CS 184: COMPUTER GRAPHICS
Lecture #14 -- We: 3/10, 1999.
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Preparation:
HAND-IN: Take-Home Quiz#2
Read: Ch 14.7 "Steropsis"; Ch 6.1 "Projections"
Lecture Topics
Review of:
Warp 3D viewing frustum into canonical half-cube: Matrix 6.48
Check what this does to a few specific points: Eye, Front, Back, ...
Clipping in 3D:
Various options: Do it in z and then in 2D; do it in 3D; do it in 4D.
Study Ch. 6.5.4.
Determine camera parameters to reproduce actual viewing geometry.
Vanishing Points and Vanishing Lines
Vanishing point = projection of point at infinity of a straight line or
a bundle of parallel lines;
Can be found with a parallel ray through eye point: determine intersection
with imaging plane.
Vanishing line = "horizon" of a plane = collection of the vanishing
points of all the lines in the plane.
Parallel planes have the same vanishing line; pick the one through
eye point and find intersection with imaging plane.
n-Point Perspectives
Art schools make a big fuss about drawing worlds with 1-, 2-, or 3-point
perspectives,
showing the corresponding number of vanishing points for bundles of
parallel lines.
However, this really only makes sense for "brick" worlds with three
sets of dominant directions.
In worlds with more than 3 major directions in which we find many edges,
each such bundle of parallel lines, can, and typically will, produce
its own vanishing point.
The only situation when such a bundle does not produce a vanishing
point is
when it lies parallel to the imaging plane.
Thus an octahedron with 6 pairs of parallel edges can have 6 vanishing
points,
and can thus be rendered in "6-point perspective" !
What is the minimum number of vanishing points that it can produce
?
-- Well, it can be oriented in such a way that one of its triangular
faces lies parallel
to the imaging screen; then 3 parallel bundles do not have a vanishing
point, and there remain only three.
Similarly, an icosahedron (20 triangles) with 15 pairs of parallel
edges can have
a maximum number of 15 vanishing points and a minimum number of 12.
What are the maximum and minimum number for a hexagonal prism
?
Or for all the
Platonic solids ?
Current Homework Assignment:
ASG#6:
"Perspective Projections and Stereo Viewing"
DUE: Saturday 3/13/99, 11:59pm.
CAN BE DONE WITH YOUR PARTNER OF CHOICE !
Read Ch. 3.6 "Filling Polygons", Ch. 19.2.8 "Filled Primitives",
Ch. 18.3.8 "Rasterization"
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