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Linear Perspective fromBrunelleschi to LeonardoLinear Perspective fromBrunelleschi to Leonardo
Edward ChangUC Santa Barbara
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Perspective 2
Perspective
Place a 3D scene on a 2D canvasFormalized by Brunelleschi in
15AD1500 - 1900, one of the standard
painting techniquesCreate a systematic illusion of
receding forms behind the flat surface
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Perspective 3
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Perspective 4
Perspective
Giotto (15AD)Lines and planes situated above eye-level
should appear to incline downwards and move away from the viewer
Those below eye-level should incline upwards
Those to the left inclines to right and those to the right inclines to left
There should be some sense of the horizontal and vertical division
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Perspective 5
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Perspective 6
Perspective
BrunelleschiP: Outline a rectangle as an open
window through which the objects to be painted are seen
E: Determine the eye-level (height) of a man , H (horizon)
V: Decide the point at which the centric ray strikes the picture plane P
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Perspective 7
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Perspective 8
Perspective
BrunelleschiP, E, H and VDivide the base into scales (braccia =
1/3 E)Top viewSide viewFront view
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Perspective 9
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Perspective 10
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Perspective 11
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Perspective 12
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Perspective 13
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Perspective 14
Camera
(X, Y, Z) real coordinate(x, y, z) projected coordinatef: focal lengthx = X * f/Zy = Y * f/Z
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Perspective 15
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Perspective 16
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Perspective 17
2D -> 3D
What 3D information that we can recover from a 2D image mathematically?Distance pointDistance of objects Sizes...Slants...Tilts...
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Perspective 18
2D -> 3D
EV or H
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Perspective 19
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Perspective 20
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Perspective 21
The Distance Point
VZ = EV
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Perspective 22
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Perspective 23
Vanishing Point
The intersection of a set of parallel lines that are not parallel to the picture plane
From V, one can recover the slant of a set of parallel lines
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Perspective 24
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Perspective 25
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Perspective 26
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Perspective 27
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Perspective 28
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Perspective 29
Distance?
With checker boardWithout checker board
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Perspective 30
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Perspective 31
Object Height
EHorizonT: top, B: bottom of an objectheight = TB / HB
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Perspective 32
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Perspective 33
Major Contributions to Pictorial Representation
Art Theorists (Car inventors)Painters (Drivers)