Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Path: utzoo!utgpu!water!watnot!watmath!clyde!rutgers!lll-lcc!pyle
From: pyle@lll-lcc.UUCP
Newsgroups: comp.graphics
Subject: Bounding extent questions
Message-ID: <656@lll-lcc.aRpA>
Date: Sat, 7-Mar-87 23:46:35 EST
Article-I.D.: lll-lcc.656
Posted: Sat Mar  7 23:46:35 1987
Date-Received: Sun, 8-Mar-87 14:48:10 EST
Organization: Lawrence Livermore Labs, Livermore Ca
Lines: 28
Keywords: Bounding ellipsoids, Cluster spheres, bounding spheres


Some questions please:


1.)  Does anyone know how to determine a bounding ellipsoid for an arbitrary
     object?  Kajiya stated in one of his papers that one could be created
     via a "principal axis transformation on the covariance of the points."
     Can someone tell me what this involves?

2.)  Has anyone ever implemented a cluster sphere hierarchy for a ray-tracer?
     Can the hierarchy be constructed automatically, given a set of local
     bounding spheres?

3.)  Given a unit object (see Roth's paper, 1982, in Computer Graphics and
     Image Processing), like a unit cube, can one determine its bounding
     sphere in world coordinates, just given the local-to-world transform?
     If the scaling factor was even in X, Y and Z, I concluded that it was
     possible.	I was wondering if it was still obtainable, given that the
     cube is transformed into, for example, a retangular box.



Thanks a bunch,

Ernie Pyle


P.S.  Responses via E-Mail would be just great.