🟣 Circle Collision Detection

Simple circle collision detection using the distance formula.

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📐 Formula

$$√((x₂ - x₁)² + (y₂ - y₁)²) ≤ r₁ + r₂$$

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🖼️ Demonstration

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🧠 Explanation

Circle Positions

Circle A = (2, 3)
Circle B = (5, 5)

Radii

r1 = 8
r2 = 9

Distance Calculation

dx = 5 - 2 = 3
dy = 5 - 3 = 2

distance = Math.sqrt(dx*dx + dy*dy)

distance = Math.sqrt(3*3 + 2*2)
distance = Math.sqrt(13)

distance ≈ 3.6

Collision Check

3.6 <= 17

✅ Collision detected

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🚀 Optimized JavaScript

function circleCollision(c1, c2) {

    const dx = c2.x - c1.x;
    const dy = c2.y - c1.y;

    const distanceSquared = dx * dx + dy * dy;

    const radiusSum = c1.radius + c2.radius;

    return distanceSquared <= radiusSum * radiusSum;
}

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📦 Example

const player = {
    x: 2,
    y: 3,
    radius: 8
};

const enemy = {
    x: 5,
    y: 5,
    radius: 9
};

console.log(circleCollision(player, enemy));

Output

true

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🎮 Use Cases

• Game Development
• Physics Engines
• Hitboxes
• Particle Systems
• Simulations

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⚡ Complexity

Time Complexity: O(1)
Space Complexity: O(1)