bmarsh@cod.NOSC.MIL (William C. Marsh) (10/17/90)
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?
Does anybody out there have code to do a rotations of a 2D bitmap in 3D using
the shear transform? This seems much more straight-forward than doing a
'normal' transformation backwards (to avoid holes).
Thanks in Advance!
Bill
--
Bill Marsh, Naval Ocean Systems Center, San Diego, CA
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"If you are not part of the solution, you're part of the problem..."awpaeth@watcgl.waterloo.edu (Alan Wm Paeth) (10/18/90)
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