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.