vegetarian lasagne, black coffee

[pigseatingfigs]

OK all you intelligent people, how can I formally represent uncertainty in distances? That is, I want to be able to say, X is a certain distance and angle from Y, but both of these are within +-20%, or something similar. I also need a way of comparing statements so that one with less uncertainty can be given priority. Try to make it in the form

Comments

[chickenfeet2003]

OK, let's make r+/-e the distance from X to Y and a+/-b the angle.

Now, it seems reasonable to make the metric of uncertainty the area of the the "box" in which Y may lie. This is actally a rhomboid but for reasonably small values of b it approximates to a rectangle, of which the area is 4er.sin(b).

[pigseatingfigs]

bollocks, sorry, I forgot to say that they have to move on a grid, and so all angles must be represented by x=2, y=3 and so on. They can't move diagonally. I do like the box idea though, can I represent that in a grid?

[chickenfeet2003]

So how is percentage error in the angle measured? And can I assume that the metric for distance is the number of grid square sides traversed so the distance from (x1, y1) to (x2, y2) is x2-x1+y2-y1 rather than sqrt[(x2-x1)^2+(y2-y1)^2]?

[pigseatingfigs]

I had to adapt it so that I can say it is 4 squares (+-1 sqaure) left and 5 squares (+-2 squares) up, and so on. So a 20% error on a distance of 4 would be represented by 1 (even though that is actually 25%). In time, I would hope to be able to make the grid squares small enough so that this doesn't matter, but for now they are quite big. Sorry, I should have been clearer - I assume that because it is the main thought occupying my head at the moment other people will be able to see what I mean instantly!

[chickenfeet2003]

In that case the "rectangle of uncertainty" idea seems appropriate and essentially trivial to calculate. In your given example giving an uncertainty value of 8

[pigseatingfigs]

I shall try it out - thanks!