The answer if fairly trivial, although the derivation is a little tedious. It exploits the symmetry properties of the projectile motion ignoring air resistance. In terms of the maximum height (H) of the projectiles motion and the desired range to target (R), the firing angle theta is given by

theta = tan-1[4H/R]


Interesting note: both the projectile velocity and gravitational acceleration drop out during the derivation, suggesting that the problem is one purely of the geometry of parabolas!

Cheers,

Timkin

Edited by - Timkin on October 23, 2001 11:46:23 PM

Thank you, Timkin! That''s precisely what I''ve been looking for. I always suspected it would be a purely geometrical solution.

I think what I want to do will be fairly robust for what I need. The goal isn''t to find the optimal firing solution, merely *A* firing solution. My game is meant to be mostly comprised of human players with autonomous units here and there.

By finding the highest obstacle, I can be fairly sure it will clear other obstacles if I ensure that the unit is firing from as far away as it can. This means that it creates the widest and tallest arc it can. If it can''t create this arc, it moves forward (or actually to the next node on a path) which invalidates the previous firing solution.

At any rate, thank you to everyone who replied. I''ll put you in the credits