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).
- 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).
- 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!