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How to make sprites rotate towards coordinates using trigonometry in Scratch

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MC

MathCoder_Sam

Posted on July 21, 2025 • Advanced

📐 Trigonometry Help - Sprite Rotation Issues

Hey everyone! I’m struggling with trigonometry in Scratch and need some help. 😅

I’m trying to make a sprite rotate towards specific x,y coordinates using this formula:

atan2((x - xpos)/(y - ypos))

The problem: When I point to coordinates below the sprite, it rotates in the opposite direction instead of pointing down! 🤔

Scratch’s direction system seems so inefficient for this kind of math. Has anyone dealt with this before? Any help would be appreciated!

MM

MathMaster_Pro

Replied 30 minutes later • ⭐ Best Answer

Great question @MathCoder_Sam! This is a classic trigonometry issue that many developers encounter. Let me explain the problem and provide a complete solution:

🧮 Understanding the Problem

flowchart TD A[Coordinate System] --> B[Scratch Directions] A --> C[Mathematical Angles] B --> D[0° = Up, 90° = Right] C --> E[0° = Right, 90° = Up] F[atan2 Function] --> G[Returns Math Angles] G --> H[Need Conversion] H --> I[Scratch Direction System] J[Quadrant Issues] --> K[Quadrant I & III: Same tan value] J --> L[Quadrant II & IV: Same tan value] K --> M[Need atan2 for disambiguation] style A fill:#e1f5fe style F fill:#f3e5f5 style J fill:#ffebee style H fill:#e8f5e8

🔧 The Complete Solution

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

    // Custom block: Rotate Towards Point
define rotate towards x: (target x) y: (target y) with speed: (rotation speed)

// Calculate the differences
set [dx v] to ((target x) - (x position))
set [dy v] to ((target y) - (y position))

// Proper atan2 implementation
if <(dy) = [0]> then
if <(dx) > [0]> then
set [target direction v] to [90]  // Right
else
set [target direction v] to [-90]  // Left
end
else
// Calculate base angle
set [base angle v] to ([atan v] of ((dx) / (dy)))

// Adjust for quadrants
if <(dy) > [0]> then
set [target direction v] to (base angle)  // Quadrants I & II
else
set [target direction v] to ((base angle) + [180])  // Quadrants III & IV
end
end

// Smooth rotation towards target
set [angle difference v] to ((target direction) - (direction))

// Normalize angle difference to [-180, 180]
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 <(angle difference) > (rotation speed)> then
turn cw (rotation speed) degrees
else
if <(angle difference) < (0 - (rotation speed))> then
turn ccw (rotation speed) degrees
else
point in direction (target direction)
end
end

🎯 Advanced Rotation System

For even smoother rotation with easing:

    // Enhanced rotation with easing
define smooth rotate towards x: (target x) y: (target y)

// Calculate target direction using proper atan2
set [dx v] to ((target x) - (x position))
set [dy v] to ((target y) - (y position))

// Handle edge cases
if <((dx) = [0]) and ((dy) = [0])> then
stop [this script v]  // Already at target
end

// Calculate angle in degrees (Scratch format)
if <(dy) = [0]> then
if <(dx) > [0]> then
set [target angle v] to [90]
else
set [target angle v] to [-90]
end
else
set [raw angle v] to ([atan v] of ((dx) / (dy)))
if <(dy) > [0]> then
set [target angle v] to (raw angle)
else
set [target angle v] to ((raw angle) + [180])
end
end

// Calculate shortest rotation path
set [angle diff v] to ((target angle) - (direction))
repeat until <(angle diff) <= [180]>
change [angle diff v] by [-360]
end
repeat until <(angle diff) > [-180]>
change [angle diff v] by [360]
end

// Smooth rotation with easing
set [rotation speed v] to ((angle diff) * [0.1])  // 10% easing
if <([abs v] of (rotation speed)) < [0.5]> then
point in direction (target angle)  // Snap when close
else
turn cw (rotation speed) degrees
end

🚀 Instant Rotation (No Animation)

If you just need instant rotation without smooth animation:

    // Instant rotation to target
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))

// Quick atan2 implementation
if <(dy) = [0]> then
if <(dx) > [0]> then
point in direction [90]
else
point in direction [-90]
end
else
point in direction (([atan v] of ((dx) / (dy))) + ((180) * <(dy) < [0]>))
end

📊 Understanding Scratch’s Direction System

Key differences between mathematical angles and Scratch directions:

    // Direction conversion reference
// Mathematical: 0° = Right, increases counter-clockwise
// Scratch: 0° = Up, increases clockwise

// Convert math angle to Scratch direction:
define math to scratch angle: (math angle)
set [scratch direction v] to ((90) - (math angle))

// Convert Scratch direction to math angle:
define scratch to math angle: (scratch direction)
set [math angle v] to ((90) - (scratch direction))

🎮 Practical Example: Turret Tracking

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

    // Turret that tracks the player
when flag clicked
forever
// Get player position
set [player x v] to (x position of [Player v])
set [player y v] to (y position of [Player v])

// Calculate distance
set [distance v] to ([sqrt v] of (((player x) - (x position)) ^ (2) + ((player y) - (y position)) ^ (2)))

// Only track if player is in range
if <(distance) < [200]> then
smooth rotate towards x: (player x) y: (player y)

// Fire if facing the right direction
set [angle to player v] to ([atan v] of (((player x) - (x position)) / (((player y) - (y position)) + (0.001))))
if <([abs v] of ((direction) - (angle to player))) < [5]> then
broadcast [fire projectile v]
end
end
end

🔍 Debugging Tips

  • Visualize angles: Use the “say” block to display calculated angles
  • Check quadrants: Test with targets in all four quadrants
  • Handle edge cases: What happens when dx or dy is zero?
  • Normalize angles: Keep angles within [-180, 180] range
  • Use small steps: For smooth rotation, use small angle increments

This should solve your rotation issues completely! The key is proper quadrant handling and understanding Scratch’s coordinate system. 🎯

MC

MathCoder_Sam

Replied 1 hour later

@MathMaster_Pro This is absolutely incredible! 🤯

I never understood the quadrant issue before - your explanation with the coordinate system differences makes perfect sense. The smooth rotation with easing is exactly what I needed for my game!

The turret tracking example is pure gold. Thank you so much! 🙏

GT

GameTech_Wizard

Replied 2 hours later

Excellent tutorial @MathMaster_Pro! 👏

For anyone working with advanced rotation mechanics, here are some additional use cases:

  • Orbital motion: Sprites rotating around a central point
  • Projectile prediction: Leading targets that are moving
  • Camera following: Smooth camera rotation in 3D-style games
  • Steering behaviors: AI entities that smoothly turn toward goals
  • Physics simulation: Realistic angular momentum and rotation

Trigonometry opens up so many advanced game mechanics! 🎮

VB

Vibelf_Community

Pinned Message • Moderator

📐 Master Advanced Mathematics in Scratch!

Fantastic discussion on trigonometry and rotation mechanics! For those ready to dive deeper into mathematical programming, our community specializes in:

  • 🧮 Advanced mathematical algorithms and formulas
  • 🎯 Precision targeting and tracking systems
  • 🌀 Complex rotation and transformation mechanics
  • 🚀 Physics simulation and realistic movement

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