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Solid Modeling package

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  • Subject: [mg132533] Solid Modeling package
  • From: "Dr. Robert Kragler" <kragler at>
  • Date: Wed, 9 Apr 2014 04:13:46 -0400 (EDT)
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  • Reply-to: kragler at

Hello Mathematica Users,

I have just finished a package "SolidModeling.m" on _Solid Modeling_ (using 
Mathematica V8) together with two explanatory articles

                 TMJ_SolidModeling_Px.ext              (where *x*=1,2 and the 
extension is either *nb* or *pdf*)

which can be downloaded from my Mathematica website :;jsessionid=1F3E6519A7EAE115B01D1D01D5E0816B?p_p_id=110_INSTANCE_1ABc&p_p_lifecycle=0&p_p_state=maximized&p_p_mode=view&p_p_col_id=column-1&p_p_col_pos=1&p_p_col_count=2&_110_INSTANCE_1ABc_struts_action=%2Fdocument_library_display%2Fview&_110_INSTANCE_1ABc_folderId=109694429

(sorry for this lengthy URL for the subdirectory "Solid_Modeling",
  but the URL for the higher-level website is more readable : )

The package includes besides basic primitives more sophisticated solids such as 
superquadrics, 151 polyhedra, and 3D objects either defined by closed algebraic 
surfaces or Boolean functions. The 3D objects are subjected to geometric 
transformations such as scaling, rotation and translation and thus can be 
deformed, oriented and positioned at any spatial location. By means of Boolean 
operators (such as union, difference, intersection, symmetric difference, nor, 
xnor, nand, complement) applied to these solids it is possible to combine them 
to more complex bodies. Operations typical for constructive solid geometry such 
as extrusion and sweeping are introduced and will admit the creation of 3D 
solids from 2D Boolean functions by extrusion. Skewed objects such as prisms 
etc. are generated by sweeping too.

All procedures required are provided in the package SolidModeling.m, many 
examples for the creation of solids and their manipulation are given in the two 
supplemental articles.

In addition, another useful tool for orientation of 3D objects is 
viewPointSelector which facilitates the determination of an optimal viewpoint. 
Unfortunately, this viewpoint selector which was implemented in Mathematica V5.2 
became obsolete since V6. However, due to private communication with Alexander 
Elkins and the MathGroup Archive from 2008 an improved version was constructed 
which generates a floating interactive palette.
        Just see :  "viewPointSelector.nb"   and 
"viewPointSelector_GeneratingPalette.nb" .


Robert Kragler

Prof. Dr. Robert Kragler
Hasenweg 5
D-88090 Immenstaad, Germany
Phone : +49 (7545) 2833 or 3500
Email : kragler at

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