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cyates

Orthonormality

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A non-orthonormal basis for the 3D space of a game? I doubt ever. Did you have any ideas for a non-orthonormal game yourself perhaps? If you mean non-orthonormal transformations: as soon as rotation is used, so basically still hardly ever.

Greetz,

Illco

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Yeah, I am talking about the basis vectors, not transformations. I didn't think it would ever happen. I am just learning about Euclidean space, and I was thinking of how it could be done, but then realized why is a better question. I wouldn't think there would ever be a need to. Would take away the usefullness of dot product for one thing, which would make everything so much more difficult.

Stupid question, forget I asked. :)

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It is not a stupid question at all. However, concluding that the dot product is rendered virtually useless is a gross mistake, I'm afraid. Just because the basis vectors of your Euclidean space (x,y,z) are orthonormal does not mean that any two vectors within that space are orthonormal! So for individual vectors within the space the dot product is very useful: it computes the angle between two vectors and is used a lot (I mean: A LOT).

Oh I see now you said: it would take away only one use of the dot product. Yeah, it takes away the use 'testing whether the basis vectors are orthonormal'. You could, but you would always find that they are.

Greetz,

Illco

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