Sample Problem: Rotating a 2D Character

The Problem
In a top down shooter, there is a scripted in game cutscene where an explosion happens and the player must turn to face the explosion. The turn to face the explosion must be a smoothed transition and since the cutscene can be triggered in a variety of ways, the initial direction of the player can be different between playthroughs. We need to know the angle the player needs to rotate and whether the direction they need to rotate is clockwise or anticlockwise.

The Variables
The current variables we have access to is the initial direction the player is facing (Vector C) , the position of the player (P) and the position of the explosion (E).

The Solution
The first step is to calculate the direction towards the explosion from the player, which can be done by subtracting P from E. This gives us Vector N and since we don't care about the distance between the two positions, we can normalise Vector N.

Since we now have two unit vectors (Vector N and Vector C), we can calculate the angle between them by using the dot product calculation. So the angle is equal to arccos(dotProduct(Vector C, Vector N)). However, this doesn't tell us if the direction we need to rotate is clockwise or anti clockwise.

This can be done with the cross product. However, since both vectors are in 2D space, they need to be converted into 3D vectors. Once the cross product is calculated we can determine the direction of the rotation needed. If the z component of the resultant vector is positive then the rotation is anti clockwise, which means if the z component is negative then the rotation is clockwise.