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    <p>Instead of tracing the path by stepping along the line - you want to jump right to the next possible tile (the border). This can be calculated fairly simply. I will use your sample numbers above.</p> <ol> <li>Calculate the line eqn (y= .286x + 2.471)</li> <li>You are starting on tile 2,3 and moving towards tile 5,4. So calculate the y value when x goes to 3 (the border to the tile immediately to the right). It is 3.329. </li> <li>Then calculate the x value when y goes to 4 (the border to the tile immediately above). It is 5.346.</li> <li>Starting at 2,3 and moving right gets to 3,3.329. Moving up gets to 5.346,4. You intersect on the right(moving 2 -> 3 on x doesn't move a tile on y). You don't intersect above until you are on tile 5 in the x.</li> <li>The tile calculated in 4 becomes your new comparison (3,3). Repeat from step 2.</li> </ol> <p>This process only incurs one calculation per tile moved (regardless of your precision or how big the tiles are) and is exact. Note that the values calculated can be stored and reused instead of blindly calculating both intersections over and over. In the above we know (step 4) that we don't move up a tile until x=5. So the entire path can be inferred without another calculation (2,3 -> 3,3 -> 4,3 -> 5,3 -> 5,4). </p> <p>It is also possible to precalculate all the transistions instead of doing them stepwise although this would only be beneficial if you always need the entire path (you don't since you want to stop processing once you find an obstacle).</p> <p>Two caveats. Be careful about signs and which way the line is going - many a bug happen by not paying close attention to negative slopes. Also, using reals you almost never will cross diagonally (two borders at once) but you should be aware of it (handle it in the code) just in case. </p> <p>There is a name for this method but I can't remember it off the top of my head. I believe it might be from Game Programming Gems series but maybe someone else can provide a better reference.</p>
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    1. POC#: 2D sub-Tile Line intersection
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    1. COExcellent Answer, thanks. I will accept it as soon as SO allows it (13 hours left)
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    2. COIndeed! It's very smart. I'm trying to implement it but I can't find a way to code the 4th step (I can't find the perfect if/else condition that decide which is the new comparison point). Do you remember the name of that algorithme so I can look for an implementation example?
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