First of all, I am not a mathematician so please excuse my novice way of describing the problem at hand...
I have several sets of data which represent x,y coordinates in various skewed/oblique systems, and I want to convert them all to a common ortho-canonical system, in order to later "stack" them on top of each other in a single plot. Let's assume a skewed system is as shown here:
where (x,y) the coordinates of a point in this systen, (a,b) the origin, φ the angle between the x and y axes (<>90 degrees), and θ the angle between the x axis and the horizontal plane. I can calculate the angle φ from known points within the axes, and I think I can also calculate θ.
From my research so far, I believe this transformation needs to happen in 3 steps:
- Make the x axis horizontal (eliminate the θ angle).
- Make the φ angle 90 degrees (make the y axis vertical).
- Move the axes origin to a common point for all data sets (e.g. 0,0).
So basically, I need the equations for each of these steps.
A similar question was answered here
which offers the equations for the 2nd step, but I have not been able to successfully complete the first step, in order to check if these equations work correctly.
Any help would be welcome!
