Calculating Lead For Projectiles

Author: Daniel Brauer

These functions calculate an intercept point based on the current positions and constant velocities of a shooter and a target, along with a projectile speed. They're really good for shooting asteroids with machine guns, but won't work as well for targets that can dodge.

How to use the intercept function
This is an example of how to call FirstOrderIntercept. The result is that interceptPoint is the point in space where the projectile can hit the target. If you fire a projectile at that point, and the target doesn't accelerate, you'll hit it (except when hitting it is impossible).

Calculating the intercept point
This code is based on solving the first order (velocity, no acceleration) version of the problem. It properly handles the situation where the target's relative velocity and the shot velocity are equal, which causes a singularity if not dealt with specially. Also, it returns the target's current position if there are no positive solutions. This is because it's not always possible to intercept a target. For example, the target may be moving away from the shooter with a velocity higher than the shot velocity.

License
The MIT License (MIT)

Copyright (c) 2008 Daniel Brauer

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