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Topic: Solid Modeling package
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Dr. Robert Kragler

Posts: 20
Registered: 3/18/08
Solid Modeling package
Posted: Apr 9, 2014 4:14 AM
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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 :

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