Date: Mon, 29 Apr 1996 19:32:04 -0700
From: ix.netcom.com!elements (William L. Anderson)

* A new test routine has representations of the n-dimensional sphere,
  ellipsoid, cylinder, and elliptical torus.  The software computes
  position vector, Jacobian matrix, and Hessian matrix on these
  n-dimensional objects.

* Metrics other than the Euclidean metric can be specified.  One
  well-known example is the hyperbolic metric.

* Using the above capabilities, GEODES can approximate minimum-length
  geodesics on n-dimensional manifolds embedded in a non-Euclidean
  space.

Date: Wed, 9 Oct 1996 08:18:58 -0700
From: ix.netcom.com!elements (William L. Anderson)

* An improved manifold.c routine is more concise, yet still has
  representations of the n-dimensional sphere, ellipsoid, cylinder,
  and elliptical torus.

* Efficiency of tridiagonal solver is improved by precomputing
  constant pivots, and reusing them.

* A few variable are given more descriptive names.  A few comments
  have been improved.

I hope this submission is useful to others in academia and industry.
The GEODES routine is being used by a Canadian engineering company to
compute geodesic cutting paths on a machine parts represented by
B-spline patches.

Thank you,
Bill Anderson
Elements Research
7501 Windyrush Road
Charlotte, NC 28336-3115
704-543-9180
elements@ix.netcom.com


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