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In the example picture below, I know the points $A$, $B$, $C$ & $D$. How would I go about calculating $x$, $y$, $z$ & $w$ and $O$, but as points on the actual plane itself (e.g. treating $D$ as $(0, 0)$, $A$ as $(0, 1)$, $C$ as $(1, 0)$ and $B$ as $(1, 1)$.

enter image description here

Ultimately I need to be able to calculate any arbitrary point on the plane so I'm unsure as to whether this would be possible through linear interpolation of the results above or whether I would actually just have to do this via some form of Matrix calculation? I don't really know matrix math at all!

Just looking for something I can implement in JavaScript (in an enviroment that does support matricies).

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    Two points can be used to determine and compute a line. Two nonparallel lines can be used to determine and compute an intersection. Thus you can use (I.) `A` and `C` to form `AC`, `B` and `D` to form `BD`, `AC` and `BD` to find `O`; (II.) `A` and `B` to form `AB`, `C` and `D` to form `CD`, `AB` and `CD` to find `f1`; (III.) `A` and `D` to form `AD`, `B` and `C` to form `BC`, `AD` and `BC` to find `f2`; (IV.) `f1` and `O` to form `f1O`, `f1O` and `BC` to find `x`, `f1O` and `AD` to find `z`; (V.) `f2` and `O` to form `f2O`, `f2O` and `DC` to find `y`, `f2O` and `AB` to find `w`.2011-08-28
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    Thanks very much! I'm not sure why I didn't just see this. It certainly works to calculate the points (and I can happily work out the points relative to the plane). However this method of just using points hasn't helped me when interpolated across the whole plane for many points, so now I guess I'm going to have to bite the biscuit and go for a matrix projected transformation instead.2011-08-28

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