Linear Perspective fromBrunelleschi to LeonardoLinear Perspective fromBrunelleschi to Leonardo

Edward ChangUC Santa Barbara

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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

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

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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BrunelleschiP, E, H and VDivide the base into scales (braccia =

1/3 E)Top viewSide viewFront view

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Camera

(X, Y, Z) real coordinate(x, y, z) projected coordinatef: focal lengthx = X * f/Zy = Y * f/Z

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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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2D -> 3D

EV or H

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The Distance Point

VZ = EV

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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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Distance?

With checker boardWithout checker board

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Object Height

EHorizonT: top, B: bottom of an objectheight = TB / HB

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Major Contributions to Pictorial Representation

Art Theorists (Car inventors)Painters (Drivers)