Square-wise distance

Question

I had a hard time finding a good title for this. Feel free to edit it if you find something more appropiate.

What I'm trying to do is finding a function such that, given a point $C$ (center), gives the square-wise distance from any point to $C$.

Now, for a simple definition of square-wise dist, imagine a square of a fixed size centered at $C$ and aligned to the $x$ and $y$ axis. I want each point of this square to be at the same square-wise distance from $C$, so it's the same as euclidean distance but changing circle by square.

How would I go into computing that? I can't wrap my head around it...

Hint: Consider each of the x-coordinate and the y-coordinate of the said two points. — Ivan Wangsa, Aug 11 '14 at 08:44
I'll have a look into that link. I didn't know this had a name! PD: Btw this is all related to a shader I'm writing, so when I get back home I'll edit my question and post a graphical representation of both euclidean distance and this distance with colors, I think that might also help to clearify my question for other readers. — Setzer22, Aug 11 '14 at 11:51

score 3 · Accepted Answer · answered Aug 11 '14 at 08:55

3

If $C = (x_c, y_c)$, and $P = (x,y)$, then: $$d(P,C) = \sup\{|x_c - x|, |y_c - y|\}$$ does the job.

answered Aug 11 '14 at 08:55

Ivo Terek

77,665

sorry, what's sup? I assume it's the supreme of the set (idk if that's english) i.e. max, right? – Setzer22 Aug 11 '14 at 11:46
That's right (: – Ivo Terek Aug 11 '14 at 11:47
Nice, thanks! Then that does the job. I just came to that thinking: Well, if the point lies whithin a square's perimeter the largest of the x and y coordinates must be the side of the square. Then I saw your answer, so it makes sense. – Setzer22 Aug 11 '14 at 11:50

score 2 · Answer 2 · answered Aug 11 '14 at 09:00

2

Square-wise distance

2 Answers2