Ben: I would add to your reading list the article A Coordinate Free Geometry ADT (1997) by Stephen Mann, Nathan Litke, Tony DeRose http://citeseer.ist.psu.edu/191514.html in which they argue a point that has been made in computer graphics over and over, that confusing affine and vector spaces, or even two different coordinate systems of a common affine space, leads to hard- to-catch errors. Apparently, this has been a steady source of bugs in Computer Graphics as well as any other applications. -- Herve On Mar 12, 2007, at 2:04 PM, Ben FrantzDale wrote:
Anyone interested in this should read up on affine spaces. Absolute temperature is an affine point; difference between affine points are vectors.The same goes for positions in space or time.
Note that Boost already touches on these ideas in Boost.Date_Time ( http://www.boost.org/doc/html/date_time.html). A Time is an affine point, a Time Duration is a vector. (I believe a Time Period could be called a "bound vector".)
See also http://en.wikipedia.org/wiki/Affine_space http://benfrantzdale.livejournal.com/206467.html – what I wrote about this when first heard about affine spaces. —Ben