Newsgroups: comp.graphics
Path: utzoo!utgpu!jarvis.csri.toronto.edu!dgp.toronto.edu!elf
From: elf@dgp.toronto.edu (Eugene Fiume)
Subject: Re: the word "bitmap"
Message-ID: <8901111331.AA25073@explorer.dgp.toronto.edu>
Organization: University of Toronto, CSRI
References: <450@orbit.UUCP> <1198@hydra.riacs.edu> <1304@luth.luth.se> <3155@cloud9.Stratus.COM>
Date: Wed, 11 Jan 89 08:31:43 EST

In article <3155@cloud9.Stratus.COM> cme@cloud9.Stratus.COM (Carl Ellison) writes:
>
>Meanwhile, to me as a mathematician, both "bitmap" and "pixmap" are improper
>because the word "map" makes no sense.  In both math and computer science,
>"map" means a device, table, algorithm, ..., for mapping from one domain to
>another.

This is entirely incorrect.  It is not hard to define a bitmap
precisely as a function (taking the integers to booleans).  Programming
methodologists have defined the semantics of arrays (in programming
languages) similarly.  See Gries' book, for example.  Furthermore, it
is easy to define boolean rings and algebras over bitmaps.

Lastly, as I stated in an earlier posting, bitmaps should be dissociated
from images.  Yet another "map" (mathematically precise and well defined,
I might add) must be specified to associate a bitmap with an image.  In
this manner, one can define the semantics of things like moving a bitmap
across an image, or defining a pixel aspect ratio.  Once again, an image
can be characterised as yet another map (this time over the reals rather
than the integers).
-- 
Eugene Fiume
Dynamic Graphics Project
University of Toronto
elf@dgp.toronto.edu