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I've heard that geometric algebra is really useful, but I'd be curious to hear of concrete examples. For common computer graphics it feels like the standard vector + vector math (dot product, cross product, etc) and matricies are more or less sufficient. What does geometric algebra help you do?

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I'm not an expert, but my understanding is: matrix rotations in 3d can lead to gimbal lock. That's why most 3d engines use quaternions instead. Geometric algebra offers a simpler alternative to quaternions.

Euler angles are what that leads to gimbal lock. Constructing a rotation matrix from them inherits this issue.

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