Implement 3D pocket-ball collision logic #179
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- Give options for introspecting other roots besides min
- This will enable further refinement over the ball-pocket collision time, which takes into account more than just the ball colliding with the edge of a vertical cylinder
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Pocket collision logic for 3D is added. If ball lands in pocket circle, pocket. If ball flies through with outflux height <7/5*R, the ball is pocketed. Otherwise it is not. Details in
ball_pocket_collision_time_airbornedocstringquadratic.solve and quartic.solve now have the same ins/outs
quadratic.solve is now a general quadratic solver, capable of returning complex roots
It's also less susceptible to catastrophic cancellation (a numerical stability issue)
roots.core got an upgrade. Of note is filter_non_physical_roots and filter_non_physical_roots_many, which take roots and determine heuristically whether they are non-negative, finite, and have a permissibly small imaginary component. This logic existed in the quartic solver, but now has been exposed as a core functionality that can be used any collection of roots (e.g. those calculated from the quadratic solver).