I am creating a chess game and programming the movement for the piece that moves diagonal, but I have a problem, I cannot figure out how to find how many squares the piece is moving through, relative to the two points eg: 6,1 and 3,4 goes through 4 tiles, and I need a formula that finds this distance with any diagonal line, so I can then use that number for how many times the pathfinding must loop, I have looked at other equations, bot nothing seems to work with my particualar problem.
how do I find the number of squares a line passes through on a diagonal axis?
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geometry
dynamic-programming
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0See for example this question: http://math.stackexchange.com/questions/1121541/number-of-unit-squares-that-meet-a-given-diagonal-line-segment-in-more-than-one – 2017-02-06
1 Answers
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6,1 and 3,4 goes through 4 tiles
That's because $\lvert 6-3\rvert = \lvert 1-4\rvert = 4-1$. In other words, the absolute difference in $x$ coordinate equals the absolute difference in $y$ coordinate as it is a diagonal movement, and both of these equal the number of squares minus one. The minus one is because you start counting at $1$ for distance $0$.