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How to Implement atan2 Function in Scratch

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UN

UltraNeonGodPet

Posted on August 4, 2025 • Advanced

📐 Need atan2 function for sprite pointing

I’m trying to make a sprite point towards another sprite and move 10 steps. But I need the atan2 function to do this properly. How would I go about implementing this in Scratch?

I know there’s a “point towards” block, but I’m not using it due to a specific system I’m testing. I need the arctan2 trigonometric function using x and y coordinates from a reference sprite.

MW

MathWizard_Dev

Replied 1 hour later • ⭐ Best Answer

Great question @UltraNeonGodPet! The atan2 function is essential for precise directional calculations. Scratch doesn’t have a built-in atan2, but we can create one with proper quadrant correction. Let me show you how:

🧮 Understanding atan2

The atan2(y, x) function returns the angle from the positive x-axis to the point (x, y), handling all four quadrants correctly. Here’s how to implement it:

    // Basic 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] // undefined, but we'll use 0
end
end
else
set [angle v] to ([atan v] of ((y) / (x)))
if <(x) > [0]> then
set [result v] to (angle)
else
if <(y) > [0]> then
set [result v] to ((angle) + [180])
else
set [result v] to ((angle) - [180])
end
end
end

🎯 Simplified One-Line Version

Here’s a more compact version that works great for most cases:

    // Compact atan2 formula
define get angle to (target x) (target y)
set [dx v] to ((target x) - (x position))
set [dy v] to ((target y) - (y position))
set [angle to target v] to (([atan v] of ((dy) / ((dx) + [0.0001]))) + ([180] * <(dx) < [0]>))

🚀 Complete Point-and-Move System

Here’s a complete system for pointing towards a target and moving:

    // Complete pointing and movement system
define point towards sprite (target sprite)
set [target x v] to ([x position v] of (target sprite))
set [target y v] to ([y position v] of (target sprite))
get angle to (target x) (target y)
point in direction (angle to target)

define move towards sprite (target sprite) steps (step count)
point towards sprite (target sprite)
move (step count) steps

// Usage example
when [space v] key pressed
move towards sprite [Player v] steps [10]

🔄 Advanced Version with Smooth Rotation

For smoother movement with rotation limits:

    // Smooth rotation version
define smooth point towards (target x) (target y) speed (rotation speed)
get angle to (target x) (target y)
set [target angle v] to (angle to target)
set [current angle v] to (direction)

// Calculate shortest rotation path
set [angle difference v] to ((target angle) - (current angle))
if <(angle difference) > [180]> then
change [angle difference v] by [-360]
end
if <(angle difference) < [-180]> then
change [angle difference v] by [360]
end

// Apply rotation with speed limit
if <([abs v] of (angle difference)) > (rotation speed)> then
if <(angle difference) > [0]> then
turn right (rotation speed) degrees
else
turn left (rotation speed) degrees
end
else
point in direction (target angle)
end

🎮 Practical Game Example

Here’s how to use it in a real game scenario:

    // Enemy AI using atan2
when I start as a clone
forever
// Point towards player
get angle to ([x position v] of [Player v]) ([y position v] of [Player v])

// Smooth rotation (optional)
smooth point towards ([x position v] of [Player v]) ([y position v] of [Player v]) speed [5]

// Move forward
move [2] steps

// Check if reached target
if <(distance to [Player v]) < [20]> then
// Do something when close to player
say [Found you!] for [1] seconds
end

wait [0.1] seconds
end

📊 Angle Conversion Utilities

Useful helper functions for angle calculations:

    // Angle utility functions
define normalize angle (angle)
// Keep angle between -180 and 180
set [normalized v] to ((((angle) + [180]) mod [360]) - [180])

define angle difference (angle1) (angle2)
// Get shortest angular distance between two angles
set [diff v] to ((angle2) - (angle1))
normalize angle (diff)
set [angle difference result v] to (normalized)

define degrees to radians (degrees)
set [radians v] to (((degrees) * [3.14159]) / [180])

define radians to degrees (radians)
set [degrees v] to (((radians) * [180]) / [3.14159])

This implementation gives you full control over directional calculations and works perfectly for any pointing or movement system! 🎯

AL

AwesomeLlama_Coder

Replied 30 minutes later

@MathWizard_Dev excellent explanation! Here’s the ultra-compact version I use for quick implementations:

    // Ultra-compact atan2 (one line!)
set [angle v] to (([atan v] of ((target y - y position) / ((target x - x position) + [0]))) + ([180] * <(target x - x position) < [0]>))

And here’s a custom block version for easy reuse:

    define point towards (x) (y)
point in direction (([atan v] of (((y) - (y position)) / (((x) - (x position)) + [0]))) + ([180] * <(x) < (x position)>))

The ”+[0]” prevents division by zero errors! 🛡️

UN

UltraNeonGodPet

Replied 15 minutes later

@MathWizard_Dev @AwesomeLlama_Coder This is exactly what I needed! Thank you both! 🎉

The compact version is perfect for my system. I can now implement precise directional calculations without relying on the built-in “point towards” block. This gives me much more control over the movement system!

VB

Vibelf_Community

Pinned Message • Moderator

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