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I'm doing some 3D graphics work and hit a snag. The problem should be easy enough, but I couldn't find any general solution after some personal brainstorming. I kinda feel stupid for asking something that's probably a trivial trigonometry problem, but here goes:

I have two 3-dimensional points: $ P _ 1 $ and $ P _ 2 $. Starting from $ P _ 1 $, I need to move towards $ P _ 2 $ by "$ N $" units. $ N $ is guaranteed to be less than the distance from $ P _ 1 $ to $ P _ 2 $. Thus, I need to find the point $ P _ 3 $ which is $ N $ units away from $ P _ 1 $, moving from $ P _ 1 $ towards $ P _ 2 $. It's using $ x $, $ y $, and $ z $ values, but a solution with just $ x $ and $ y $ is probably sufficient for me to figure the rest out.

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    You need the unit vector for $P_1P_2$ multiplied by $N$ and added to $P_1$ – 2017-02-24
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    So, in other words, (( P2 - P1)/|P2-P1|) * N) + P1 – 2017-02-24
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    Yes that's it.. – 2017-02-24
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    Note that that formula works even without any restrictions on $N$. If $N$ is greater than the distance between $P_1$ and $P_2$, then $P_2$ is between $P_1$ and $P_3$. If $N$ is negative, then $P_1$ is between $P_2$ and $P_3$. – 2017-02-24

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