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🧮 Mathematical

Physics calculations (gravity, velocity, collision)

Why Math Matters in Games

Math is the invisible engine behind almost every game mechanic.
It controls how objects move, fall, bounce, collide, and react.

In game development, three of the most important physics concepts are:

• Gravity
• Velocity
• Collision detection & response

These allow your game world to feel dynamic, physical, and alive.

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Gravity

Gravity is a constant downward force that accelerates objects over time.

Most games simulate gravity by increasing the object’s vertical velocity each frame:

this.vy += this.gravity;

Then apply that velocity to position:

this.y += this.vy;

What this means:

• Objects fall faster the longer they fall
• Jumping feels natural
• Characters don’t float or stop mid‑air

Gravity is usually a small number like 0.5 or 0.7.

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Velocity

Velocity is the speed and direction of an object’s movement.

Games typically track:

• vx → horizontal velocity
• vy → vertical velocity

Movement happens by adding velocity to position:

this.x += this.vx;
this.y += this.vy;

Velocity can be changed by:

• Player input
• Gravity
• Collisions
• Friction
• Forces or impulses

Velocity is the foundation of smooth, continuous motion.

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Collision

Collision math determines:

• When two objects touch
• Where they touch
• How they should respond

Basic collision detection (AABB)

Axis‑Aligned Bounding Box (AABB) is the simplest method:

if (this.x < other.x + other.width &&
    this.x + this.width > other.x &&
    this.y < other.y + other.height &&
    this.y + this.height > other.y) {
    // collision happened
}

Collision response

Once a collision is detected, you adjust position or velocity:

• Stop falling when hitting the ground
• Bounce off walls
• Take damage
• Trigger events

Example:

if (collidingFromTop) {
    this.vy = 0;       // stop falling
    this.y = other.y - this.height;
}

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Example Code (Simple & Clear)

class GameObject {
    constructor(x, y) {
        this.x = x;
        this.y = y;
        this.vx = 0;
        this.vy = 0;
        this.gravity = 0.7;
    }

    update() {
        // apply gravity
        this.vy += this.gravity;

        // apply velocity
        this.x += this.vx;
        this.y += this.vy;
    }

    collidesWith(other) {
        return (
            this.x < other.x + other.width &&
            this.x + this.width > other.x &&
            this.y < other.y + other.height &&
            this.y + this.height > other.y
        );
    }
}

This demonstrates:

• Gravity
• Velocity
• Collision detection
• Physics‑based movement

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Why?

Physics calculations show that you understand:

• How movement works mathematically
• How to simulate real‑world forces
• How to detect and respond to collisions
• How to update game objects each frame
• How to combine math + code to create gameplay

These are essential skills for building any interactive game.

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String Operations

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