# Camera space angular distance for up(y), forward(z), and sideways(x) vectors question

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What are the effects of applying a transformation matrix (camera space) to the view (if any) when the angles between the up (y), forward (z), and sideways (x) vectors are not 90 degrees? The camera object implementation that I am using doesn't enforce the up, forward, and sideways vectors to be perpendicular to each other. It only looks for 0 degree cases. Is this something that needs to be enforced? (Linear algebra isn't my strong suite) Thanks.

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With an orthonormal basis, think of your 3D space as being divided up into a grid of cubes. Once this basis is no longer orthogonal, your space becomes divided up by parallelepipeds. It basically skews your space depending on how parallel the basis vectors are, but other than that there are no serious math issues (other than parallel basis vectors which you already check for) and everything should work the same. You will have to go through your code and re-work all the math that might have previously assumed orthogonal/orthonormal basis vectors (i.e. the inverse is no longer just the transpose).

It's hard to verbalize the effect, you'd simply have to try it out and see for yourself.

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Ah! So would that explain the occasional stretching and skew effect I see when the up, forward, and side vectors are not orthonormal?

Thanks again for the response.

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