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Although the graph of a parametrized surface can be viewed and manipulated on the computer screen as a surface in 3D, it is not quite suitable for printing on a 3D printer since such a surface has zero thickness, and thus it does not correspond to physical object.

To produce a 3D printout of a surface, it needs to be endowed with some "thickness".  To do that, we move every point from the surface in the direction of that point's nomral vector by the amount ±T/2, where T is the desired thickness.  The locus of the points thus obtained forms a thin shell of thickness T around the original surface, thus making it into a proper solid. The result then may be saved into a file in the STL format and be sent to a 3D printner for reproduction.

The worksheet attached to this post provides a facility for translating a parametrized surface into an STL file.  It also provides a command for viewing the thickened object on the screen.  The details are documented within that worksheet.

Here are a few samples.  Each sample is shown twice—one as it appears within Maple, and another as viewed by loading the STL file into MeshLab which is a free mesh viewing/manipulation software.


Here is the worksheet that produced these:  thicken.mw



Featured Post

I faced the issue of having to remove sections from a maple document in order to export to a pdf without the indentation and lines that come when you export documents with sections. Here is small tool I wrote that removes all sections in a maple document. It takes a target file as the first argument and writes that file without sections to the destination file specified as the second argument.

RemoveSection := module()
    local ModuleApply := proc(target, destination)
        XMLTools:-WriteFile(destination, subsindets(XMLTools:-ReadFile(target), ':-specfunc'(_XML_Section), section_handler));
    end proc;
    local section_handler := proc(s)
        local partresult := remove(type,[op(s)],`=`);
        return op(subsindets(partresult, ':-specfunc'(_XML_Title), f -> `_XML_Presentation-Block`("",_XML_Group("view"="presentation","inline-output"="false",    
    end proc;
end module:

#RemoveSection takes two arguments the first is the target file and the second is the destination file where the target file will be written without sections



Download RemoveSection.mw


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