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Quadratic vector extrapolation

  1. Sep 26, 2007 #1
    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.

    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?

    Attached Files:

  2. jcsd
  3. Sep 26, 2007 #2
    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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