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  • Raycasting "fisheye effect" question

    - by mattboy
    Continuing my exploration of raycasting, I am very confused about how the correction of the fisheye effect works. Looking at the screenshot below from the tutorial at permadi.com, the way I understand the cause of the fisheye effect is that the rays that are cast are distances from the player, rather than the distances perpendicular to the screen (or camera plane) which is what really needs to be displayed. The distance perpendicular to the screen then, in my world, should simply be the distance of Y coordinates (Py - Dy) assuming that the player is facing straight upwards. Continuing the tutorial, this is exactly how it seems to be according to the below screenshot. From my point of view, the "distorted distance" below is the same as the distance PD calculated above, and what's labelled the "correct distance" below should be the same as Py - Dy. Yet, this clearly isn't the case according to the tutorial. My question is, WHY is this not the same? How could it not be? What am I understanding and visualizing wrong here?

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  • Raycasting tutorial / vector math question

    - by mattboy
    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). 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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