does anyone know if regular 2d transformations work with space curves in the same manner. Say can I put in operators in I, J, or K and expect it to behave the same way I'd expect a 2d curve to do?
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r(t) = sin(x)i+cos(y)j+z is a spiral. If I were to manipulate i and j in certain ways, should I expect that spiral to behave as if I were to do y=2sin(x) to y=sinx? I imagine with certain consistances to manipulation, there is to be some uniformity expected, but perhaps that is not the case at all and maybe I should be looking at piecwise variations of space curves and what not to model things in nature. Otherwise I could take expected cases and forms, then transform them to more adequatly fit forms of natural experiences.