Hi, I need to extrapolate vector [tex]v_{-1}[/tex] from [tex]v_{0}[/tex], [tex]v_{1}[/tex] and [tex]v_{2}[/tex] (see attached pic), so that if [tex]v_{2}[/tex] is on the right/left (2D case for simplicity) of [tex]v_{1}-v_{0}[/tex], [tex]v_{-1}[/tex] would also be on the right/left.(adsbygoogle = window.adsbygoogle || []).push({});

My initial solution was like this:

[tex]v_{2} - v_{1} = v_{1} - v_{0} + dv[/tex],

[tex]v_{1} - v_{0} = v_{0} - v_{-1} + dv[/tex],

and from there

[tex]v_{-1} = 3(v_{0} - v_{1}) + v_{2}[/tex].

This, however, produces ugly results when abs ([tex]v_{2} - v_{1}[/tex]) < abs ([tex]v_{1} - v_{0}[/tex]) - point [tex]v_{-1}[/tex] is placed very far from [tex]v_{0}[/tex]. So I need a better formula for this.

Any help?

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# Homework Help: Quadratic vector extrapolation

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