Raycasting tutorial / vector math question

Posted by mattboy on Game Development See other posts from Game Development or by mattboy
Published on 2012-12-05T19:03:20Z Indexed on 2012/12/05 23:21 UTC
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vector

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ray-casting

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raycasting

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vector-algebra

I'm checking out this nice raycasting tutorial at http://lodev.org/cgtutor/raycasting.html and have a probably very simple math question.

In the DDA algorithm I'm having trouble understanding the calcuation of the deltaDistX and deltaDistY variables, which are the distances that the ray has to travel from 1 x-side to the next x-side, or from 1 y-side to the next y-side, in the square grid that makes up the world map (see below screenshot).

enter image description here

In the tutorial they are calculated as follows, but without much explanation:

//length of ray from one x or y-side to next x or y-side
double deltaDistX = sqrt(1 + (rayDirY * rayDirY) / (rayDirX * rayDirX));
double deltaDistY = sqrt(1 + (rayDirX * rayDirX) / (rayDirY * rayDirY));

rayDirY and rayDirX are the direction of a ray that has been cast.

How do you get these formulas? It looks like pythagorean theorem is part of it, but somehow there's division involved here. Can anyone clue me in as to what mathematical knowledge I'm missing here, or "prove" the formula by showing how it's derived?

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