CS 791 Assignment 3 extensions
What follows are some suggested non-trivial extensions to the implementation
component of assignment 3. You are welcome (and indeed encouraged) to
dream up your own ideas for extensions. These are presented very roughly
in increasing order of when they occured to me. The harder ones make fine
topics for final projects in the course.
Note that not all extensions are created equal. You don't get full
marks just for having an extension. If you want to think of me as
cruel, consider this as being similar to the "subjective marks"
component of the cs488 final project.
- Add a second layer of inference to the interiors of large
regular polygons, as described in Section 3 of
my paper.
- Implement the "rosette transform" to generate new tilings
suitable for this construction technique. Adjust the contact
positions by moving them away from edge centres as necessary.
- Implement "two-point patterns".
- Implement other rendering styles, most obviously interlacing.
Note that in this case, you can get away with making local
decisions about the over-under relationships at crossings
(that is, there's a cheap way to figure out the interlacings
without actually doing a depth-first search).
- Implement a colouring technique that automatically attempts
to colour regions in a way consistent with the Zellij style
of star pattern design.
- Add a method for automatically decorating the ribbons and
interiors of the star pattern with small elements such as
floral motifs.
- Figure out how to turn the straight bands of the star pattern
into spline curves in an attractive way. See
this page for inspiration.
- Extend the technique to some non-periodic tilings, for example
Kepler's Aa tiling or tilings produced by placing regular polygons
at the vertices of
Quasitiler-type tilings. More information
about these extensiosn can be found in my thesis.
- Build star patterns from tilings produced using the
overlay-dual
technique. This approach presents the interesting possibility of
building a pattern with a large, many-pointed central star.
- Build star patterns containing stars with unusual numbers of
points or in unusual combinations. See
Jay Bonner's page
on star patterns for some ideas.
- Extend the star patterns to non-Euclidean geometry, either on
the surface of a sphere or in the hyperbolic plane. Alternatively,
extend them to polyhedra.
- Perform other geometric transforms on star patterns, such as
circular inversion.