2D Rotated Rectangle Collision
by Eric Meythaler

The Method

Step 3

The third step in this algorithm is to calculate scalar values that will allow us to identify the maximum and minimum projected vectors for each of the rectangles. While it might seem natural to use the norm (length) of the vectors, this won’t work as coordinates with negative values will return a positive scalar value. The simplest and cheapest solution is to take the dot product of each of the vectors and the axis. This will give us an essentially meaningless scalar value, however, this value will be indicative of the vector’s position on the axis. To use our above example:

Figure 6. The minimum and maximum scalar values

Step 4

Now identify the maximum and minimum scalar values (the ones that we just calculated) for rectangle A and rectangle B. If the minimum scalar value of B is less than or equal to the maximum scalar value of A and/or the maximum scalar value of B is greater than or equal to the minimum scalar value of A then our objects overlap when projected onto this axis.

Figure 7. No Overlap = No Collision

Repeat

Repeat steps 2, 3, and 4 for each of the axes. If all of the axes show an overlap then there is a collision, if even one of the axes shows no overlap then there is no collision.

Optimizations

Contents

	Introduction
	The Method Steps 1 & 2
	The Method Steps 3 & 4
	Optimizations

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