math - how to define n-dimensional vector rotation and reflection in haskell? -

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how define vector rotation , reflection in general function work in n dimensions in haskell?

currently have dot product, normalization , projection done stuck on reflection , rotation.

data vector s = vector {len::s,arr::a}  normalize :: vector s → vector s normalize =  tovector . uncurry (zipwith (/))                       . (id&&&(repeat . sqrt . sum . map (^2)))                       . fromvector  dot        :: vector s → vector s → dot v = sum ∘ zipwith (*) (fromvector v) ∘ fromvector  project    :: vector s → vector s → vector s project v = tovector ∘ uncurry (zipwith (*))                      ∘ (fromvector&&&(repeat ∘ (v`dot`)))

i've been searhing days seems using haskell understand mathematics can cause problems when there no clear code (or no code @ all) , tutorials on n-dimensional vectors go past knowledge in mathematics.

regarding mathematical aspects of n-dimensional rotations, might recommend publications of andrew j. hanson of computer science department of university of indiana. in particular:

“rotations n-dimensional computer graphics” https://www.cs.indiana.edu/pub/techreports/tr406.pdf

that paper successor “geometry n-dimensional computer graphics” https://classes.soe.ucsc.edu/cmps161/winter14/papers/pv/ggndgeom.pdf

the mathematics require knowledge of vector arithmetic , linear algebra, if you’re going performing n-dimensional transformations, recommended way math.


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