Game Dev Movement cheatsheet with examples

aka My Cheat Sheet of Helpful Code

I created a blog post way back title Game Snippets I Always Forget. I put it up basically as a dumping ground for random game related bits of code I found myself looking up over.. and over. A few of them are a bit cryptic but that’s mostly due to me quickly logging in and pasting before Id forget. While now I have (most) memorized I figured I would revisit the article and add some examples that may help others out. The following are examples dealing with movement, angles, and directions.

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Game Related Snippets I always Forget

When I sit down to prototype something new I always find myself looking up the same snippets to do the same types of things. I figured I might as well record them somewhere so I know an easy place to look when I do forget. All the samples will be in Javascript and should be able to be easily converted to any other language.

Distance Formula

Obviously a pretty important one, used to tell the distance between 2 objects. Can be used for simple radius collisions as well.

var distance = Math.sqrt((x2 - x1) *(x2-x1) + (y2 - y1) * (y2-y1));

Move toward an object (Without rotation) with easing

x += (targetX-x)/speed;
y += (targetY-y)/speed;

Angle Based Movement

I always see myself needing this one, whether its for an Asteroids clone, or a follow the leader type game.

velX = Math.cos((angle * Math.PI / 180) * thrust);
velY = Math.sin((angle * Math.PI / 180) * thrust);


How do I make something slow down if no force is applied?

velX *= .98; //Any val under 1 is suitable for your needs
velY *= .98

2D Matrix

This is a pretty simple one I know.. but I always seem to forget it. This is how to store a 2d matrix in an array. And how to find a value you need.

// 2d matrix[y * width + x]
var arr = [],
     width = 10;

for(x=0; x<width; x++){
    for(y=0; y<width; y++){
        arr[y * 10 + x] = x + y; //Or whatever value you need to assign

//Retrieve a value from x:5, y:2
var val = arr[2 * 10 + 5];

//get the x and y from a 1d array
var index = 12,
    x = index % width, // 2
    y = Math.floor(index / width); // 1

Move towards and object at a constant speed

    var tx = targetX - x,
        ty = targetY - y,
        dist = Math.sqrt(tx*tx+ty*ty),
        rad = Math.atan2(ty,tx),
        angle = rad/Math.PI * 180;;

        velX = (tx/dist)*thrust;
        velY = (ty/dist)*thrust;


Project a point in front of an object

    x + length * Math.cos(angle*Math.PI / 180);
    y + length * Math.sin(angle*Math.PI / 180);

Get the angle between objects

    var x = targetX - this.x,
        y = targetY - this.y;

     return Math.atan2(x,-y);

Plot points around a circle

    var rad = 500,
        total = 50,
        centerX = 250,
        centerY = 250;

    for(var i = 0; i < total; i++){
        var x = centerX + rad * Math.cos(2 * Math.PI * i / total),
            y = centerY + rad * Math.sin(2 * Math.PI * i / total);   

        ctx.lineTo(x, y);