range based algorithms

Manhattan distance

The taxicab distance between two points in a Euclidean space with fixed Cartesian coordinate system is the sum of the lengths of the projections of the line segment between the points onto the coordinate axes. For example, in the plane, the taxicab distance between the point P1 with coordinates (x1, y1) and the point P2 at (x2, y2) is |x1 - x2| + |y1 - y2|.

so, say you've got one person at [2,3] and another at [6,10], the distance between the two would be |2 - 6| + |3 - 10| = 11. If 11 > rangeMax then OutOfRange.

this formula can also be useful for path finding.

[Edited by - ferr on July 4, 2007 12:32:31 AM]

Squared Distance works well for less-than and greater-than checks, but not for printing out the range (since the distance stays squared). The valid "in-range" zone will be more circular than the Manhattan Distance (which is more like a diamond).

If you want to convert squared distance to "real" distance, then just take the square root of (x*x+y*y)

int diffX = x1 - x2;int diffY = y1 - y2;if (diffX*diffX + diffY*diffY < range*range){  // it's within range}

Wow! great responses! Thanks a bunch!