Vector addition, vector norms, and inner product seem to be most easily expressed in Cartesian coordinates. Are there certain operations for which other coordinate systems are more efficient?

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What are the advantages to using some other coordinate systems other than the Cartesian (for example polar coordinates) for computer graphics applications?

Vector addition, vector norms, and inner product seem to be most easily expressed in Cartesian coordinates. Are there certain operations for which other coordinate systems are more efficient?

What are the advantages to using some other coordinate systems other than the Cartesian (for example polar coordinates) for computer graphics applications?