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I am working on SLAM, the localization problem in robotics. I have a trajectory generated from my odometry sensors that is composed of a set of points ( O ). ( S ) is the starting point end ( E ) is the ending point of the trajectory. These points can define a polyline

S[itex]\mapsto[/itex]O[itex]\mapsto[/itex]O[itex]\longmapsto[/itex]E

the arrows represent the transactions which are known and are not identical. The drawing is a 1D case but I am working on 3D.

Say I correct the ending ( E ) and move it forward a certain amount [itex]\delta[/itex].

S[itex]\mapsto[/itex]O[itex]\mapsto[/itex]O[itex]\longmapsto[/itex][itex]\stackrel{\delta}{\rightarrow}[/itex]E

I know that the correction of E affects the rest of the points but I don't know how. So I need to suppose an intelligent way to reshape the rest of the trajectory, in this case to stretch it. There's not a specific way to define "intelligent", I just would like to know if there's a known way to apply the correction to the whole trajectory in a way that make sense.

Maybe someone that works with computer graphics knows a simple idea?

some people suggested the use of springs but for a different case which you cannot easily apply to this case.

thanks and regards

S.

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# Polyline reshaping

Can you offer guidance or do you also need help?

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