0
$\begingroup$

I have a function that solves a problem when a specific angle equals $0$. The same function can be used with non-zero angles if you compute the problem from other coordinate system.

The scheme of the problem is: Scheme

I need help to figure out the transformation matrix between these two coordinate system, both $B_1 \to B_0$ and $B_0 \to B_1$.

Thanks

$\endgroup$
0
$\begingroup$

I have figured out the answer. In case someone needs something like this, I post it here.

$B_1 \to B_0$:

$$\begin{pmatrix}x\\\ y\\\ z\\\ 1\end{pmatrix}=\begin{pmatrix}1 & 0 & 0 & 0\\\ 0 & cos(ψ) & sin(ψ) & -h·tan(ψ)\\\ 0 & -sin(ψ) & cos(ψ) & 0\\\ 0 & 0 & 0 & 1\end{pmatrix}·\begin{pmatrix}x'\\\ y'\\\ z'\\\ 1\end{pmatrix}$$

$B_0 \to B_1$:

$$\begin{pmatrix}x'\\\ y'\\\ z'\\\ 1\end{pmatrix}=\begin{pmatrix}1 & 0 & 0 & 0\\\ 0 & cos(ψ) & -sin(ψ) & h·sin(ψ)\\\ 0 & sin(ψ) & cos(ψ) & h·sin^2(ψ)/cos(ψ)\\\ 0 & 0 & 0 & 1\end{pmatrix}·\begin{pmatrix}x\\\ y\\\ z\\\ 1\end{pmatrix}$$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.