February 15, 2010, 06:43  #1 
Prophet
Join Date: Mar 2008
Posts: 2,712

accurate distance
I distinctly remember someone implementing a correct distance function, and thought it made it into the V dev code. I seem to remember being pleased that radius 15 destruction actually destroyed those points within a distance of 15. However, distance() in 3.1.2 is the same hack it used to be. I checked some revs on my machine I haven't deleted, and no diff there either.
Did anyone ever release something with a correct distance function? Is there some reason not to use it? 
February 15, 2010, 14:31  #2 
Swordsman
Join Date: Jul 2008
Posts: 308

I don't know the answer to your exact question, but fast integer distance functions are pretty standard fare in all sorts of games:
Code:
static int isqrt(int num) { if (num == 0) return 0; int n = (num / 2) + 1; int n1 = (n + (num / n)) / 2; while (n1 < n) { n = n1; n1 = (n + (num / n)) / 2; } return n; } static int distance(int x1, int y1, int x2, int y2) { int dx = x2  x1; int dy = y2  y1; return isqrt(dx*dx + dy*dy); } 
February 15, 2010, 15:03  #3 
Knight

But unless there's some magic I'm not aware of going on in the background, it takes 1 move to move straight and 1 move to move diagonally... not 1 to move straight and sqrt(2) to move diagonally, or 2 to move straight and 3 to move diagonally... so why should distance calculations be any different from movement when it comes to detection, archery, spellcasting, and even lighting?
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February 15, 2010, 15:42  #4 
Prophet
Join Date: Apr 2007
Location: Seattle, WA
Posts: 6,706
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btw, you don't actually have to compute the square root to do distance calculations.
x^2 + y^2 <= r^2 is a lot easier than sqrt(x^2 + y^2) <= r 
February 15, 2010, 19:40  #5  
Angband Devteam member

Quote:


February 15, 2010, 19:40  #6 
Prophet
Join Date: Mar 2008
Posts: 2,712

Suppose dx > dy. The distance function in V is currently dx + (dy/2) .
I agree with Pete that one should just use distance_squared when possible, which is presumably all of the time. The only time I imagine nonsquared distance is needed in *bands is for ball damage effects, but they don't properly work off of distance anyway, and their answer is a small lookup table or perhaps the travesty above. These are computable in constant time, so speed is not relevant. 
February 16, 2010, 15:22  #7 
Angband Devteam member
Join Date: Aug 2008
Location: Philadelphia, PA, USA
Age: 42
Posts: 1,516

I wrote the patch to do this (modulo community suggestions), but it was before I had commit access and it never made it into V.
I will dig it up and see if it still worksit kind of dropped off my radar but I do think it would be nice. 
February 18, 2010, 21:30  #8 
Prophet
Join Date: Mar 2008
Posts: 2,712

I think you need to change your distance function to round. Consider radius 1 and radius 2 balls. I think the current implementation is right, although familiarity does cause bias.
For a radius 1 ball, distance \sqrt{2} is inside the ball. Also, distance \sqrt{5} is inside a radius 2 ball, but distance \sqrt{8} is not. In these cases rounding works. Of course, I don't think the distance function should be called for inclusion in a ball. Instead there should be a macro inside_ball(dx, dy, r). The only times I know of that distance is important besides ball inclusion is for reduction in ball damage or minuses on ranged attacks. Nevertheless it might be good to be consistent. 
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