Visual Imaging in the Electronic Age - Cornell Program of ... · PDF fileVisual Imaging in the...
Transcript of Visual Imaging in the Electronic Age - Cornell Program of ... · PDF fileVisual Imaging in the...
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Visual Imaging in the
Electronic Age
Perspective Transformations
Lecture # 3
August 30, 2016
Prof. Donald P. Greenberg
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• We have seen how a pinhole camera
(or camera obscura) works
• We have also seen Brunelleschi’s
experiment with his perspective panels
• Both are obviously two dimensional
and exist on a planar (flat) surface
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Perspective Depth
• We now know how to mathematically (and
geometrically) construct the perspective image.
(e.g., xs, ys)
• But how do we find the third dimension (zs)?
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How a Camera Lens Works
• Rays which pass through the focal point are bent
to leave the lens perpendicular to its principal
axis.
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® Donald P. Greenberg - Cornell Program of Computer Graphics
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® Donald P. Greenberg - Cornell Program of Computer Graphics
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Railroad Tracks in Perspective
elevation
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How a Camera Lens Works
• Rays which pass through the focal point are bent
to leave the lens perpendicular to its principal
axis.
• Rays which are perpendicular to the principal
axis of the lens are bent through the focal point.
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How a Camera Lens Works
f
P(xe, ye, ze)
P(xp, yp, zp)
-zp - 2f
Ze
Xe
Ye
A
A
B
B
f
-yp
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e
ep
e
ep
z
x
f
x
z
y
f
y
,Using triangles A and A':
fz
y
f
y
p
pe
2
Using triangles B and B':
e
ep
e
ep
z
yfy
z
xfx ,
How a Camera Lens Works
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f
fz
y
y
z
f
y
y p
e
p
ee
p 2 ,
We know that:
e
p
e
p
z
ffz
z
f
f
fz 2
2 ,2
e
pz
ffz
2
2
How a Camera Lens Works
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How a Camera Lens Works
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Camera
Film
Plane
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Camera
Film
Plane
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® Donald P. Greenberg - Cornell Program of Computer Graphics
http://upload.wikimedia.org/wikipedia/en/5/5f/DoF-sym.png
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Perspective Projections in
Computer Graphics
Eye coordinate systemPlan or elevation view
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Object Space
(One point
perspective)
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Image Space
(One point
perspective)
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Object Space
(Two point
perspective)
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Image Space
(Two point
perspective)
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Object Space
(Three point
perspective)
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Image Space
(Three point
perspective)
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3D Perspective Image
(x & y coordinates in virtual image
space)
e
e
pz
xfx
e
e
pz
yfy
e
e
pz
xx constant
e
e
pz
yy constant
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e
pz
ffz
2
2
e
pz
z1
21constantconstant
3D Perspective Image
(z depth coordinate in virtual image
space)
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Equivalent Distorted Geometries
in Virtual Image Space
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® Donald P. Greenberg - Cornell Program of Computer Graphics
Mapping a Viewing Frustum
to a Standard Viewbox
11
ze = DXe
Frustum of vision Screen coordinate system
Ze
Ye
ze = F
Xs
Ys Zs
1
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Viewing Frustum - User Parameters
Location and Orientation (vectors):
Eye location of eye point
At a point along view direction vector
Up a vector defining the Y axis on the hither plane
Shape (scalars):
fov field of view angle
aspect view plane aspect ratio
hither perpendicular distance to hither plane
yon perpendicular distance to yon plane
At
Up
Eye
aspect =
width / height
hitheryon
fov
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Uses of Perspective in Enlarging
Architectural Space (3D)
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Palazzo Spada
Borromini
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Imss,Firenze 2004 - 3 Scenografia prospettica
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Imss,Firenze 2004 - 3 Scenografia prospettica
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Imss,Firenze 2004 - 3 Scenografia prospettica
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Imss,Firenze 2004 - 3 Scenografia prospettica
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Imss,Firenze 2004 - 3 Scenografia prospettica
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Imss,Firenze 2004 - 3 Scenografia prospettica
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Imss,Firenze 2004 - 3 Scenografia prospettica
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Borromini
Palazzo Spada
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Borromini
Palazzo Spada
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Video - Palazzo Spada Video(spada.wmv)
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® Donald P. Greenberg - Cornell Program of Computer Graphics
Probe Demo
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® Donald P. Greenberg - Cornell Program of Computer Graphics
End. . .