🎯 Bézier Curves for Projectiles in Roblox: Making Arcs Magical

Ever launched a fireball in Roblox and thought, “Hmm… that looked kinda stiff”? Or maybe you wanted your arrows to fly in a smooth arc instead of dropping like a brick 🧱.

Well, here’s the secret: Bézier curves. They’re not just fancy math; they’re your ticket to projectiles that feel alive, controllable, and—let’s be real—way cooler to show off.

But how do they work in Roblox, and why should you even care? 🤔 Stick around, because by the end of this, you’ll know how to make your projectiles dance through the air like they’ve got a mind of their own.

🚀 Why Physics Alone Isn’t Enough

Roblox’s physics engine does a great job of making objects fall realistically. You set a velocity, Roblox handles the rest. Easy, right?

But here’s the problem: realistic ≠ fun.

Maybe you’re building a magic system where spells swoop dramatically. Or a sci-fi blaster where plasma bolts curve toward enemies. Physics alone? Too predictable.

This is where Bézier curves step in. They give you control over style, not just realism. And once you see how easy they are to use, you’ll never go back.

🌀 What’s a Bézier Curve Anyway?

Imagine you’ve got three points:

• Start point (P0) → where your projectile begins.

• End point (P2) → where it lands or explodes.

• Control point (P1) → a “magnet” pulling the curve toward itself.

Now, instead of your projectile just flying straight, it follows a path that bends toward that control point.

The magic formula looks like this:

B(t) = (1 - t)² * P0 + 2(1 - t)t * P1 + t² * P2

Yeah, it looks mathy. But don’t freak out 🙃. All it means is:

• When t = 0, you’re at the start.

• When t = 1, you’re at the end.

• Everything in between is the smooth curve.

And here’s the kicker: you can stack more points (like a cubic Bézier with 4 points) for even wilder curves. But let’s not run before we walk.

🎨 Why Bézier Curves Are Perfect for Projectiles

So why should you care? Well, Bézier curves let you do things like:

Stylized magic attacks → Fireballs that arc dramatically instead of just plopping down.✨ Guided arrows → They bend slightly toward the target, looking intentional.✨

Cinematic effects → Imagine a dragon breathing fire that curves smoothly across the sky.

In short: control + creativity. And here’s the fun part—you decide exactly how “curvy” or “direct” things look by moving just one control point.

🛠️ Implementing Bézier Curves in Roblox

Okay, let’s get our hands dirty. 🧑‍💻

Here’s a Lua function that calculates a point on a quadratic Bézier curve:

local function quadraticBezier(t, p0, p1, p2)
	return (1 - t)^2 * p0 
		+ 2 * (1 - t) * t * p1 
		+ t^2 * p2
end

But wait—Roblox positions aren’t numbers, they’re Vector3. Don’t worry, we just apply the formula to each axis:

local function quadBezierVector3(t, p0, p1, p2)
	local x = quadraticBezier(t, p0.X, p1.X, p2.X)
	local y = quadraticBezier(t, p0.Y, p1.Y, p2.Y)
	local z = quadraticBezier(t, p0.Z, p1.Z, p2.Z)
	return Vector3.new(x, y, z)
end

Now you can give it:

• p0 → start position

• p1 → control point

• p2 → end position

And boom 💥, you’ve got a point along the curve.

🏹 Making a Projectile Follow the Curve

Let’s put this into motion. Imagine you’re firing an arrow. Instead of relying on physics, you’ll update its position along the Bézier curve over time:

Bézier Curves for Projectiles in Roblox

Now when you call launchProjectile, your arrow, fireball, or potato (hey, you do you 🥔) will glide beautifully through the air.

🎯 But What About Collisions?

Ah, good question. Right now, our projectile just follows the path and disappears. What if it hits something early?

Two common tricks:

1. Raycasting → On each step, cast a ray from the last position to the new one. If it hits something, stop.

2. Touched event → If your projectile is a Part, you can connect a Touched event.

Raycasting is usually smoother because it handles fast projectiles that might skip through objects.

🔮 Taking It to the Next Level

Alright, you’ve got a working projectile. But let’s push it further:

• Dynamic control point → Instead of a fixed curve, calculate the control point based on the target’s position, player’s aim, or even randomness for flavor.

• Cubic Bézier curves → With 4 points, you get even more control. Imagine projectiles that zigzag slightly before hitting.

• Easing effects → Play with how t increases. Instead of linear time, ease in/out for cinematic slowdowns.

Once you start layering these tricks, your projectiles stop being “objects” and start becoming experiences. ( Bézier Curves for Projectiles in Roblox )

🧩 When to Use Physics vs. Bézier

Let’s be clear: you don’t always need Bézier curves.

• Use physics → When you want realistic gravity, interactions, or ragdoll-style chaos.

• Use Bézier → When you want precise control, stylization, or cinematic flair.

Think of physics as realism and Bézier as art direction. Knowing when to use which? That’s the mark of a pro.

🌟 Wrapping It Up | Bézier Curves for Projectiles in Roblox

Bézier curves might sound intimidating at first, but in practice, they’re just smooth math magic 🎩. With only a few lines of code, you can transform boring straight shots into cinematic projectiles that wow your players.

So next time you’re working on your Roblox game and you think, “Hmm, this feels a little flat”—try adding a curve. Literally.

And here’s the fun part: once you’ve mastered projectiles, you’ll start to see Bézier curves everywhere. Pathfinding. UI animations. Even camera movement. But that’s a story for another day… 👀