PolygonIntersections

PolygonIntersections is an option for Graphics3D and funtions that return Graphics3D objects.

Options[Graphics3D, PolygonIntersections]

{PolygonIntersectionsTrue}

When the setting  PolygonIntersections→False  is used the graphics are rendered as a collection of non-intersecting triangles.  In the next cell I make a Graphics3D object with non-default setting (PolygonIntersections→False).

RowBox[{RowBox[{gr, =, RowBox[{Graphics3D, [, RowBox[{RowBox[{{, , RowBox[{Polygon[{{0 ... ,, 0, ,, 2}], }}]}], }}], ]}]}], , }}], ,, PolygonIntersectionsFalse}], ]}]}], ;}]

I can't inderstand why but my attempt to display the graphics in the next cell doesn't work when using Mathematica 4.1 under Windows 98.

Show[gr, PlotRange->All] ;

On my computer the above graphics can be displayed if I nest use of Show, and specify (PlotRange->All).

Show[Show[gr], PlotRange->All] ;

The next cell shows us how Mathematica divided the above polygons into non-intersecting triangles.

polygons = Cases[Show[gr], _Polygon, {0, -1}]//Chop

RowBox[{{, RowBox[{RowBox[{Polygon, [, RowBox[{{, RowBox[{RowBox[{{, RowBox[{0, ,, 0, ,, 1.}], ... RowBox[{0.5, ,, 1., ,, 2.}], }}], ,, RowBox[{{, RowBox[{0.5, ,, 0, ,, 1.}], }}]}], }}], ]}]}], }}]

Created by Mathematica  (May 16, 2004)

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