Henry, I make a monthly series of "Mathematical Impressions" videos vaguely characterized as 'cool mathematical topics' for the Simons Foundation web site. One from a few months ago was an introduction to 3D printing mathematical objects. See: http://www.georgehart.com/MathematicalImpressions/activities.html There are also lots of mathematical examples available on this page and by following its links: http://www.georgehart.com/rp/rp.html As to your questions: Your are right that most CAD systems are not designed with mathematical structures in mind. I usually write my own software for families of objects I am interested in, but there are a few programs designed for creating mathematical objects. (See the video above for examples.) STL is the standard format, so if you create an STL file, anyone anywhere with access to a 3D printer will be able to reproduce the object it describes. STL only describes shape, not color, so you'll need to use less standard formats if you are creating an object with a colored surface. Gcode is specific to each 3D printer, so is not transportable at all and I don't recommend you put effort into generating Gcode. Each 3D printer comes with its own custom software that imports STL and generates the Gcode (or other internal format) needed. Structural engineers have software that imports STL (and other) format files, allows you assign material properties, and calculates its load carrying capability, wind load resistance, etc., using finite element methods, but I have not used such software. George http://georgehart.com On 4/5/2013 10:02 AM, Henry Baker wrote:
I've done some research on how to design objects & 3D print them, but none of these CAD systems seems to be interested in producing mathematical objects. In fact, the whole process of generating these drawings seems exceedingly cumbersome & labor-intensive.
It looks like I might have to generate my own objects using low-level file formats.
It would appear that the 2 low level formats currently in use are the 'STL' file format, which is basically a long list of flat triangular facets given by triples of triples (X,Y,Z) points, which describe oriented triangles in 3-space.
http://en.wikipedia.org/wiki/STL_(file_format)
This file is sent to a 'slicer', which produces a 'path program' to direct the path of the printing nozzle for each 2D 'slice' of the 3D object.
http://en.wikipedia.org/wiki/G-code
If I'm trying to produce a 3D print of a mathematical structure, it might be easiest to simply generate my own G-code file, except for the fact that this G-code file probably contains a lot of 3D-printer-specific information.
Has anyone on this list gone to these levels of detail?
Also, I haven't been able to find any simple programs to do minimal structural analysis on these models -- e.g., to determine if they can even stand on their own.
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