Newsgroups: comp.graphics
Path: utzoo!utgpu!watserv1!watcgl!awpaeth
From: awpaeth@watcgl.waterloo.edu (Alan Wm Paeth)
Subject: Re: 3D Rotations of 2D Bitmap
Message-ID: <1990Oct17.195341.18615@watcgl.waterloo.edu>
Keywords: bitmap rotations
Organization: University of Waterloo
References: <2364@cod.NOSC.MIL>
Date: Wed, 17 Oct 90 19:53:41 GMT
Lines: 26

In article <2364@cod.NOSC.MIL> bmarsh@cod.NOSC.MIL (William C. Marsh) writes:
>Now, before anyone responds with a "read the FAQ", I have, and this question
>is about a different problem.  I need to rotate a 2D bitmap around all three
>axis (X and Y, in addition to Z).  I haven't been able to locate the article
>referenced in the FAQ, so the code I have does little good to explain how I
>could expand the shear transform method to all three dimentions?

The FEQ cites the original three-shear rotation work appeared in the 1986
Proceedings of Graphics Interface (Vancouver), but many foreign libraries don't
receive GI. Given the number of requests for reprints received over the years
I published an extended version in _Graphics Gems_, edited by A. Glassner
(Academic Press, 1990). [Just printed and not yet mentioned in the FEQ].

Regarding 3D rotation of a 2D bitmap: both the '86 paper and its revision cite
the Master's work of R. Krieger, who describes a 2D (but non-shear) technique
specifically aimed at perspective transformations. It is generally useful for
texture mapping, orthographic 3D rotation is a specific case (eyepoint at inf).

    /Alan Paeth
    Computer Graphics Laboratory
    University of Waterloo

------
PS - Krieger's MMath essay ``3-D Environments For 2-D Animation'' (1984) has
been reprinted as a report and may be ordered c/o Tech Report Secretary/
Dept of Computer Sci./University of Waterloo/Waterloo, Ontario N2L 3G1/Canada