我找到了满足我的要求的解决方案。解决方案是，首先找到一个B样条曲线，该样条线在最小二乘方意义上近似点，然后将该样条曲线转换为多段贝塞尔曲线。B样条线确实具有以下优点：与贝塞尔曲线相反，它们不会通过控制点，并且提供了一种方法来指定近似曲线的所需“平滑度”。生成此类样条曲线所需的功能在scipy提供python绑定的FITPACK库中实现。让我们假设我读我的数据导入列表
x和
y的话，我可以这样做：
import matplotlib.pyplot as pltimport numpy as npfrom scipy import interpolatetck,u = interpolate.splprep([x,y],s=3)unew = np.arange(0,1.01,0.01)out = interpolate.splev(unew,tck)plt.figure()plt.plot(x,y,out[0],out[1])plt.show()
如果希望曲线更平滑，则可以将
s参数增加到
splprep。如果我希望近似值更接近数据，则可以减小
s参数以减少平滑度。通过以
s编程方式遍历多个参数，我可以找到适合给定要求的良好参数。
不过，问题是如何将结果转换为贝塞尔曲线。Zachary
Pincus在此电子邮件中的答案。我将在此处复制他的解决方案，以完整回答我的问题：
def b_spline_to_bezier_series(tck, per = False): """Convert a parametric b-spline into a sequence of Bezier curves of the same degree. Inputs: tck : (t,c,k) tuple of b-spline knots, coefficients, and degree returned by splprep. per : if tck was created as a periodic spline, per *must* be true, else per *must* be false. Output: A list of Bezier curves of degree k that is equivalent to the input spline. Each Bezier curve is an array of shape (k+1,d) where d is the dimension of the space; thus the curve includes the starting point, the k-1 internal control points, and the endpoint, where each point is of d dimensions. """ from fitpack import insert from numpy import asarray, unique, split, sum t,c,k = tck t = asarray(t) try: c[0][0] except: # I can't figure out a simple way to convert nonparametric splines to # parametric splines. Oh well. raise TypeError("only parametric b-splines are supported.") new_tck = tck if per: # ignore the leading and trailing k knots that exist to enforce periodicity knots_to_consider = unique(t[k:-k]) else: # the first and last k+1 knots are identical in the non-periodic case, so # no need to consider them when increasing the knot multiplicities below knots_to_consider = unique(t[k+1:-k-1]) # For each unique knot, bring it's multiplicity up to the next multiple of k+1 # This removes all continuity constraints between each of the original knots, # creating a set of independent Bezier curves. desired_multiplicity = k+1 for x in knots_to_consider: current_multiplicity = sum(t == x) remainder = current_multiplicity%desired_multiplicity if remainder != 0: # add enough knots to bring the current multiplicity up to the desired multiplicity number_to_insert = desired_multiplicity - remainder new_tck = insert(x, new_tck, number_to_insert, per) tt,cc,kk = new_tck # strip off the last k+1 knots, as they are redundant after knot insertion bezier_points = numpy.transpose(cc)[:-desired_multiplicity] if per: # again, ignore the leading and trailing k knots bezier_points = bezier_points[k:-k] # group the points into the desired bezier curves return split(bezier_points, len(bezier_points) / desired_multiplicity, axis = 0)因此B样条曲线，FITPACK，numpy和scipy挽救了我的一天：）
