[math-fun] 3D printing of mathematical objects ??
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.
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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-- Forewarned is worth an octopus in the bush.
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.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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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-- Forewarned is worth an octopus in the bush. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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On 5 Apr 2013 at 7:02, 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.
I'm not sure what you mean by "mathematical objects". But you should contact Bathsheba Grossman who has been doing this sort of stuff for many years. I'm sure she'll be willing to give you advice on how she designs stuff. Check out <http://www.bathsheba.com/> I have one of these: <http://www.bathsheba.com/math/120cell/> and it is really nice. /bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
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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participants (6)
-
Bernie Cosell -
Fred lunnon -
George Hart -
Henry Baker -
James Propp -
Michael Kleber