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Implementing atan2 function in Scratch for sprite rotation

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MD

MathCoder_Dev

Posted on November 22, 2024 • Advanced

📐 Need help implementing atan2 in Scratch

Hey everyone! I’m working on a project where I need sprites to accurately point towards specific (x, y) coordinates. I’ve been trying to implement an atan2 function in Scratch but I’m running into issues.

Currently I’m using:

point in direction (([atan v] of ((y1-y2)/(x1-x2))))

This works sometimes, but when I try to point at coordinates to the left of the sprite, it points in the opposite direction. I know this is related to the quadrant problem with regular atan, but I can’t figure out how to handle it properly in Scratch.

Any help with implementing a proper atan2 function would be greatly appreciated! 🙏

TM

TrigMaster_Pro

Replied 25 minutes later • ⭐ Best Answer

Great question @MathCoder_Dev! The atan2 function is indeed tricky to implement in Scratch, but it’s totally doable. Let me break down the problem and provide you with a complete solution:

🤔 Understanding the Problem

The issue you’re experiencing is called the “quadrant problem.” The regular atan function only returns values between -90° and 90°, which means it can’t distinguish between angles in different quadrants.

flowchart TD A[📍 Target Point] --> B{Which Quadrant?} B -->|Quadrant I| C[0° to 90°] B -->|Quadrant II| D[90° to 180°] B -->|Quadrant III| E[180° to 270°] B -->|Quadrant IV| F[270° to 360°] C --> G[✅ atan works correctly] D --> H[❌ atan gives wrong result] E --> I[❌ atan gives wrong result] F --> J[❌ atan gives wrong result] G --> K[🎯 Correct Pointing] H --> L[🔄 Need atan2 correction] I --> L J --> L L --> K style A fill:#e1f5fe style G fill:#e8f5e8 style H fill:#ffebee style I fill:#ffebee style J fill:#ffebee style K fill:#f3e5f5

🔧 The Complete atan2 Implementation

Here’s a robust atan2 implementation that handles all quadrants correctly:

    // Complete atan2 implementation
define atan2 (y) (x)
if <(x) = [0]> then
if <(y) > [0]> then
set [result v] to [90]
else
if <(y) < [0]> then
set [result v] to [-90]
else
set [result v] to [0]
end
end
else
set [result v] to ([atan v] of ((y) / (x)))
if <(x) < [0]> then
if <(y) > [0]> then
change [result v] by [180]
else
change [result v] by [-180]
end
end
end

🎯 Point Towards Implementation

Now you can use this to create a “point towards” function:

    define point towards x: (target x) y: (target y)
set [dx v] to ((target x) - (x position))
set [dy v] to ((target y) - (y position))
atan2 (dy) (dx) :: custom
point in direction (result)

⚡ One-Line Solution (Advanced)

For those who prefer a more compact solution, here’s a one-line atan2:

    // One-line atan2 (math coordinates)
set [angle v] to (([atan v] of ((y) / ((x) + (0)))) + ((180) * <(x) < [0]>))

// For Scratch's coordinate system (point towards)
define point towards (target x) (target y)
set [dx v] to ((target x) - (x position))
set [dy v] to ((target y) - (y position))
point in direction (([atan v] of ((dx) / ((dy) + (0)))) + ((180) * <(dy) < [0]>))

🔍 Understanding the Edge Cases

The + (0) in the denominator prevents division by zero errors when the target is directly above or below the sprite.

🧪 Testing Your Implementation

Here’s a test setup to verify your atan2 function works correctly:

    when flag clicked
// Test all quadrants
point towards x: [100] y: [100] :: custom  // Quadrant I
wait (1) seconds
point towards x: [-100] y: [100] :: custom // Quadrant II
wait (1) seconds
point towards x: [-100] y: [-100] :: custom // Quadrant III
wait (1) seconds
point towards x: [100] y: [-100] :: custom // Quadrant IV

🎮 Practical Applications

  • Enemy AI: Make enemies face the player
  • Projectiles: Shoot bullets towards targets
  • Turrets: Rotate turrets to track moving objects
  • Pathfinding: Orient sprites along movement paths

⚠️ Common Pitfalls to Avoid

  • Don’t forget to handle the division by zero case
  • Remember Scratch uses a different coordinate system than standard math
  • Test with targets in all four quadrants
  • Be careful with the order of dx and dy in your calculations

This should solve your pointing problem completely! Let me know if you need clarification on any part! 📐✨

MD

MathCoder_Dev

Replied 2 hours later

@TrigMaster_Pro This is absolutely perfect! Thank you so much! 🎉

I implemented your complete atan2 function and it works flawlessly in all quadrants. The explanation about the quadrant problem really helped me understand what was going wrong.

The one-line solution is particularly elegant - I’ll definitely be using that in my future projects!

GM

GameMath_Expert

Replied 1 hour later

Excellent explanation @TrigMaster_Pro! 👏

For anyone interested in the mathematical background, atan2 is essentially solving this problem:

  • atan(y/x) gives you an angle, but loses information about which quadrant
  • atan2(y,x) uses both x and y signs to determine the correct quadrant

This is why it’s so useful for game development - you get the full 360° range instead of just ±90°!

VB

Vibelf_Community

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