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...
Visual Imaging in the
Electronic Age
Perspective Transformations
Lecture # 3
August 30, 2016
Prof. Donald P. Greenberg
• 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
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)?
How a Camera Lens Works
• Rays which pass through the focal point are bent
to leave the lens perpendicular to its principal
axis.
® Donald P. Greenberg - Cornell Program of Computer Graphics
® Donald P. Greenberg - Cornell Program of Computer Graphics
Railroad Tracks in Perspective
elevation
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.
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
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
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
How a Camera Lens Works
Camera
Film
Plane
Camera
Film
Plane
® Donald P. Greenberg - Cornell Program of Computer Graphics
http://upload.wikimedia.org/wikipedia/en/5/5f/DoF-sym.png
Perspective Projections in
Computer Graphics
Eye coordinate systemPlan or elevation view
Object Space
(One point
perspective)
Image Space
(One point
perspective)
Object Space
(Two point
perspective)
Image Space
(Two point
perspective)
Object Space
(Three point
perspective)
Image Space
(Three point
perspective)
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
e
pz
ffz
2
2
e
pz
z1
21constantconstant
3D Perspective Image
(z depth coordinate in virtual image
space)
Equivalent Distorted Geometries
in Virtual Image Space
® 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
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
Uses of Perspective in Enlarging
Architectural Space (3D)
Palazzo Spada
Borromini
Imss,Firenze 2004 - 3 Scenografia prospettica
Imss,Firenze 2004 - 3 Scenografia prospettica
Imss,Firenze 2004 - 3 Scenografia prospettica
Imss,Firenze 2004 - 3 Scenografia prospettica
Imss,Firenze 2004 - 3 Scenografia prospettica
Imss,Firenze 2004 - 3 Scenografia prospettica
Imss,Firenze 2004 - 3 Scenografia prospettica
Borromini
Palazzo Spada
Borromini
Palazzo Spada
Video - Palazzo Spada Video(spada.wmv)
® Donald P. Greenberg - Cornell Program of Computer Graphics
Probe Demo
® Donald P. Greenberg - Cornell Program of Computer Graphics
End. . .