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I'm toying around with an algorithm to determine placement of 3D objects into a larger 3D space. I immediately thought of using matrices.

It's been some years since my Linear Algebra courses. I was hoping someone could provide some references or even examples to help get me started.

Bonus points for:

  • Collision detection
  • Object rotation
  • Alternatives to matrices
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The question is too broad to provide specific examples. If you want a reference, I highly recommend Real-Time Rendering. Chapters that would interest you:

  • Chapter 4, Transforms: Covers matrix transformations and operations, including object rotation. It also covers quaternions which are the usual alternatives to matrices. One of the advantages of quaternions is that they don't suffer from gimbal lock.
  • Chapter 16, Intersection Test Methods: Covers numerous algorithms for detecting collisions between various shapes.
  • Chapter 17, Collision Detection: Covers advanced collision detection algorithms like BSP trees.

The book provides a summary of the linear algebra needed in the appendix if you need a review. The other chapters contain a wealth of information on computer graphics. If you are into this field, you can't go wrong with this book.

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