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Dan Zuras wrote:
If we are to generalize this discussion into something more appropriately standardizable like a definition of midpoint, I think failing on too narrow [u,v] or even [u,u] would be unreasonable from the user's perspective. But Nate, as the B&B guy in the room, I'm sure you have working stopping criteria other than blowing up when an interval gets too narrow. What's wrong with using width(xx) > 0? Actually I suspect you actually use width(xx) > eps where eps > 0. Both work in the sense of preventing infinite recursions & both allow one to use a more reasonable definition of midpoint.
Nothing's wrong with that. As I mentioned from the get-go, the ills can be cured by tedious and defensive programming. I think others have already attested to this, as well. But the learning curve for the uninitiated has to come from somewhere, and its very easy to make mistakes... and no one wants thier real-time radar-tracking B&B algorithm of the future to crash once the missile leaves the launching pad.
That's why if we are careful perhaps there is an opportunity to help educate users in ways that won't hurt so much. All the fun and sarcasm aside, that is my main point.
Nate