python 贝塞尔曲线_python – 使用多段三次贝塞尔曲线和距离以及曲率约束逼近数据...
我找到了满足我的criterea的解决方案.解决方案是首先找到近似于最小二乘意义的点的B样条,然后将该样条转换为多段贝塞尔曲线. B样条确实具有以下优点：与贝塞尔曲线相比,它们不会通过控制点以及提供指定近似曲线的期望“平滑度”的方式.生成这样的样条线所需的功能在FITPACK库中实现,scipy为其提供了python绑定.让我假设我将数据读入列表x和y,然后我可以这样做：
import matplotlib.pyplot as plt
import numpy as np
from scipy import interpolate
tck,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()
结果如下所示：
如果我想让曲线更平滑,那么我可以将s参数增加到splprep.如果我希望近似值更接近数据,我可以减小s参数,以减少平滑度.通过以编程方式遍历多个参数,我可以找到符合给定要求的良好参数.
但问题是如何将该结果转换为贝塞尔曲线. Zachary Pincus在this email年的答案.我将在这里复制他的解决方案,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,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)
所以B-Splines,FITPACK,numpy和scipy救了我的一天:)