We provide an efficient algorithm to detect whether two given trigonometric curves, i.e. two parametrized curves whose components are truncated Fourier series, in any dimension, are affinely equivalent, i.e. whether there exists an affine mapping transforming one of the curves onto the other. If the coefficients of the parametrizations are known exactly (the exact case), the algorithm boils down to univariate gcd computation, so it is efficient and fast. If the coefficients of the parametrizations are known with finite precision, e.g. floating point numbers (the approximate case), the univariate gcd computation is replaced by the computation of approximate gcds. Our experiments show that the method works well, even for high degrees.

我们提供了一种有效的算法来检测两条给定的三角曲线（即两条参数化的曲线，其分量在任何维度上均被截短的傅里叶级数）是否仿射等效，即是否存在将一条曲线变换到另一条曲线的仿射映射。如果参数化的系数准确（确切的情况）已知，则该算法归结为单变量gcd计算，因此它高效且快速。如果参数化系数以有限的精度已知，例如浮点数（近似情况），则单变量gcd计算将替换为近似gcds的计算。我们的实验表明，该方法即使在高度情况下也能很好地工作。