2
$\begingroup$

I've seen similar questions, but none worded quite like what I'm asking here. I'm not a math major, so I may have follow-up questions if answers befuddle me.

Scenario: I'm trying to emulate a rabbit's "hop" in computer software (this is 2D, BTW)

Question: If I know where the rabbit is standing (p1) and where the rabbit is hopping to (p2), how can I create a formula that achieves an arc or parabola (either would suffice, but a parabola seems to make more sense, since the distances will sometimes vary).

Additional Info:

  1. When the Y values of p1 and p2 are the same, I would like a specific height of the apex (vertical height of apex = half of the distance between the X values of p1 and p2).
  2. When the Y values of p1 and p2 are different, I need to determine a reasonable height for the apex that doesn't look ridiculous (how could I specify a reasonable focus?).

If I have asked in the wrong place, I will happily follow links to the right place. Thanks in advance!

  • 1
    Do you want a formula for the arc of the parabola, i.e. $y$ in terms of $x$, or do you want a parameterization, i.e. both $x$ and $y$ as functions of time $t$?2012-05-24

2 Answers 2