Given a ray in a 2D world at position p with initial velocity u and acceleration a how can I tell when it's within a certain distance r from a certain point.
Uniform motion: s = ut + at^2/2
Or p(t) - p(0) = ut + at^2 / 2
You want the first t >= 0 for which (p(t) - C).(p(t) - C) = r^2.
If u and a could be non-perpendicular then I think you have to solve a quartic.
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5 years ago