# Questions tagged [rigid-transformation]

Rigid transformations are mappings from one reference frame to another reference frame in the Euclidean space $\mathbb R^n$. They comprise translation, rotation (and sometimes reflection). More formally, rigid transformation are elements of the matrix Lie group SE($n$), the specially Euclidean group. If reflection is included, these proper rigid transformations are elements of the matrix Lie group E($n$), the Euclidean group.

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### Can the location of the 4th vertex of a projected rectangle be calculated?

In another thread, "Can we compute the location of the unseen point" we are trying to calculate the 2D location in an image, of an arbitrary point Q on a rectangle when we know the 2D ...
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### Closest rigid-body pose and velocity along a screw motion to a given pose

Given two rigid-body poses given by dual quaternions ${\bf q}_1$ and ${\bf q}_2$, where ${\bf q}_1 = e^{{\bf v} t}$ is some pose along a screw motion. The screw is given by dual vector (Pluecker ...
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### Rotate a frame by the given theta about an axis of another frame

I have two frames ($F_1$ and $F_2$) both are represented wrt frame $O$ (origin frame). Therefore, $T_1$ and $T_2$ are known. Also, I know the frame $F_2$ relative to $F_1$, i.e., $T_{rel}$ is known. ...