Mathematica Journal
Volume 10, Issue 4


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Making Holes and Windows in Surfaces
Alan Horwitz

In this article, we demonstrate makehole, a program which removes points from any Graphics or Graphics3D picture whose coordinates satisfy a stated condition. We also demonstrate transparent and makewindow, programs which make an entire or a specific portion of an opaque surface into a transparent mesh. We use these programs to view the region of integration for a triple integral. This article uses Mathematica 5.2, but with minor modifications all three programs work in Mathematica 6, as well as earlier versions. The makehole program duplicates some of the functionality of the RegionPlot3D command and RegionFunction option of the ParametricPlot3D command in Version 6, while the transparent program behaves like the PlotStyle -> None option of the Plot3D command (see Editor's Note for a demonstration of the Mathematica 6 code).



About the Author
Alan Horwitz received a B.S. from Ohio State University in 1980 and an M.A. in 1985 and a Ph.D in 1988 from SUNY at Stonybrook. He is currently a faculty member in the Mathematics Department at Marshall University.

Alan Horwitz
Dept. of Math, Marshall University
Huntington, West Virginia 25755

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