~~NOTOC~~
<=[[4rpl:start| Index]] \\
<=[[4rpl:start#math_utility| Math Utility]]



====== BallisticArcLateral ======
BallisticArcLateral(<-from <-lateralSpeed <-target <-maxHeight) ->travelTime ->gravity ->fireVelocity

===== Description =====
 Solve the firing arc with a fixed lateral speed. Vertical speed and gravity varies.
 This enables a visually pleasing arc.
 Not every combination of inputs has a computable output. In the case the ballistic arc does not have a solution, zeros are returned for all values.

 - from: Vector point projectile will fire from\\
 - lateralSpeed: scalar speed of projectile along XZ plane\\
 - target: Vector point projectile is trying to hit\\
 - maxHeight: the world height for the projectile to peak at. When testing with a ground based unit, this needed to be higher than the unit position.

 Returns:\\
 - fireVelocity: Vector firing velocity\\
 - gravity: gravity necessary to projectile to hit precisely max_height\\
 - travelTime: The time it takes the projective to reach to target.

This API synergizes with the [[4rpl:commands:ballisticarcpos|BallisticArcPos]] API which is a [[4rpl:commands:movetowards|MoveTowards]] type of API but for arcs rather than a straight line which can use the returned variables to enact a smooth and visually appealing parabolic motion for a custom unit.

===== Examples =====
<code 4rpl>
BallisticArcLateral(V3(10 1 10) 0.5 V3(50 5 40) 30) ->travelTime ->gravity ->fireVel
</code>
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