   The software in this directory is devoted to a transformation of
polygons and curves explored during Summer Research Project. The
mathematical paper about the properites of the transformation can be
obtained from Geometry Center by mail.  It also stored in
/usr5/reports91/arek/mathpaper.wn .

Contents:

mppt.m   - the Mathematica (ASCI) code of the package Midpoint Polygon 
           Transformation. The package  might be a useful tool for various 
	   animations, e.g. the changing of shape of polygons, curves and 
	   surfaces  to  an  ellipse, knots unraveling, ordered movement of 
	   particles, etc.It defines eight functions which illustrate 
	   linear transformations of polygons in a plane and the theorems 
	   stated the paper "Midpoint Polygon Transformation". The enables the 
	   user to explore further properties of particular polygons and the 
	   transformation.       
	
mppt.doc - the documentation to the package mppt.m. 



The following mpptnotebook files are only useful on the NeXT and are
in the file mmpt.next.tar.m.  mppt.m can be used without these files.

mpptnotebook.doc - The documentation for mpptnotebook.ma and
		   mpptnotebook.mb.

mpptnotebook.ma and mpptnotebook.mb - the Mathematica notebook written
                                      on the NEXT computer.  The
                                      numerous examples introducing
                                      the package mppt.m and the
                                      theory behind the midpoint
                                      polygon transformation are
                                      written in this notebook.

	                              Arek Goetz 
				 (u21569@uicvm.uic.edu)
		           University of Illinois at Chicago
			  
	   			      