing points Horizon line Orthogonals Orthogonals Back edges Front edge Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  127. 127. TWO-POINT PERSPECTIVE Vanishing points Horizon line Orthogonals Orthogonals Back edges Front edge Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  128. 128. TWO-POINT PERSPECTIVE Vanishing points Horizon line Orthogonals Orthogonals Back edges Front edge WALLS! Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  129. 129. TWO-POINT PERSPECTIVE Vanishing points Horizon line Orthogonals Orthogonals Back edges Front edge WALLS! Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  130. 130. TWO-POINT PERSPECTIVE Vanishing points Horizon line Orthogonals Orthogonals Back edges Front edge WALLS! Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  131. 131. TWO-POINT PERSPECTIVE Vanishing points Horizon line Back orthogonals Orthogonals Orthogonals Back edges Front edge WALLS! Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  132. 132. TWO-POINT PERSPECTIVE Vanishing points Horizon line Back orthogonals Orthogonals Orthogonals Back edges Front edge WALLS! Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  133. 133. TWO-POINT PERSPECTIVE Vanishing points Horizon line Back orthogonals Orthogonals Orthogonals Back edges Front edge WALLS! ROOF! Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  134. 134. TWO-POINT PERSPECTIVE Vanishing points Horizon line Back orthogonals Orthogonals Orthogonals Back edges Front edge WALLS! ROOF! THERE’S YOUR BOX! Any structure’s form can be reduced to a simple box. All convergent lines are drawn from each of the corners. Notice how the side of the box must be perfectly vertical.Tuesday, February 26, 13
  135. 135. TWO-POINT PERSPECTIVE Next, try lowering the horizon line. Notice that the viewer’s position in relationship to the box appears lower. Also, note that if the front edge is higher than the horizon line, the box’s roof will be invisible.Tuesday, February 26, 13
  136. 136. TWO-POINT PERSPECTIVE Next, try lowering the horizon line. Notice that the viewer’s position in relationship to the box appears lower. Also, note that if the front edge is higher than the horizon line, the box’s roof will be invisible.Tuesday, February 26, 13
  137. 137. TWO-POINT PERSPECTIVE Next, try lowering the horizon line. Notice that the viewer’s position in relationship to the box appears lower. Also, note that if the front edge is higher than the horizon line, the box’s roof will be invisible.Tuesday, February 26, 13
  138. 138. TWO-POINT PERSPECTIVE Next, try lowering the horizon line. Notice that the viewer’s position in relationship to the box appears lower. Also, note that if the front edge is higher than the horizon line, the box’s roof will be invisible.Tuesday, February 26, 13
  139. 139. TWO-POINT PERSPECTIVE Next, try lowering the horizon line. Notice that the viewer’s position in relationship to the box appears lower. Also, note that if the front edge is higher than the horizon line, the box’s roof will be invisible.Tuesday, February 26, 13
  140. 140. TWO-POINT PERSPECTIVE Next, try lowering the horizon line. Notice that the viewer’s position in relationship to the box appears lower. Also, note that if the front edge is higher than the horizon line, the box’s roof will be invisible.Tuesday, February 26, 13
  141. 141. TWO-POINT PERSPECTIVE Next, try lowering the horizon line. Notice that the viewer’s position in relationship to the box appears lower. Also, note that if the front edge is higher than the horizon line, the box’s roof will be invisible.Tuesday, February 26, 13
  142. 142. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  143. 143. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  144. 144. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  145. 145. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  146. 146. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  147. 147. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  148. 148. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  149. 149. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  150. 150. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  151. 151. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  152. 152. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  153. 153. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  154. 154. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  155. 155. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  156. 156. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  157. 157. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  158. 158. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  159. 159. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  160. 160. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  161. 161. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  162. 162. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  163. 163. TWO-POINT PERSPECTIVE For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  164. 164. TWO-POINT PERSPECTIVE Notice that the second cube’s top is invisible because its front edge rises above the horizon line! For a greater challenge, begin stacking boxes atop one another and adding additional boxes along the bottom orthogonals.Tuesday, February 26, 13
  165. 165. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  166. 166. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  167. 167. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  168. 168. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  169. 169. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  170. 170. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  171. 171. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  172. 172. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  173. 173. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  174. 174. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  175. 175. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  176. 176. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  177. 177. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  178. 178. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  179. 179. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  180. 180. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  181. 181. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  182. 182. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  183. 183. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  184. 184. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  185. 185. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  186. 186. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  187. 187. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  188. 188. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  189. 189. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  190. 190. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  191. 191. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  192. 192. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  193. 193. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  194. 194. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  195. 195. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  196. 196. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  197. 197. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  198. 198. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  199. 199. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  200. 200. TWO-POINT PERSPECTIVE Finally, add details like windows, doors, or signs to your boxes to give them visual interest. To do this, simply draw bands stretching from the box’s front edge back to the vanishing point.Tuesday, February 26, 13
  201. 201. Tuesday, February 26, 13
  202. 202. Tuesday, February 26, 13
  203. 203. FINETuesday, February 26, 13

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