平滑2D曲线

Question

我正在尝试从3D网格的提取边界中获得一条曲线。我执行以下操作以提取边界：

1-将3d网格划分为多个区域。

2-提取每个区域的边界

3-将3D边界转换为X-Y平面

4-分割边界

下图显示了结果边界

坐标点示例

X            Y
0.24628 1.49185
0.26724 1.49886
0.26145 1.49709
1.09528 1.21106
0.24628 1.49185
0.26724 1.49886
0.26854 1.49843
0.26145 1.49709
0.27626 1.50001
0.28379 1.50117
0.28052 1.49995
0.29360 1.50299
0.30082 1.50435
0.31017 1.50628
0.31869 1.50840
0.31892 1.50806
0.31310 1.50721
0.32771 1.50982
0.32776 1.50974
0.32273 1.50908
0.33226 1.51077
0.33587 1.51100
0.33716 1.51156
0.35389 1.51406
0.34641 1.51295
0.35603 1.51355
0.36336 1.51487
0.35952 1.51450
0.37433 1.51553
0.37424 1.51531
0.36849 1.51516
0.37762 1.51612
0.39076 1.51885
0.38323 1.51721
0.39896 1.52063
0.39360 1.51947
0.40832 1.52167
0.39940 1.52079
0.40585 1.52160
0.41145 1.52172
0.41705 1.52184
0.44010 1.51656
0.43655 1.51850
0.43308 1.52038
0.42088 1.52166
0.42924 1.52165
0.45349 1.51545
0.44314 1.52105
0.44609 1.51949
0.44128 1.52194
0.44346 1.51851
0.43612 1.52077
0.43352 1.52161
0.45740 1.51952
0.45362 1.52152
0.45902 1.51864
0.45718 1.51776
0.44799 1.52223
0.45641 1.52190
0.45276 1.52210
0.46447 1.52093
0.46262 1.52249
0.45878 1.52173
0.47343 1.52308
0.46783 1.52254
0.48399 1.52349
0.51303 1.50714
0.51572 1.50538
0.52216 1.50146
0.47684 1.52328
0.51830 1.50370
0.56776 1.48180
0.49813 1.52070
0.50241 1.51843
0.50621 1.51529
0.50965 1.51151
0.49087 1.52312
0.49571 1.52185
0.51155 1.51048
0.51743 1.50665
0.51595 1.50950
0.52167 1.50431
0.52152 1.50752
0.60742 1.46625
0.60089 1.46988
0.59427 1.47344
0.58765 1.47702
0.52324 1.50821
0.53034 1.50552
0.53514 1.50419
0.54106 1.49936
0.54553 1.49744
0.55001 1.49553
0.55442 1.49351
0.57071 1.48188
0.57622 1.48183
0.58207 1.47688
0.55988 1.48783
0.56496 1.48702
0.55865 1.49114
0.56980 1.48577
0.65251 1.44821
0.64822 1.45052
0.63995 1.45493
0.62263 1.46408
0.63582 1.45711
0.63266 1.45877
0.62757 1.46143
0.66556 1.44139
0.65897 1.44477
0.64444 1.44978
0.65149 1.44698
0.61362 1.46728
0.62044 1.46407
0.60674 1.47039
0.67856 1.44030
0.67426 1.44258
1.08037 1.21854
1.08367 1.21654
1.08742 1.21428
1.09026 1.21255
0.64367 1.45327
0.67167 1.44238
0.80349 1.37805
0.83693 1.35981
0.70140 1.43402
0.69392 1.43810
0.69163 1.43933
1.07434 1.22838
0.83009 1.36350
0.68492 1.44079
1.07049 1.22964
1.07401 1.22600
1.07766 1.22044
1.08714 1.21527
1.09326 1.21187
1.09528 1.21106
0.75771 1.40927
0.75171 1.41250
0.82535 1.37218
0.81628 1.37709
0.82059 1.37477
0.78098 1.39647
0.79159 1.39056
0.78660 1.39332
0.76986 1.40262
0.76715 1.40411
0.76388 1.40590
0.75928 1.40841
0.75789 1.40840
0.74587 1.41221
0.73972 1.41662
0.84214 1.35978
0.83556 1.36343
0.84109 1.36350
0.82945 1.36790
0.82338 1.37248
0.81674 1.37601
0.80968 1.37878
0.78124 1.39398
0.77590 1.39922
0.78676 1.38842
0.79204 1.38798
0.79777 1.38182
0.80297 1.38219
0.70403 1.43426
0.70939 1.43395
0.69775 1.43844
0.70302 1.43797
0.72189 1.42546
0.72809 1.42115
0.73366 1.42121
0.71565 1.42973
1.02362 1.26324
1.02790 1.25927
1.03297 1.25290
1.03732 1.25075
1.03167 1.25609
1.03570 1.25336
1.07091 1.23630
1.07433 1.23212
1.04194 1.24911
1.04686 1.24801
1.05225 1.24701
0.89862 1.33866
0.88048 1.34835
0.87569 1.35094
0.88905 1.34370
0.88686 1.34488
0.88223 1.34740
0.87377 1.35197
0.99367 1.28666
1.00647 1.27936
0.74504 1.41621
0.88074 1.34740
0.87411 1.35094
0.88826 1.33991
0.88732 1.34374
0.84792 1.36006
0.85374 1.36074
0.86725 1.35408
0.86039 1.35723
1.01659 1.26882
1.02050 1.26590
1.01152 1.27520
1.01537 1.27215
1.05677 1.24591
1.06151 1.24448
1.06584 1.24230
1.06970 1.23928
0.92078 1.33298
0.91777 1.33456
0.91618 1.33539
0.91196 1.33758
0.90920 1.33893
0.97498 1.30304
0.91081 1.33406
0.90963 1.33746
0.90193 1.33908
0.89438 1.34089
0.89976 1.34070
0.99758 1.28554
1.00174 1.28305
0.97934 1.29917
0.99152 1.29012
0.98521 1.29424
0.99577 1.28780
0.93860 1.32947
0.95180 1.32233
0.94649 1.32523
0.95703 1.31941
0.95579 1.32010
0.96171 1.31675
0.94571 1.32566
0.94042 1.32850
0.93912 1.32861
0.93204 1.33136
0.92474 1.33369
0.91717 1.33555
0.92264 1.33544
0.91508 1.33731
0.96647 1.31145
0.97034 1.30845
0.97396 1.30499
0.95091 1.32440
0.95694 1.31976
0.96123 1.31751
0.95508 1.32193

Answer 1

尝试此代码并将输入与您的输入进行比较。

% Generate Noisy coordinates of a circle
h = viscircles([0,0],100);
x_noisy = h.Children(1).XData + randn(1,182);
y_noisy = h.Children(1).YData + randn(1,182);

% Smooth the coordinates
x_smooth = smoothdata(x_noisy,'gaussian',20);
y_smooth = smoothdata(y_noisy,'gaussian',20);

% Display the results 
plot(x_noisy, y_noisy)
hold on
plot(x_smooth, y_smooth)
hold off
axis image
legend('Noisy', 'Smoothed')

Answer 2

这是我在评论中表示的一个例子。想法是使用极坐标对点进行排序，独立平滑坐标并转换回笛卡尔坐标。如果您的曲线中有回圈，这将无法正常工作！

% Transform in polar coordinates
[theta , rho] = cart2pol(x,y);

% Sort data by angle
data = sortrows([theta , rho]);
theta = data(:,1);
rho = data(:,2);

% Smooth coordinates
theta = smooth(theta);
rho = smooth(rho , 10); % More aggressive smoothing for rho. You might
                        % have to adapt the type of smoothing to the 
                        % actual data of course.

% Transform back in cartesian coordinates
[X , Y] = pol2cart(theta , rho);

% Plot original and smooth result
plot(x,y,'b.')
hold on;
plot(X,Y , 'r-')