Speaking of sphere and torus eversions: before I die (about fifty years from now) I'd like a chance to play in a virtual environment featuring self-intersecting surfaces that can be manipulated by the user, and evert a sphere with my (avatar's) own two hands. Anyone know if anybody's working on this? I'm imagining a virtual surface with frictional properties than permit one to twist it much as one does when making balloon animals. (Jaron Lanier, are you listening?) Jim Propp On Friday, April 5, 2013, Fred lunnon <fred.lunnon@gmail.com> wrote:
I hadn't come across torus eversion before; see also
http://mathoverflow.net/questions/96701/surface-eversions-generalizing-from-...
WFL
On 4/5/13, Michael Kleber <michael.kleber@gmail.com> wrote:
Henry Segerman wrote an Intelligencer article for me about getting
started
in this area. Check out
http://www.ms.unimelb.edu.au/~segerman/papers/3d_printed_visualisation.pdf
George Hart, of course, is likely to have more to say than you can shake
a
stick at, even for large values of stick.
--Michael
On Fri, Apr 5, 2013 at 10:02 AM, Henry Baker <hbaker1@pipeline.com> 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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