Document edge case for orientation vector representation #4803
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| This edge case occurs because when an object is oriented nearly parallel to the Z-axis (pointing straight up or down), the axis of rotation (OX, OY, OZ) becomes aligned with the Z-axis. | ||
| In this configuration, there are infinite valid combinations of the orientation axis and Theta that represent the same physical orientation, similar to the gimbal lock problem in Euler angles. |
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In this configuration, there are infinite valid combinations of the orientation axis and Theta that represent the same physical orientation, similar to the gimbal lock problem in Euler angles.
It's not quite the same; there aren't infinite configurations, it's still just one OV to one orientation. There's a discontinuity, where there are two well-defined regions and no way to smoothly transition between them. You just might see huge jumps in theta values and eyeballing values to estimate distance between orientations becomes impossible.
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got it. Corrected to 1:1 and emphasized the discontinuity
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| If your application requires orientations near these poles, be aware that: | ||
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| - Small changes in OZ near the threshold may cause discontinuous changes in how the orientation is represented |
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This one seems to imply the OX/OY/OZ might jump too, which it won't. I think the next bullet down covers this better.
| - For the north pole (OZ approaching +1): `Theta = -atan2(Y', -X')` | ||
| - For the south pole (OZ approaching -1): `Theta = -atan2(Y', X')` | ||
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| Where X' and Y' are components of the transformed X-axis basis vector. |
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I am not sure anyone will understand what this means.
biotinker
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Consider adding a reference to axis angles for their utility in measuring distance between orientations.
Otherwise LGTM.
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As described in the new section, there is a piece of the OV representation that is discontinuous and conditional on OZ pointing directly up, and was very confusing to me. After talking to Peter L about it, I now understand it better and want to provide this context to all Viam developers and/or docs readers.