# Quadratic vector extrapolation

1. Sep 26, 2007

### makc

Hi, I need to extrapolate vector $$v_{-1}$$ from $$v_{0}$$, $$v_{1}$$ and $$v_{2}$$ (see attached pic), so that if $$v_{2}$$ is on the right/left (2D case for simplicity) of $$v_{1}-v_{0}$$, $$v_{-1}$$ would also be on the right/left.

My initial solution was like this:
$$v_{2} - v_{1} = v_{1} - v_{0} + dv$$,
$$v_{1} - v_{0} = v_{0} - v_{-1} + dv$$,
and from there
$$v_{-1} = 3(v_{0} - v_{1}) + v_{2}$$.

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

Any help?

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2. Sep 26, 2007

### makc

okay, this forum is titled "physics and math help". so, once in a god knows how many month I post for help, and what do I receive? a warning? if this is how you intent to help, well... screw you and your warnings. you may ban me right away, I will get help at some other place :(

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