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4

Your statement about the need to reimplement the same feature in order to test it could be applied for all software which needs to be unit-tested and it is not specific only to your problem. A unit test does not implement redundant functionality, in this case an error cannot be attributed to a faulty implementation in the tested code, as it can just as ...


2

A general approach would be to construct a so called axis-angle representation and convert that to a rotation matrix representation. On order to do so, one could start with a normal vector of the triangle. Let's take the $P_1P_2$ line and construct the perpendicular of the triangle from $P_3$ to $P_1P_2$. Let's call $P_4$ the point where the ...


2

No difference at all although φ∈[−π,π) is much more reasonable and intuitive. It is just a matter of system definition.


1

Assuming frame $0$ is the 'absolute frame', if we let $^j P_i$ be the $i^{th}$ position/orientation expressed in the $j^{th}$ coordinate frame, then what you're asking for is the sequence $$\{(^0P_i)_{i=1 ... N}\},$$ correct? Using your sequence of measurements $\{(x_i, y_i, \theta_i)_{i=1 ... N}\}$, it's straightforward to compute the $i^{th}$ 2-D ...


1

Each step can be represented by its transformation matrix, $$ \begin{bmatrix} \cos{\theta'_{i}} & -\sin{\theta'_{i}} & x'_{i}\\ \sin{\theta'_{i}} & \phantom{-}\cos{\theta'_{i}} & y'_{i} \\ 0 & 0 & 1 \end{bmatrix}. $$ The world position at each step $i$ is the rightward-propagating product of the transforms up to that point, $$ \...


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