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Direction formula assistance for tower defense

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TD

TowerDefender_Pro

Posted on August 5, 2024 • Intermediate

🎯 Need help with direction calculations in tower defense

I’m working on a tower defense game and I’ve got the distance calculation working using the Pythagorean theorem. However, I’m really struggling with the atan direction formula to make my towers point towards enemies.

I’ve tried multiple tutorials and even used AI assistance, but nothing seems to work correctly. The towers either don’t rotate at all or point in completely wrong directions.

For context, I’m using step-based movement rather than direct X/Y positioning. Can someone help me understand what I’m doing wrong? 🤔

MC

MathCoder_Expert

Replied 3 hours later • ⭐ Best Answer

Great question @TowerDefender_Pro! Direction calculations can be tricky, but once you understand the concept, it becomes much easier. Let me break down the atan2 implementation for you:

📊 Direction Calculation Flow

Here’s how direction calculation and pointing works:

flowchart TD A[🎮 Start Direction Calculation] --> B[Get Current Position] B --> C[Get Target Position] C --> D[Calculate Delta X] D --> E[Calculate Delta Y] E --> F[dx = target_x - current_x] F --> G[dy = target_y - current_y] G --> H{Check for Zero Division} H -->|dy = 0| I[Handle Special Case] H -->|dy ≠ 0| J[Calculate atan2] I --> K[Set Direction = 90° or -90°] J --> L[angle = atan(dx/dy)] L --> M{Check Quadrant} M -->|dy < 0| N[Add 180° to angle] M -->|dy ≥ 0| O[Keep angle as is] N --> P[Final Direction] O --> P K --> P P --> Q[Point in Direction] Q --> R[🎯 Sprite Now Facing Target] style A fill:#e1f5fe style B fill:#f3e5f5 style J fill:#e8f5e8 style P fill:#fff3e0 style R fill:#fce4ec

🧮 Understanding atan2 in Scratch

Since Scratch doesn’t have a built-in atan2 function, we need to create our own. Here’s the formula:

    define atan2 (y) (x)
set [result v] to (([atan v] of ((y) / ((x) + (0)))) + ((180) * <(x) < [0]>))

🎯 Point Towards Any Position

Here’s a custom block that makes any sprite point towards specific coordinates:

    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))
point in direction (([atan v] of ((dx) / ((dy) + (0)))) + ((180) * <(dy) < [0]>))

🏰 Tower Defense Implementation

For your tower defense game, here’s how to make towers track enemies:

    // In your tower sprite
when flag clicked
forever
set [closest enemy v] to []
set [shortest distance v] to [999999]

// Find closest enemy
repeat until <(length of [enemy list v]) = [0]>
set [current enemy v] to (item (1) of [enemy list v])
set [distance v] to ([sqrt v] of (((x position of (current enemy)) - (x position)) ^ (2)) + (((y position of (current enemy)) - (y position)) ^ (2)))

if <(distance) < (shortest distance)> then
set [shortest distance v] to (distance)
set [closest enemy v] to (current enemy)
end

delete (1) of [enemy list v]
end

// Point towards closest enemy
if <not <(closest enemy) = []>> then
point towards x: (x position of (closest enemy)) y: (y position of (closest enemy))
end

wait (0.1) secs
end

🔧 Step-Based Movement Alternative

Since you mentioned using step-based movement, here’s an alternative approach:

    // Calculate direction and move with steps
define move towards x: (target x) y: (target y) speed: (speed)
set [dx v] to ((target x) - (x position))
set [dy v] to ((target y) - (y position))
set [distance v] to ([sqrt v] of ((dx) ^ (2)) + ((dy) ^ (2)))

if <(distance) > (speed)> then
set [move x v] to ((dx) / (distance)) * (speed)
set [move y v] to ((dy) / (distance)) * (speed)
change x by (move x)
change y by (move y)
else
go to x: (target x) y: (target y)
end

⚠️ Common Pitfalls to Avoid

  • Division by zero: Always add a small value (like 0) to prevent division errors
  • Coordinate systems: Remember Scratch uses a different coordinate system than standard math
  • Performance: Don’t calculate directions every frame - use timers for optimization
  • Edge cases: Handle situations where target and source positions are identical

The key is understanding that we’re converting Cartesian coordinates to polar coordinates (angle and distance). Hope this helps! 🎯

TD

TowerDefender_Pro

Replied 2 hours later

@MathCoder_Expert This is absolutely perfect! 🎉

I tested your atan2 implementation and it works flawlessly. My towers are now properly tracking enemies and the rotation looks smooth and natural.

The step-based movement solution is exactly what I needed. Thank you for explaining the math behind it too - it really helps me understand what’s happening!

VB

Vibelf_Community

Pinned Message • Moderator

🎯 Master Advanced Game Mathematics!

Excellent discussion on direction calculations! For those looking to dive deeper into game mathematics and create more sophisticated tower defense mechanics, our community can help you with:

  • 🧮 Advanced trigonometry and vector math
  • 🎯 Predictive targeting algorithms
  • ⚡ Performance optimization techniques
  • 🏰 Complex tower defense AI systems

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