Newsgroups: comp.graphics
Path: utzoo!utgpu!jarvis.csri.toronto.edu!dgp.toronto.edu!elf
From: elf@dgp.toronto.edu (Eugene Fiume)
Subject: Re: Clarification of mapping question
Message-ID: <8805030234.AA03672@explorer.dgp.toronto.edu>
Keywords: 2d mapping
Organization: University of Toronto, CSRI
References: <862@agora.UUCP>
Date:	Mon, 2 May 88 21:14:39 EDT

As I mentioned in a previous comp.graphics submission that may not have
gotten beyond our local net, we developed an approach based on conformal
mapping which will allow you to go from an arbitrary simple polygon to
another.  Mapping from a rectangle to a simple polygon is obviously a
subcase.  It is also possible to map a simple polygon bijectively to a
circle or to a half-plane.  A description of the approach can be found in:

E. Fiume, A. Fournier, and V. Canale, ``Conformal texture mapping'',
Proceedings of Eurographics '87, Elsevier Science Publishers
(North Holland), Amsterdam (1987), pp53-64.

Our work is partially based on some software written by Lloyd Trefethen
that's available from netlib.  His software is useful if you just want
to map points in one polygon to another conformally.  The hard part,
graphically speaking, is doing filtering, assuming you are interested
in doing something like mapping a texture onto a polygon.
-- 
Eugene Fiume
Dynamic Graphics Project
University of Toronto
elf@dgp.utoronto (BITNET); elf@dgp.toronto.edu (CSNET/UUCP)