分段多项式拟合并保证断点处连续

Question

有一条曲线，需要用多项式拟合
但是用一个多项式拟合不好
分段多项式拟合效果挺好，但是不能够保证在断点处连续并导数和曲率一致

Answer 1

断点处提前几个索引试试，

import matplotlib.pyplot as plt
import numpy as np

list1 = [176.55823623919866, 175.82629227599108, 174.6682288122686, 174.1676016833001, 173.18851142144007, 171.50626507572986, 171.30220775004557, 171.36967661238003, 171.28415302420305, 171.28824729828153, 171.57034121168718, 172.33094464950744, 173.23238914855358, 173.55613816498442, 174.3453315452684, 175.8405706931801, 176.55279402689868, 176.61370282973544, 176.81582616485196, 177.02915557477107, 176.8786448208988, 176.81439985226544, 176.71451411266156, 176.66586750119254, 176.30753368473069, 176.19523098955372, 176.07119928600355, 175.72179761793777, 175.43552045631185, 175.06619996031966, 174.53081306978117, 174.18429472985528, 173.8891857051452, 173.64330751640563, 173.1717933351755, 172.75272880991568, 172.73580347692774, 172.71686474342098, 172.69409149798975, 173.08779491052138, 173.34364100632905, 173.59571062466185, 174.12459693708425, 175.3580464862954, 175.45959761884262, 175.96958585972754, 176.25514442769904, 176.64561729822563, 176.9716561653289, 176.91158660669385, 176.8209116100747, 176.76023627503446, 176.75061872853308, 176.358077514346, 176.105301140804, 175.75253205020002, 175.32592030580872, 174.4561198543027, 174.16318576040058, 173.6955522308555, 173.36361683009068, 173.27786291152492, 172.8430468018013, 172.44916449098338, 172.37925152892035, 172.37302861988064, 172.539243589413, 172.6076027962434, 173.30903687629709, 173.6726484459664, 174.38075179088534, 174.35096455596033, 175.88411630813638, 176.37365460037168, 176.5190359013566, 176.7555013354064, 176.8843429579835, 176.9999143606833, 176.9612688170496, 176.96293657390825, 176.78778110739344, 176.45215828729877, 176.06391950355714, 175.456133611344, 175.10238577582405, 174.13589426350123, 173.71856168991667, 172.75506195819366, 172.52619234873043, 172.20232568127273, 172.08540070952418, 172.10597477088277, 172.08271329913669, 172.6095880484391, 172.94377522421826, 173.6300070707046, 175.6046559431482, 175.81133042253938, 176.23806059573772, 176.4665155497212, 176.68100141799786, 177.03103128679953, 176.98421637958953, 177.00073049644882, 177.1587220488691, 177.03429777263233, 176.71990304220589, 176.5086407982305, 176.1615847526818, 175.8794207695718, 175.0735855383626, 174.36140581932358, 173.8720499315276, 173.62378250358805, 173.29302157102185, 173.0649065230465, 172.4622044831749, 172.5280950017399, 172.5286747359581, 172.5466194931676, 173.36197557152252, 174.13684369851603, 174.10727291964182, 175.10324893539504, 175.44506588924463, 175.9011658131806, 176.08419194245582, 176.43925933374413, 176.63149256351699, 176.73270643092494, 176.7927115430335, 176.78706440505482, 176.77445250937208, 176.8142036430795, 176.50057944916426, 176.12232222126266, 176.08393647672386, 175.37657408094051, 175.41663659071116, 174.62594785220216, 174.04457169863505, 173.60811211235833, 173.36957821789835, 172.8836504665457, 172.60100177086554, 172.63361517776903, 172.81888582450216, 172.99742334589592, 173.35580779710824, 174.00521684611465, 174.30966818533145, 175.28536562770532, 175.66609314531235, 175.90367459742978, 176.4527738516087, 176.90924497036588, 176.9817389651164, 177.0012641104389, 177.16628613206575, 177.11344509698452, 177.04358001411137, 176.89912996902325, 176.5341418640653, 176.2978147271377, 175.1242588850196, 175.67265226808763, 174.62241233471624, 174.04836019341488, 172.89651207557196, 172.56515161301024, 172.48394284336726, 172.3725575380836, 172.3607151337593, 172.6939537797305, 173.23320994088365, 173.3725417745558, 173.73128516054635, 174.4379216822258, 175.53190635723456, 176.06270831282416, 176.39342939266135, 176.68157793103921, 177.0099858820125, 177.25187668065863, 177.36100632781813, 177.55343593476798, 177.47722670635673, 177.38131049205398, 177.0301008802558, 176.57932362376525, 176.26150568641026, 175.93049640705155, 174.05658379742297, 173.8494293764074, 173.29399494753386, 173.06571316986881, 172.54102581069657, 172.37061972099286, 172.47303701367443, 172.3893822185587, 172.7330071403166, 172.97039275988143, 173.5848272047908, 174.59132738492374, 174.428044597701, 175.2273312893782, 175.87873553926326, 176.30461280490263, 176.71866140171576, 177.01993002417984, 177.0844410062251, 177.12444366484917, 177.3012076876708, 177.32753216669667, 177.47365825023536, 177.34445972416944, 176.6568052203644, 176.34618723106024, 175.95155021561112, 175.5433400026391, 174.14982598610834, 172.70018498277074, 172.3636772790286, 171.35804046813456, 170.95783150186915, 170.79158718440846, 170.89054877009738, 171.18440150525686, 171.50733374367994, 172.5164540673539, 173.2980006609825, 175.34746104889584, 176.3750613338565, 176.87531317442603]

def QXNH(list):
    lists1 = [[],[]]
    lists2 = [[],[]]
    lists1[0] = np.array(list[0:101])
    lists1[1] = np.array(list[98:234])
    lists2[0] = np.arange(1, len(list[0:101])+1, 1)
    lists2[1] = np.arange(99, 235 , 1)
    z = [[],[]]
    p = [[],[]]
    for i in range(2):
        x = lists2[i]
        y = lists1[i]
        z[i] = np.polyfit(x, y, 76)  # 用高次多项式拟合
        p[i] = np.poly1d(z[i])
        print(p[i])  # 打印拟合多项式
        yvals = p[i](x)  # 也可以使用yvals=np.polyval(z1,x)
        plot1 = plt.plot(x, y, '*', label='original values')
        plot2 = plt.plot(x, yvals, 'r', label='polyfit values')
    plt.xlabel('x axis')
    plt.ylabel('y axis')
    plt.legend(loc=4)  # 指定legend的位置
    plt.title('polyfitting')
    plt.show()
    plt.savefig('p1.png')

QXNH(list1)