Drawing Perspective Images Brunelleschi’s Experiment · 2019. 9. 2. · Drawing Perspective...
Transcript of Drawing Perspective Images Brunelleschi’s Experiment · 2019. 9. 2. · Drawing Perspective...
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Introduction to Perspective Geometry
Brunelleschi’s Experiment
Visual Imaging in the Electronic AgeDonald P. Greenberg
September 8, 2020
Lecture #2
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• Required Reading:
Art Perspective Handout: PDF
• References:
– Martin Kemp. "The Science of Art: Optical Themes in Western Art from
Brunelleschi to Seurat" Yale University Press
– Ingrid Carlbom , Joseph Paciorek. "Planar Geometric Projections and Viewing
Transformation," Computing Surveys, vol. 10, no. 4, December 1978
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The Flagellation of Christ, c. 1458-60. Piero della Francesca. Tempera. 59 x 81.5 cm. Urbino, Galleria
Nazionale delle Marche.
1458
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Gustave Caillebotte, Paris Street; Rainy Day From Charles H. and Mary F. S. Worcester Collection,
Oil on canvas
1877
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Light as Rays
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Albrecht Durer. Untitled (Artist using a glass to take a portrait). From Underweysung der
Messung mit dem Zirkel und Riichtscheyt, 1st Ed, 1525. Woodcut print.
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Reference
• Ingrid Carlbom , Joseph Paciorek. "Planar Geometric Projections and
Viewing Transformation," Computing Surveys, vol. 10, no. 4, December
1978.
(This reference contains a matrix method for combining all of the above types
of projections)
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Diagram from Axonometric and Oblique Drawing: A 3-D Construction, Rendering, and Design
Guide by M. Saleh Uddin. New York: McGraw-Hill. © 1997. P. 9.
Projectors are
perpendicular to the
image plane
Object faces are
parallel to the image
plane
Orthographic Projections
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Planar Geometric Projections
Parallel
Oblique
Multiview
Orthographic
Isometric
Perspective
One-point Two-point Three-pointOrthographic
Axonometric Cavalier Cabinet
Dimetric Trimetric
Planar Geometric Projections
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Diagram from Axonometric and Oblique Drawing: A 3-D Construction, Rendering, and Design Guide by
M. Saleh Uddin. New York: McGraw-Hill. © 1997. P. 9.
Projectors are not
parallel but converge
on a single focal point
(eye, camera)
Perspective Projection
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Picture Plana Looking Through a Window
Note: all rays converge on our one cyclopean eye
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One Point Perspective
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David Macauley,
Locating the Vanishing Point
Locating the Vanishing Point
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What is a one-point perspective?
What is a two-point perspective?
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Perspective Projection (2-point)
Rays of light travel from the object,
through the picture plane, and to the
viewer's eye. This is the basis for
graphical perspective.
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What is a one-point perspective?
What is a two-point perspective?
What is a three-point perspective?
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Computer Graphics Perspective Image Generation
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Camera
PerspectiveTransform
RasterOperations
ImageStorage
Display
Model
Standard Computer Graphics Pipeline
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Camera
PerspectiveTransform
RasterOperations
ImageStorage
Display
RasterOperations
VisibilityShading
Model
Standard Computer Graphics Pipeline
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Model
The camera location, view direction, and frustum must be defined relative to
the object.
View
direction
Camera
Camera Definition
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Y
Z
X
The model is described in a
right handed coordinate system.
Model Coordinate System
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Y
Z
X
Ze
Xe
Ye
The model is described in a
right handed coordinate system.The eye coordinate system
is a left handed coordinate
system.
Eye Coordinate System
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Note the eye coordinate system is a left-handed coordinate system
Picture Plane
Ye
Eye Coordinate System
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Left Handed Right Handed
x
y
z
x
y
z
z
yx
z
yx
Left Handed and Right Handed Coordinate Systems
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Picture Plane
Point On Object
Ze = D
ZeXe
Ye
Ze = 0
P(xe, ye, ze)
P(xs, ys)
S
S
Simple Perspective Transformation
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S
display
screenze = 0
P(xe, ye, ze)
P(xs, ys)
D
O
Elevation drawn in the Ye, Ze plane.
Ye
Ze
Simple Perspective Transformation
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e
e
e
e
e
es
e
es
z
Dy,
z
Dxx
z
y
D
y,
z
x
D
x
==
==
ss y
e
es
e
es
Sz
Dyy
Sz
Dxx == ,
To convert to a dimensionless fraction,
can divide by the window size S.
Simple Perspective Transformation
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Transformations - video
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Note that the entire image through
the pinhole is totally in focus on a
single image plane.
Pinhole Camera
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Ibn al-Haitham (Al-Hazen)
Credited with the having built the
first camera obscura in the 10th
Century.
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Camera Obscura
http://en.wikipedia.org/wiki/Camera_obscura
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Brunelleschi’s Perspective Experiment
• How do you draw a perspective image?
• How do you know it is correct?
Martin Kemp. THE SCIENCE OF ART, Chapter 1 (Linear perspective from Brunelleschi to Leonardo),
pp. 9-15. AVAILABLE ON COURSE WEBSITE
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Brunelleschi’s Perspective Experiment
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Ghiberti’s Baptistry
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Brunelleschi’s Experiment
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Brunelleschi Video (render01_wmv)
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Brunelleschi’s Experiment
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Brunelleschi’s Experiment
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End. . .