How to interpolate a set of points in 3D using Matlab (or Excel)
I have 19 points (x, y, z values) which can be joined up to produce a curve (very angular).
Is there a way to output 100 points (x, y, z values) which include the original 17 points after smoothing the data?
My aim is to simply make the line produced, look less angular. I don't want to depart from the original data points. I don't simply want to fit the curve, I also want a set of x, y, z values that make up as even a spread of points as possible.
If it helps to have my data, here it is...
---X--- ---Y--- ---Z---
-0.068 80.022 38.332
19.096 170.231 36.322
79.634 240.105 37.22
99.516 248.922 38.474
129.064 254.685 38.027
169.675 234.899 37.043
199.516 219.014 37.425
249.516 186.386 38.009
299.339 174.74 39.54
329.215 190.977 39.46
379.057 266.463 37.359
399.664 313.317 37.647
449.917 389.269 38.097
499.452 390.591 39.341
549.449 410.569 37.419
599.015 430.785 39.443
619.293 435.193 38.714
[UPDATE]: Here is all of my data (Eastings, Northings and Ground Elevations). I have manipulated it so that I can use it to plot a diagram and to collect the data into a long list of X, Y, Z points.
clear
XYZ=[-0.981 228.186 41.706 19.558 318.061 41.859 39.295 354.756 40.47 58.865 376.792 39.303 79.826 388.557 41.881 99.07 396.376 40.793 128.889 402.102 40.302 168.454 383.616 41.969 199.438 367.254 42.87 248.22 334.199 42.459 299.662 322.407 42.887 329.13 338.72 41.936 379.011 414.38 42.538 398.925 461.024 40.579 448.964 536.678 41.016 498.674 538.02 42.433 549.046 558.505 42.987 599.089 578.825 41.388 619.513 583.596 41.116
-0.459 168.609 39.534 18.72 258.139 37.039 39.19 294.992 36.651 59.44 316.886 38.745 78.96 328.97 37.646 98.491 336.517 37.363 128.616 342.212 39.449 169.277 323.234 38.724 199.75 307.82 39.494 248.486 273.63 37.803 298.848 262.947 38.076 328.525 279.219 38.518 379.188 354.13 37.9 399.106 401.214 39.985 449.016 476.406 37.01 498.736 478.979 38.417 548.892 498.121 38.377 598.835 518.866 39.27 619.431 522.964 38.652
-0.315 148.334 39.125 19.282 238.135 38.831 38.929 275.114 38.766 59.107 296.971 36.86 79.658 308.222 37.573 98.877 317.103 39.28 129.343 322.55 39.346 168.458 302.85 37.183 199.447 287.361 39.494 248.515 254.097 37.082 299.258 242.268 38.203 328.867 258.877 38.243 378.966 334.294 37.886 398.553 380.9 39.661 449.357 457.216 37.151 499.188 458.425 39.993 548.447 478.633 39.044 599.289 498.829 38.229 619.362 502.861 38.28
-0.77 128.802 40.307 18.84 218.299 37.872 39.619 255.281 38.875 59.158 277.506 38.86 79.475 289.08 38.727 98.903 297.194 39.254 128.637 303.058 40.618 169.416 283.797 39.046 199.218 268.002 39.514 248.851 234.409 38.522 299.708 222.995 38.598 328.737 239.682 39.346 379.221 315.113 39.674 398.469 361.458 40.085 449.262 437.299 38.544 499.091 438.992 39.367 548.492 458.732 40.047 599.105 479.647 39.072 619.42 483.704 40.14
-0.582 126.998 42.05 19.007 217.113 42.128 39.658 252.392 42.117 58.79 275.466 42.097 78.995 286.233 42.1 98.972 295.658 42.09 129.273 301.556 42.12 169.316 281.063 42.049 199.634 265.439 42.085 248.752 232.621 42.08 299.1 220.782 42.143 328.877 237.643 42.145 379.427 312.91 42.095 398.721 360 42.106 449.135 435.791 42.183 499.252 437.276 42.118 548.493 457.293 42.113 599.462 477.004 42.119 619.612 482.107 42.129
-0.346 123.16 41.94 19.179 213.589 41.992 39.444 250.331 41.987 59.072 271.995 42.065 79.307 283.649 42.022 99.006 292.466 42.056 128.633 297.74 41.918 169.34 278.56 42.011 199.026 262.206 41.932 248.941 229.711 42.027 299.509 217.911 42.066 328.821 234.132 41.946 379.845 310.058 42.021 398.534 356.907 42.014 448.593 432.35 42.003 499.106 433.69 41.987 548.428 454.372 41.974 599.328 474.769 42.067 618.992 478.889 41.937
0.732 122.04 40.776 19.669 212.233 39.128 40.645 248.583 39.894 60.286 271.062 39.729 80.595 282.456 40.269 99.954 291.342 40.844 130.501 297.006 40.859 169.595 277.813 40.096 200.624 261.129 40.458 250.007 229.335 40.355 299.901 217.206 40.553 329.726 233.434 40.522 380.156 308.505 40.544 399.69 355.738 40.892 449.73 432.099 40.119 500.35 433.178 40.041 549.542 452.726 40.361 599.9 472.971 40.571 620.914 478.13 40.873
-1.344 121.36 38.071 17.996 211.825 37.099 39.218 248.06 37.203 58.015 269.734 36.847 78.048 281.708 37.956 98.076 290.618 38.462 128.584 296.649 38.488 169.011 276.388 37.434 199.064 260.174 38.327 247.515 227.828 38.149 298.297 216.494 38 328.879 232.531 38.172 378.679 307.684 37.624 398.234 355.057 38.044 448.11 430.336 37.532 498.174 432.199 37.789 547.705 451.963 37.549 599.229 472.621 38.385 618.971 476.745 38.149
-0.025 120.11 34.797 20.25 211.177 34.062 39.791 247.155 34.197 60.031 268.877 34.045 79.895 281.005 34.402 98.319 289.127 35.76 128.885 295.177 35.434 169.826 275.718 34.468 199.41 259.111 34.855 249.34 227.082 34.555 299.862 215.112 35.461 329.614 231.681 35.356 380.185 307.267 35.34 399.585 353.472 35.311 449.785 430.221 34.802 499.27 431.338 34.628 548.82 450.964 35.164 599.091 471.717 35.328 620.312 475.724 35.55
-0.22 119.594 33.729 19.409 209.329 32.717 38.952 245.437 33.72 59.524 268.074 33.425 79.777 279.98 33.954 98.221 288.432 34.334 129.045 294.204 34.573 169.076 274.494 33.237 198.901 258.488 33.931 248.337 225.817 33.355 298.963 214.171 34.017 329.011 230.691 34.245 379.806 305.861 34.482 399.2 353.067 34.781 448.965 429.152 33.325 498.859 429.646 34.004 549.241 449.899 33.331 599.566 469.81 33.805 619.033 475.192 34.044
-0.225 118.011 32.993 18.767 208.144 32.997 38.816 244.302 32.999 59.56 266.523 33 79.533 278.085 32.99 98.422 286.837 32.993 129.264 292.591 32.991 168.522 272.813 33 198.936 256.937 32.993 248.787 224.365 33 299.14 212.644 32.992 328.757 228.921 32.993 379.797 304.381 32.998 399.188 351.229 32.994 449.075 427.265 32.999 498.928 428.532 32.998 548.59 448.554 32.993 599.185 468.737 32.995 619.838 473.133 32.994
0.621 116.948 29.909 19.99 207.148 30.037 39.828 243.381 30.798 60.108 265.55 30.687 80.123 277.034 30.203 99.647 285.902 30.446 129.735 291.642 30.013 169.481 271.894 30.259 200.112 255.971 30.639 250.02 223.322 29.845 299.877 211.67 30.08 329.708 227.976 30.485 380.238 303.376 30.104 399.691 350.269 30.584 450.269 426.249 30.768 499.599 427.533 30.542 549.958 447.544 30.502 599.951 467.709 30.06 620.941 472.167 30.208
-0.764 116.091 29.656 19.114 206.308 29.417 39.503 242.409 29.762 58.815 264.591 29.656 79.524 276.201 29.433 98.229 284.95 30.045 128.936 290.766 29.586 169.234 270.961 29.458 199.626 255.101 29.597 248.778 222.44 30.026 299.703 210.767 29.356 328.629 227.031 29.329 379.544 302.545 29.563 398.596 349.349 30.033 448.827 425.363 29.419 499.04 426.678 29.556 548.678 446.571 29.945 599.294 466.821 29.69 619.696 471.208 29.793
-1.067 114.032 29.719 19.44 204.246 29.119 39.558 240.395 29.361 58.93 262.605 29.134 79.298 274.13 29.365 99.142 283.016 29.311 128.92 288.727 30.017 168.483 268.939 29.621 199.399 253.114 29.763 248.163 220.412 29.536 299.041 208.813 30.081 328.428 224.993 29.988 379.119 300.524 29.264 398.432 347.396 29.329 449.335 423.34 29.239 498.819 424.664 29.507 548.946 444.58 29.779 599.548 464.871 29.66 619.106 469.274 29.565
-0.442 112.052 29.67 19.416 202.325 30.321 39.044 238.412 30.206 58.7 260.631 29.445 79.109 272.111 29.516 98.874 280.979 29.808 129.073 286.749 30.109 168.462 266.997 30.066 199.294 251.089 29.504 248.892 218.387 29.935 299.385 206.805 29.805 328.344 222.983 30.333 379.741 298.521 29.6 399.272 345.318 29.406 449.344 421.312 29.856 498.616 422.67 29.603 548.988 442.654 29.853 599.455 462.863 29.855 619.505 467.26 30.163
0.279 111.075 31.219 19.664 201.272 31.227 40.033 237.484 31.24 60.51 259.593 31.227 80.873 271.165 31.24 99.424 279.93 31.246 129.935 285.73 31.221 169.713 265.97 31.209 199.969 250.021 31.234 250.08 217.416 31.244 300.368 205.831 31.233 329.826 222.066 31.207 380.292 297.464 31.249 399.692 344.335 31.208 450.288 420.325 31.235 500.029 421.615 31.25 549.758 441.59 31.244 599.982 461.843 31.223 620.805 466.263 31.248
-0.196 110.635 32.995 19.493 200.514 32.992 38.713 237.169 32.999 59.287 259.517 32.999 79.892 271.021 32.993 98.751 279.466 32.996 128.785 285.668 32.999 169.139 265.219 32.996 199.347 249.546 32.998 248.81 216.85 32.995 298.841 205.432 32.999 328.21 221.91 32.995 379.636 297.352 32.999 398.784 343.398 32.991 449.428 419.375 32.997 499.043 421.018 32.991 548.969 441.046 32.994 599.524 460.831 32.994 619.193 466.092 32.995
-0.132 109.594 34.42 20.125 199.858 32.732 39.776 236.054 33.054 60.129 257.645 33.431 80.851 269.508 34.218 99.269 278.227 33.904 130 283.99 34.048 169.914 264.152 33.073 200.719 248.544 34.04 249.707 215.652 33.406 300.225 203.878 34.126 329.592 220.167 33.769 380.754 296.156 34.421 399.397 342.405 33.861 450.468 418.693 33.948 499.96 420.455 33.265 549.437 440.39 33.953 599.864 460.69 34.351 620.874 465.104 34.09
-0.343 108.513 34.78 19.3 198.316 33.888 38.786 234.577 34.484 59.053 257.223 33.853 79.285 268.324 35.043 98.398 277.644 34.937 128.83 283.213 35.301 169.088 263.069 35.014 198.878 247.767 35.609 248.615 214.391 35.807 299.485 202.82 35.357 328.648 219.254 35.022 379.743 294.584 34.429 398.637 342.162 35.193 449.496 418.209 35.108 499.324 419.115 34.295 548.907 439.475 34.687 598.883 458.884 34.303 619.369 463.964 34.851
0.423 107.454 36.297 19.785 197.317 35.425 40.375 233.902 35.959 60.09 255.777 35.783 80.63 268.02 36.853 99.567 276.422 36.795 130.287 282.576 36.835 170.145 262.756 36.119 200.352 246.912 36.895 249.614 213.916 36.907 299.812 202.349 36.713 329.403 218.774 36.711 380.395 294.154 36.327 399.866 341.226 36.943 449.724 416.448 36.271 500.452 418.301 36.213 549.877 437.585 36.038 600.532 458.707 36.157 620.02 462.977 36.445
-0.088 106.391 40.184 19.793 197.12 39.075 40.586 232.691 39.109 59.812 255.447 39.332 79.952 266.173 39.494 99.221 275.594 40.444 129.757 281.51 40.035 170.036 261.36 39.122 199.869 245.174 40.197 250.045 212.441 39.611 300.362 201.267 39.588 329.451 217.04 40.17 380.741 292.932 40.168 399.997 339.678 40.689 450.209 415.475 39.322 499.581 417.128 39.793 549.785 437.368 39.621 599.735 457.43 40.383 620.764 461.816 40.233
-0.578 103.781 42.003 18.861 194.176 42.045 39.371 229.481 42.045 58.832 252.026 42.095 79.04 263.57 42.06 98.512 271.997 42.08 129.028 278.247 42.052 169.367 258.679 42.04 199.296 242.657 42.005 248.473 210.079 42.02 299.209 198.553 42.079 328.911 214.091 42.047 378.934 290.029 42.014 398.408 337.125 42.037 448.973 412.977 42.099 499.168 413.779 42.082 548.53 433.779 42.039 599.266 454.462 42.098 619.302 458.232 42.098
0.108 101.868 41.937 20.502 191.246 41.969 39.879 228.172 41.928 60.084 250.124 41.99 80.344 261.778 41.968 99.165 270.769 41.961 129.622 276.502 41.91 170.288 256.048 41.977 200.321 240.195 41.922 249.569 208.29 41.938 300.539 195.873 41.995 329.966 212.825 41.937 380.491 288.359 41.984 399.837 334.911 41.998 450.207 410.929 41.96 500.101 411.893 41.925 549.602 431.696 41.936 599.93 452.41 41.976 620.817 456.93 41.909
-0.156 100.022 40.698 19.591 190.231 39.108 39.68 226.389 39.847 59.626 248.557 39.725 79.928 260.105 40.23 99.158 268.922 40.825 129.536 274.685 40.797 169.45 254.899 40.03 199.86 239.014 40.391 249.085 206.386 40.338 299.722 194.74 40.504 329.176 210.977 40.424 379.918 286.463 40.51 399.298 333.317 40.82 449.58 409.269 40.059 499.539 410.591 40.02 549.289 430.569 40.294 599.64 450.785 40.472 619.954 455.193 40.809
-0.068 80.022 38.332 19.096 170.231 36.322 NaN NaN NaN NaN NaN NaN 79.634 240.105 37.22 99.516 248.922 38.474 129.064 254.685 38.027 169.675 234.899 37.043 199.516 219.014 37.425 249.516 186.386 38.009 299.339 174.74 39.54 329.215 190.977 39.46 379.057 266.463 37.359 399.664 313.317 37.647 449.917 389.269 38.097 499.452 390.591 39.341 549.449 410.569 37.419 599.015 430.785 39.443 619.293 435.193 38.714
-0.879 60.235 38.12 19.794 150.69 37.633 NaN NaN NaN NaN NaN NaN 79.676 220.614 38.967 99.268 229.482 38.436 129.881 235.374 38.61 169.79 215.494 39.999 199.482 199.431 39.078 249.724 166.529 38.679 299.764 155.498 39.377 329.036 171.037 38.953 379.673 247.306 38.455 399.205 293.707 38.795 449.438 369.592 39.867 499.811 371.176 38.781 549.221 390.944 39.002 599.331 411.525 39.837 619.223 415.971 38.836
-0.056 10.391 42.313 19.883 100.806 39.381 NaN NaN NaN NaN NaN NaN 79.393 170.931 40.647 99.816 179.896 40.183 129.278 185.549 40.86 169.362 165.621 40.561 199.201 149.789 40.356 249.526 117.283 40.668 299.544 104.913 41.298 329.4 121.509 41.644 379.295 197.056 40.755 399.8 244.073 41.207 449.299 319.634 40.484 499.926 320.765 41.034 549.511 341.235 40.568 599.448 361.452 40.63 619.025 366.018 40.615];
clf
hold all
%Y-DIRECTION
for k=1:19
X_vert=[XYZ(:,3*k-2)];
Y_vert=[XYZ(:,3*k-1)];
Z_vert=[XYZ(:,3*k)];
plot3(X_vert, Y_vert, Z_vert);
pause(0.01)
end
%X-DIRECTION
for k=1:27
X_horz=[XYZ(k,1:3:57)];
Y_horz=[XYZ(k,2:3:57)];
Z_horz=[XYZ(k,3:3:57)];
plot3(X_horz, Y_horz, Z_horz);
pause(0.01)
end
axis equal
%REARRANGED INTO 3-COLUMN LIST
X=[];
Y=[];
Z=[];
for k=1:19
X=[X;XYZ(:,3*k-2)];
Y=[Y;XYZ(:,3*k-1)];
Z=[Z;XYZ(:,3*k)];
end
XYZ=[X Y Z];
