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From: scm@onion.UUCP
Newsgroups: comp.graphics
Subject: Can You Transform Quadric Surfaces With 4x4 Matrices?
Message-ID: <255@onion.cs.reading.ac.uk>
Date: Mon, 26-Jan-87 06:48:28 EST
Article-I.D.: onion.255
Posted: Mon Jan 26 06:48:28 1987
Date-Received: Wed, 28-Jan-87 23:11:32 EST
Reply-To: scm@onion.Ac.Uk (Stephen Marsh)
Organization: Comp. Sci. Dept., Reading Univ. UK.
Lines: 26


        Can anyone help me with this problem? I am trying to
represent some solid objects by using quadric surfaces which
seem to be a favourite amongst geometric modellers and to
then move them around in a world model.
If I have a surface defined by
        Q(x,y,z) = ax^2 + by^2 + cz^2 + dxy + eyz + fxz
                        + gx + hy + iz + k
(ie sphere, cone etc)
does anyone know if there is a straight-forward way of
transforming this surface in my world model using the usual
4x4 scale, rotate and translate matrices?
I know that you can scale a sphere by altering k and translate
it by adding values to a,b or c, but this doesn't seem
to be a very logical approach. Will I have to re-express
these quadric solids as a lot of polygons, surface patches etc etc?
        If you know of some mathematical way of re-expressing the
above equation so that the usual transformations can be
applied, I would be pleased to hear from you.

Name: Steve Marsh
E-mail: scm@onion.cs.reading.ac.uk
Establishment: University of Reading, UK.
Research: Systems Architecture Group.
Department:  Department of Computer Science
Phone me at: (0734) 875123 ext 7881 from inside UK