I'm trying to convert local coordinate system to global coordinate system and vise versa.
I have 3 position coordinates and 3 rotating angles, so my input is (X, Y, Z, RX, RY, RZ).
I'm trying to understand the theory of this process, but I don't have enough experience in math science to extract information from math docs efficiently (I just don't understand them, but I'm trying).
So, can someone explain the coordinate system converting process in simple terms? I just feel a lack of examples.
I already read about rotating and shifting matrixes, but I can't understand how to use them to obtain new X, Y, Z and their rotating angles at the end... Just mess in my head.
In addition I'll be really thanks for the tips on researching this issue.
UPD: Here is the illustration of the problem with example.
We have two coordinate systems. A - world system, A' - local system.
Both systems has the same scale, but for example A' system has cutted axis, just to improve readability.
Magenta ball is an object, located in system A'.
His coordinates and rotation angles (let shorten it up to CRa) in this system are: (1.2, 0.7, 0, 0, 0, 0).
System A' is located in system A. System A' CRa in system A are: (0, 3, 5, 90, 0, 0).
So,
I have ball's CRa in system A'.
I have system A' CRa in system A.
I need to find ball's CRa in system A.
(and vise versa, I need to find ball's CRa in system A' in case I have system A' CRa in system A and ball's CRa in system A.)
The process of transforming between coordinates can be viewed as a two step process.
Just imagine you have these
To transform any points, or vector, from the UV system to XY system, what do you do? You would first ROTATE by some amount, to make UV match the orientation of XY, then you would TRANSLATE UV back the where XY is, right? So for example I have some point, (6,4) in the XY system. the actual representation in XY system is P = O + 6X + 4Y, which effectively, is saying you have where XY are your unit vector along the axis. Why? Because you are moving 6 in your X direction, and 4 in your Y direction, plus the distance from the origin O.
You can represent this in a matrix form: [[1,0],[0,1]] @ [6,4] + O.
Same idea applies. To represent the point in new UV, you would go about P' = I + aU + bV. where (a,b) is your new coordinates.
So effectively, you are figuring out a matrix, [[ux, uy],[vx,vy]], that when multiplied by your [a,b], gives back [6,4]. Or some matrix when multiplied by [6,4], gives you back [a,b].
In order to find this matrix, you look at the relationship between UV and XY. Does it look like that you actually rotated it by some amount, and the moved it by some amount? So that is where the (X, Y, Z, RX, RY, RZ) comes in. These represents the amount you translate (x,y,z) and rotate (RX,RY,RZ). The rest goes about how you put these in a single matrix where you can google on homogenous transformation.