Carlen, M.Gerlach, H.2012-04-122012-04-122012-04-12201210.1142/S0218216511010115https://infoscience.epfl.ch/handle/20.500.14299/79325WOS:000301239100011Enforcing a specific symmetry group on a curve, knotted or not, is not trivial using standard interpolations such as polygons or splines. For a prescribed symmetry group we present a symmetrization process based on a Fourier description of a knot. The presence of symmetry groups implies a characteristic pattern in the Fourier coefficients. The relations between the coefficients are shown for five ideal knot shapes with their proposed symmetry groups.Ideal knotsFourier knotssymmetry of curvesFourier coefficient patternGlobal CurvatureRopelengthShapestext::journal::journal article::research article