[ REQ 5005]: Re: library .off files in double precision?

["Tamara Munzner" <munzner>]

Thanks for the suggestion and the well-thought-out exposition of why
it's a good idea. Converting to double-precision has in fact been on
our list of possible things to do for a while now, but since it's not
an out-and-out bug has had relatively low priority thus far. Arguments
like yours heighten its priority. 

 -Tamara Munzner

   From: vavasis at cs.cornell.edu (Stephen Vavasis)
   Date: Fri, 5 Aug 94 21:44:24 -0400

   OK, thanks for the information.  I would like to suggest that you
   consider, for the long term, rewriting your software in double
   precision.  There will be no loss in running time because most modern
   workstations have double-precision floating point hardware.  High
   precision is necessary for almost all operations on geometric objects
   (except displaying them).  For example, in the book "Geometric and
   Solid Modeling" by C. Hoffmann, there is an entire chapter devoted to
   numerical difficulties.  The truth is that nobody knows a very good
   way to handle numerical difficulties in geometric computation, but by
   using high precision you decrease the chance of failure.  By "failure"
   I mean that floating point error in a computation causes a geometric
   impossibility (such as three lines a,b,c such that a,b are parallel,
   b,c are parallel, but a, c cross) and thereby kills the overall
   computation.

   If you assume a simple random model, and if you have seven digits of
   accuracy, then you can expect one out every 10^7 geometric
   computations to fail.  In a complicated algorithm, 10^7 geometric
   operations happen in the blink of an eye.  But if you switch to double
   precision, in the same model, one of every 10^{16} operations will
   fail.  Under this model, it would take several hundred years for a
   failure.

   -- Steve Vavasis