Dept. Computer Science
SUNY Stony Brook

CSE391 Special Topics:
Solid Modeling Projects

Prof. George W. Hart

Here are some of the projects made in this class, in the Fall 2004. This is a senior-level project seminar course in which students go through the following process:
Then the machine patiently assembles it from thin layers. The images below are of objects fabricated on a DTM 2500+ selective sintering machine run by Jim Quinn of the Materials Science department. Thank you Jim for making all these!

The software part of each project is a program which can procedurally generate an infinite variety of objects ranging from simple to complex within a family of forms. We adjust a slider on the program to select an instance of reasonable complexity for the fabrication machines we have available.

Note that the students who created these objects are not using any existing solid modeling programs---they are writing the solid modeling programs. After the initial torus exercise which everyone makes, each student chooses their own projects.  But we all discuss the underlying mathematical ideas and algorithms for all of them, so we can all help each other in debugging, etc. You can also see the projects from the first run of this class, in Fall, 2003.

For each project below, the first image is the screen shot of how the object appears rotating on the screen while being designed.  The second image is a photo of the actual fabricated object, typically two to three inches in size.






The first exercise in the class is to make a torus with openings. Sliders on the software control the number of openings around the equator and through the hole, and adjust dimensions such as the two radii, the relative size of the openings, and the thickness of the shell.






After mastering the basic torus, we explored a number of variations.  Above is one which incorporates twist as one moves from ring to ring.






Above is a similar one but more intricate.






Surprisingly, this is also a hollow torus.  Just a minor variation of the first design produces this intricate flower-like form.  Imagine coloring the vertices black and white like a checkerboard, then increase the radius of all the white ones and decrease the radius of the black ones.





In this project, a random maze is generated and used to texture the torus surface.  There is a unique path from start to finish which one can follow with a tiny ball bearing.





In this project the turbine-like form is a fancy torus. 
It is free to rotate about a shaft attached to a base.





A number of projects were geometric forms.  This is a modification of a truncated rhombicuboctahedron, designed to look like a flying object. While not the original intent, this was a pleasing serendipitous result.







Here is an indented polyhedral form.  Adjusting the software sliders moves vertices radially and over the surface while always maintaining icosahedral symmetry. The green model was made in ABS plastic on an FDM machine. (Thank you to Imin Kao for access to the FDM machine and to Juan Carlos for operating it and giving a class tour.)





Another icosahedral object generator---with somewhat different
triangulation and parameters---produces this spiky object.





Here are four separate equilateral triangles with every pair linked. 
Try making this from twelve soda straws and some string!





Three-dimensional fractals are natural for this sort of class. Here is a well known one, the Menger Sponge (in a low-order approximation).





Above is a fractal binary tree.  There are ten levels of branching, so it has 1024 terminal leaves.  Notice that every branch at every level is similar, just translated, rotated, and scaled.





Inspired by a leaf, trigonometric functions determine
the undulations and the edge shape of this surface.





This flower illustrates phylotaxis. Note the various spirals, like sunflower seeds.





Another nature-inspired design: an elegant model of a hollow spiral shell.





Although inspired by a snowflake, this project is more like six pine cones attached to the six sides of a small inner cube.  (Actually two of the arms broke off during fabrication, so they are glued back on for this photo.)





This project makes "cookies" from 2D images.  Different levels of image intensity get mapped to different thicknesses, and software sliders control filtering, thresholding, smoothing, etc. So from any image file one can create a 3D relief extrusion.