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MathGroup Archive 1997

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announcement: new Plane Tiling package

  • To: mathgroup at smc.vnet.net
  • Subject: [mg9122] announcement: new Plane Tiling package
  • From: "Xah" <xah at best.com>
  • Date: Mon, 13 Oct 1997 23:33:33 -0400
  • Organization: smtp.best.com
  • Sender: owner-wri-mathgroup at wolfram.com

A new version (v.5) of Plane Tiling package is ready. This version includes
a set of general 2d graphics cutting functions, and more than 10 other new
functions. This is a singificant upgrade than the earlier version. The
package and complete documentation for both version 2 and version 3 of
Mathematica can be downloaded from my web page
(http://www.best.com/~xah/SpecialPlaneCurves_dir/MmaPackages_dir/mmaPackages
.html). It's also available on MathSource, but the version there is not
current. I'll be happy to email the package for those who don't have web
access. 

Sample graphics generated by this package can be seen at
(http://www.best.com/~xah/MathGraphicsGallery_dir/PlaneTilingPackageDemo_dir
/planeTilingPackageDemo.html)

Here is a description:

PlaneTiling is a graphics package for generating wallpaper designs, 
tilings, plane group symmetry illustrations, and contains general two 
dimentional graphics tools. Features include: 

* Plot any wallpaper design by specifying a given fundamental motif and 
wallpaper group symmetry. 

* Plot lattice, network, unit cell, fundamental region, generators, and 
symmetry elements of any specified wallpaper group. 

* A system of functions that let you generate any periodic tilings and 
wallpaper designs easily. 

* A system of functions that manipulate Mathematica two dimentional 
graphics. 

* A system of functions that let you apply a topological transformation 
on regularly directed edges of a tiling. 

The following is a partial listing of functions exported by the package.

(*Wallpaper plotters*)
WallpaperPlot , WallpaperGroupPlot, RandomWallpaperPlot

(*lattice and grids*)
LatticeCoordinates,ColoredLatticePoints,ColoredLatticeNetwork,
  DirectedLatticeNetwork,

(*motif*)
PolygonMotif,PolygonMotif2,StarMotif,NestedPolygonMotif,RotationSymbolMotif,
ArrowMotif,VectorMotif,DoubleLineMotif,RosetteMotif,StainedGlassMotif,
  LineTransform,

(*graphics transformations*)
Transform2DGraphics,Translate2DGraphics,Rotate2DGraphics,Reflect2DGraphics,
  GlideReflect2DGraphics,

(*graphics cutting*)
CutPolygon,SlicePolygon,SlitLine,CutLine,
  SliceLine,
  Wireframe2DGraphics,ConvertCircleToLine,Cut2DGraphics,Slice2DGraphics,
  CookieStamp2DGraphics,

(*Triangle related*)
TriangleSignedArea,TriangleCentroid,TriangleOrthocenter,TriangleIncenter,
  TriangleCircumcenter,TriangleInscribedCircle,TriangleCircumscribedCircle

 Xah
 xah at best.com
 http://www.best.com/~xah/SpecialPlaneCurves_dir/specialPlaneCurves.html
 Mountain View, CA, USA


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