Re: [boost] Formal Review: Boost.Polygon starts today August 24, 2009

Subject: Re: [boost] Formal Review: Boost.Polygon starts today August 24, 2009
From: John Phillips (phillips_at_[hidden])
Date: 2009-09-01 17:03:37

Simonson, Lucanus J wrote:
> 
> I can implement a transparent floating point to fixed point
> conversion wrapping the algorithm that is integer only.  This should
> allow transparent use of the algorithm with floating point
> coordinates and no more loss of precision than floating point
> calculations themselves would produce.
> 
> 
> Thanks Jeff, Luke

   Luke,

   You have made variations of this assertion a few times in this 
thread, and I wanted to point out one problem with it.

   The distribution of the integers is not the same as the distribution 
of the floating point numbers. It is true that an x-bit integer has 
about as many distinct values as an x-bit floating point number. (Even 
more, depending on the representation used.) However, those integers are 
evenly distributed along the number line, and the floating point values 
are not. This will not cause a problem in many applications, but in any 
setting where large and small scales mix (such as polygons that are just 
off of regular, but need to be precisely defined; or systems that mix 
large and small polygons) there will be no scaling for the integers that 
both preserves the needed dynamic range and the needed precision. So the 
user will be forced to choose between overflow errors or lost precision.

                        John