Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!usc!zaphod.mps.ohio-state.edu!swrinde!ucsd!ucbvax!van-bc!tacitus!clh
From: clh@tacitus.tfic.bc.ca (Chris Hermansen)
Newsgroups: comp.graphics
Subject: Tesselating the sphere
Summary: Direct tesselations of the sphere
Message-ID: <155@tacitus.tfic.bc.ca>
Date: 16 Feb 90 21:57:15 GMT
Reply-To: clh@tfic.bc.ca (Chris Hermansen)
Organization: Timberline Forest Inventory Consultants, Vancouver BC
Lines: 32

Last week, Mike Goodchild was in Vancouver at Simon Fraser University and
gave a talk at one of Tom Poiker's evening sessions on "Tesselating the
Sphere".

This is quite a long way from my daily grind, but the subject material was
fascinating.  Basically, he spoke of performing an inital tesselation with
an octahedron, then further subdividing the triangular faces of the octahedron
with triangles.  His encoding scheme therfore required three bits for the
first subdivision and two bits for each subdivision thereafter.

Mike mentioned someone else's name as having done the seminal work on this
topic; unfortunately, I can't remember what it was.

At any rate, there were many interesting things about this tesselation.  First
of all, it didn't require some sort of projection of the sphere (eg as mappers
do), and the tessera numbering scheme presented fit nicely into a binary
digital encoding.  In particular, a 32 bit numbering (leaving one bit unused,
by my calculation, and 14 subdivisions of the initial octahedron) obtains
a pretty decent resolution on the surface of the earth (less than a kilometer,
by my calculations).

This type of representation is obviously of (at least academic) interest
to those of us who deal with digital maps and GISs; are there any readers
of this group with more info to contribute?

Chris Hermansen                         Timberline Forest Inventory Consultants
Voice: 1 604 733 0731                   302 - 958 West 8th Avenue
FAX:   1 604 733 0634                   Vancouver B.C. CANADA
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clh@tfic.bc.ca -or- Chris_Hermansen@mtsg.ubc.ca

May you work in an interesting place.