Hi there all,(adsbygoogle = window.adsbygoogle || []).push({});

I have a personal project I'm working on and since I haven't done any linear algebra in many years I'm not sure what I think is right, is right.

I'm also not entirely sure this is the right place to ask but I'm asking more for confirmation/clarification of methodology than any solving so I think this board is more appropriate than the homework one.

So here goes

I have the following:

1.The global location of node (let's call it). Let this be: [itex]X_{C},Y_{C},Z_{C}[/itex]C

2.The global rotation of(by global rotation I mean the rotation of the node as if the global origin were shifted to the centre of the node - does this have a specific term? I hope that made sense)C

Let's call the X,Y,Z rotations of[itex]\gamma[/itex],[itex]\beta[/itex],[itex]\alpha[/itex] respectivelyC

3.a point (let's call it) exists with a known offset in the local X,Y,Z directions. Let's call these offset values: XB_{L},Y_{L},Z_{L}from C. What I mean by_{L}is that ifis rotated in the X,Y,Z thenChas a new local axis and the offset occurs in that direction.C

So what I want to find is:

Thegloballocation and rotation ofgiven the above.B

What i've done but am just not sure if it's right:

I have a relative rotation matrix solved by doingC_{R}= [itex]Z \times Y \times X[/itex] rotations

which is

$$\textbf{C}_{R}=

\begin{bmatrix}

cos( \alpha) & -sin( \alpha) & 0 \\ sin( \alpha) & cos(\alpha) & 0 \\ 0 & 0 & 1

\end{bmatrix}

\begin{bmatrix}

cos(\beta) & 0 & sin(\beta) \\ 0 & 1 & 0 \\ -sin(\beta) & 0 & cos(\beta)

\end{bmatrix}

\begin{bmatrix}

1 & 0 & 0 \\ 0 & cos(\gamma) & -sin(\gamma) \\ 0 & sin(\gamma) & cos(\gamma)

\end{bmatrix}

$$

(is this in itself right? Am I correct to label itC_{R}?)

And then I do, to find theGlobal position ofB

$$\textbf{C}_{R}

\begin{bmatrix}

\gamma_{B}\\\beta_{B}\\\alpha_{B}

\end{bmatrix}=

\begin{bmatrix}

X_{C}\\Y_{C}\\Z_{C}

\end{bmatrix}$$

, solve for

\begin{bmatrix}

\gamma_{B}\\\beta_{B}\\\alpha_{B}

\end{bmatrix}

and to that answer, add

\begin{bmatrix}

X_{L}\\Y_{L}\\Z_{L}

\end{bmatrix}

Is this even correct?

Also, how does one determine the global rotation ofbased off the rotation ofBand the offset ofC. Is it just "the same"? I think i'm overcomplicating thing but i'm honestly not sure.B

In addition to the above, how does one determine the global rotation ofbased off the rotation ofBwith additionalCrotational offsetsofrelative toCB

I hope that all made sense.

regards,

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# Global position and orientation of a point relative to another

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