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);

**Friction**

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;

Example

**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++){
ctx.beginPath();
ctx.moveTo(centerX,centerX);
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);
ctx.stroke();
ctx.closePath();
}