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Add on-manifold B-splines #45

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CharlesCossette opened this issue Oct 17, 2022 · 0 comments
Open

Add on-manifold B-splines #45

CharlesCossette opened this issue Oct 17, 2022 · 0 comments
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enhancement New feature or request

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@CharlesCossette
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CharlesCossette commented Oct 17, 2022

It would be great to have interpolation capability that isnt just "linear", but that still complies with the abstraction provided by State.plus() and State.minus(). This might be kind of a tricky problem to figure out and require some derivation from scratch if it doesnt already exist out there.

This paper defines a B-spline for SE(3):
https://projet.liris.cnrs.fr/imagine/pub/proceedings/BMVC-2013/Papers/paper0094/paper0094.pdf
We could generalize from there: replace uses of exp and log with oplus and ominus appropriately and then that could be directly implementable in our framework. An input to their algorithm though is the "control points" which now become "control poses". If we want to use splines for interpolation, we will need to find a way to compute the control points that result in exact interpolation of the desired states.

@CharlesCossette CharlesCossette added the enhancement New feature or request label Oct 17, 2022
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