An algorithm to make one object follow another on a 2D grid

Question

I am using Greenfoot, but this can apply to pretty much any 2D engine.

So my question is a basic one that I somehow couldn't find an answer to already. Basically, if I have an enemy and the player, how can I make the enemy follow them? The player can move in all 4 directions, and the enemy can move in any direction, whichever one is faster. It would be done using a method that accepts an integer for speed, and an in-game object to move towards (an Actor in Greenfoot). It shouldn't simply teleport there but move closer by however much the value for speed is. And this would have to be done without rotating the image of the enemy.

This is in Java but if the answer you provide is in pseudo-code or a similar language (such as c++ or c#) I can still use it.

Answer 1

Here is a pretty simple and general method that I think satisfies the conditions.

Let's call the player position (x_p, y_p) and the enemy position (x_e, y_e).

Next, we'll calculate the direction that would move the enemy onto the player. This is (x_e - x_p, y_e - y_p). We can call this (x_d, y_d) where the d is for distance.

The next thing we want to do is to normalise the distance. This will make the length of the distance vector exactly equal to 1. This will also give non-integer values which may or may not be suitable for your grid.

You want to use the Pythagoras theorem to find the length of the vector, and divide by the length. So let's call the normal vector (x_n, y_n) which is (x_d / D, y_d / D) where D = sqrt(x_d * x_d + y_d * y_d).

Now what we have is a direction from the enemy to the player, and the length of this direction is exactly 1 unit whichever way it is pointing. We can easily adjust a speed factor here by updating the enemy with (x_n * speed, y_n * speed). This will move the enemy in exactly speed units toward the player.