Re: [boost] Preview 3 of the Geometry Library

Subject: Re: [boost] Preview 3 of the Geometry Library
From: John Phillips (phillips_at_[hidden])
Date: 2008-10-21 16:08:38

Mathias Gaunard wrote:

> 
> Apart from that, allowing multiple coordinate systems within a given 
> space would be fairly useless, and in Euclidian space the Cartesian 
> system is the best choice since it was made for algebra and computations.
> For example, points expressed in polar coordinates should automatically 
> perform conversions from/to cartesian when using get.
> 

   I disagree with this.

   The best choice of coordinate system for internal representation is 
problem dependent. Imposing transformations to and from Cartesian 
internally can cause both numeric stability problems and performance 
problems.

   Every coordinate system was created for algebra, calculus and 
computations. Making the best choice of coordinates for a representation 
can speed calculations by orders of magnitude, or even in some cases 
make problems solvable that weren't in Cartesian coordinates (because of 
a lack of an appropriate representation for the solution). This is a 
huge deal in analytic calculations (See, for example the books by Morse 
and Feshback, or the early editions of Arfken where chapters are 
dedicated to finding and operating in the best coordinate system for the 
job. Also see facilities for this work in Maple or Mathematica.), but it 
is a sometimes under appreciated aspect of numeric calculation, as well.

   This is a conceptually similar problem to the discussions about unit 
systems from a couple of years ago. High accuracy and high performance 
calculations can't afford to have hidden conversion costs in computation 
and precision imposed on them. A well designed library should make such 
hidden conversions possible for those who want them, while also not 
making them mandatory for those who can't afford to pay for them.

                        John Phillips