Published On: July 21st, 2022Categories: General0 Comments

I recently had to figure out how to move a projectile in an Arc for a project I’m working on and found that a Google search was harder than expected, so I’m writing this up in that hopes that it might help someone else! For starters, take a look at this post on how to do it in 2D, as well as some explanation on the math behind it. For our purposes, we’re going to let Unity handle calculating the arc by simply using an Animation Curve. (Kind of hilariously, I spent part of the past weekend learning Animation Curves in Unity, only to have it be the subject of my next Maya class come Monday morning. Hindsight!)

This is the code I’m using, which is hyper-specific to my project, but we can break it down in principle. (I’ll cover ScriptableObject TypeObjects in a later post, but that’s what’s going on here; Projectile is a MonoBehaviour and the class below is a ScriptableObject)

• Line 7: CurrentTime += Time.deltaTime in Update(). Duration is how long the projectile should take from firing to reach its target. linearT calculates the ratio from 0 to 1 of how close to done we are, given a desired Duration.
• Line 9: PositionXZ() is an extension function I wrote that returns a Vector3 with its Y value set to 0. This function handles moving the projectile towards the target on the X and Z axes, using Lerp and linearT to interpolate smoothly.
• Line 11: does the same thing but only for the Y axis. This ensures that we end up at the correct height for the target, in case the start and end Y positions are different.
• Line 13: uses the same 0 to 1 value in linearT to evaluate the animation curve and return a height offset value. This is multiplied by curveMaxHeight to determine the effective height at the top of the parabola.
• Line 15: adds the Lerped Y to the Offset Y to get the new effective Y. (If we’re Lerping from 0y to 0y, baseY will be 0y throughout, so the arc offset will determine the Y value alone.)

And here’s the animation curve stored in the curveHeight field:

You’ll want to manually clamp the points on the X axis at 0 and 1 to a value of 0. This ensures that at the start and end, no height is added to the projectile. Add a key point at 0.55 and set its value to .95. Set the Start and End tangents to linear; you want the projectile to shoot up towards the peak and come down towards the target quickly. In the middle, you can keep the point at Auto; grab the tangent handle and turn it clockwise so that the right hand side of the parabola is as close to a 45 degree angle as you can get it, which should push the peak to touching 1 on the Y axis.

This system works beautifully, because the offset for the mortar in the Animation Curve matches what you expect it to look like in the game, which I find makes it easier to wrap your head around how it works. You can play around with the tangents if you want to extend that hang at the top, but this works pretty well as is.

Looks pretty good, and no tricky math required… it should also be adaptable for other projectiles like rockets or arrows if you flatten out the Animation Curve. Try it out!

Edit 2022/08/20: I randomly stumbled across https://blog.terresquall.com/2019/11/coding-projectiles-for-your-tower-defense-game-part-2/ and thought it was a great explanation of the same concept; so for further reading, check it out.