Conventional computer graphics primitives are overwhelmingly based on
straight lines. NURBS and other patches decimate surfaces into
triangles for rendering. And what about the field of topology, where
straight lines and flat surfaces are degenerate cases?
Topological Computer Graphics creates some
new graphics primitives entirely about curvature, differentiability,
Multidimensional Space-Filling Curves are
generalizations of the two-dimensional curiosities constructed by
Peano and Hilbert in the late 1800s. Although filling (hyper)cubic
volumes, the space-filling curves are infinitely wiggly -- continuous
everywhere while differentiable nowhere. They can be seen as an
entirely different approach to nonlinear primitives.
Color spaces are bounded, 3-dimensional volumes.
Color Space Dimension Reduction uses
space-filling curves to organize color spaces for creating color
catalogs. It is surprising when novel counterexamples find practical
Packing Pyramids compares volumes
created by rising-factorial sums with cubes.
One problem with the straight computer graphics lines is that they are
not straight when inclined! Staircasing is a prominent artifact in
most rendering systems.
The image to the right, drawn with anti-aliased line primitives, looks
much smoother than the image above it. The degree to which lines are
perceived as smooth depends on the computed and actual
display gamma, a property of the display
If the quality of anti-aliased images is sensitive to display gamma,
does this make them a good way to measure it? A chart of complete
graphs at various computed gammas does function as a gage. But the
highly compact chart in Display Calibration
allows finer distinctions in gamma to be discerned with the unaided
eye. It uses a cleverly designed 11-level dispersed screen which
should be optimal for that number of levels.
Copyright © 2003, 2004, 2005, 2006 Aubrey Jaffer
I am a guest and not a member of the MIT Computer Science and Artificial Intelligence Laboratory.
My actions and comments do not reflect in any way on MIT.|
|agj @ alum.mit.edu