On Sat, Mar 14, 2009 at 2:26 PM, Fernando Cacciola <fernando.cacciola@gmail.com> wrote:
... For many many geometric applications, it is the topology what needs to be correct, not the geometry.
In the early years of digital geography, it was not understood that the topology had to be correct, and virtually every digital mapping project turned into a disaster. Once it became known (in the late 1960's) that the topology had to always be totally correct (no topological errors whatsoever, no matter how large the database) then it became possible to build large scale digital maps, and digital mapping became a reality.
If you do clipping for instance, it might very well not matter at all (for instance in drawing applications) if the vertices are slightly off.
In commercial digital mapping, data like water features are often "cartooned" to save memory and speed processing. In effect, intermediate coordinates are deliberately distorted, but only when it does not break the topology.
But if an entire region is included in the result when it should not, then that is a disaster for whatever application.
The GIS industry has a bunch of colorful names for such topological errors; zingers, leaks, etc, based on the appearance of map plots with various characteristic mistakes. And, yes, once the underlying rules were understood, most or even all of the geometric computation code had to be not just rewritten, but usually thrown in the trash and a fresh start made. It was actually possible to reduce the precision of coordinates and yet produce far more robust code. --Beman