Interpolating for multiple curves and finding the y axis value (2024)

x = [0,7.1702,9.1995,9.5716,11.3641,12.0744,12.5141,13.1736,13.4104,13.867,14.7294,15.1015,16.9448,17.0631,17.2322,18.3484,19.0079,20.0395,20.699,20.885,21.9673,22.4408,23.1342,24.2334,24.2672,25.3495,25.3664,26.9053,27.6494,28.3427,28.6302,28.867,31.336,31.8095,32.5197,32.6043,32.6212,35.5418,35.7159,36.1218,36.3078,38.1838,40.0113,40.7892,40.9583,41.401,41.9053,44.1496,44.425,45.2706,45.575,46.6573,46.8129,48.7542,49.3461,49.4549,49.4983,51.9051,52.1702,52.6082,52.7452,53.1172,53.4047,56.1781,57.4295,57.6325,57.7678,59.1375];

y1 = [0,0.0020385,0.0029971,0.0031692,0.0039805,0.0043153,0.0045343,0.0048942,0.0050347,0.0053227,0.0058919,0.0061278,0.0073044,0.0073855,0.0075032,0.0083247,0.0088284,0.0096041,0.0100713,0.0102005,0.010981,0.0113609,0.0119703,0.0130149,0.0130479,0.0141152,0.0141319,0.0156525,0.0163877,0.0170739,0.0173591,0.0175943,0.0201634,0.0206939,0.0215118,0.0216106,0.0216304,0.0251692,0.0253869,0.0258977,0.0261335,0.0285498,0.0309047,0.0319193,0.032142,0.03273,0.0334105,0.036545,0.0369321,0.0381116,0.0385328,0.0400127,0.040223,0.0428361,0.0436564,0.0438095,0.0438708,0.0473963,0.0477901,0.0484244,0.0485977,0.0491639,0.0495916,0.0537516,0.0556341,0.0559395,0.0561431,0.0582054];

y2 = [0,0.0012683,0.0021179,0.0022702,0.0030119,0.0033161,0.0035092,0.0038069,0.0039163,0.0041315,0.0045528,0.0047406,0.0057299,0.0057969,0.0058935,0.0065504,0.0069509,0.0075884,0.0079984,0.0081139,0.0087828,0.0090767,0.009513,0.0102275,0.0102501,0.0109859,0.0109976,0.0120843,0.0126222,0.0131294,0.0133411,0.0135161,0.0153693,0.0157302,0.0162751,0.0163402,0.0163533,0.0186568,0.0187971,0.0191247,0.0192751,0.0208039,0.0223233,0.0229833,0.0231281,0.0235096,0.0239475,0.0259189,0.0261606,0.0268967,0.027159,0.0280794,0.0282105,0.0298293,0.0303207,0.0304111,0.0304473,0.0324635,0.0326876,0.0330586,0.0331748,0.0334911,0.0337359,0.0361113,0.0371869,0.0373614,0.0374777,0.0386548];

y3 = [0,0.0006766,0.0012771,0.0013806,0.0018907,0.0021204,0.002306,0.0026193,0.0027171,0.0028934,0.0032128,0.0033498,0.0040542,0.0041021,0.0041712,0.0046468,0.0049396,0.0054045,0.0056995,0.0057817,0.0062531,0.006458,0.0067599,0.0072545,0.0072702,0.0077953,0.0078038,0.0085914,0.008973,0.0093259,0.0094717,0.0095916,0.0108428,0.0110848,0.0114515,0.0114956,0.0115044,0.0131414,0.0132431,0.0134797,0.0135881,0.01468,0.0157464,0.0162024,0.0163018,0.0165625,0.0168602,0.0181916,0.018355,0.0188555,0.0190349,0.0196682,0.0197587,0.0208751,0.0212111,0.0212726,0.0212972,0.0226611,0.0228141,0.0230691,0.0231495,0.0233696,0.0235414,0.0252623,0.026059,0.0261885,0.0262749,0.0271481];

y4 = [0,0.0001386,0.0003101,0.0003914,0.0007895,0.0009534,0.0010573,0.0012172,0.0012758,0.0013909,0.001615,0.0017137,0.0022114,0.0022435,0.0022893,0.0025888,0.0027614,0.0030217,0.0031838,0.0032293,0.0034972,0.0036189,0.0038069,0.0041348,0.0041454,0.0044929,0.0044984,0.0049984,0.0052326,0.005448,0.0055372,0.0056109,0.0064064,0.0065684,0.0068176,0.0068478,0.0068538,0.0079593,0.0080295,0.0081951,0.0082722,0.0090844,0.0098947,0.0102295,0.0103015,0.0104889,0.010701,0.0116406,0.0117567,0.0121153,0.0122452,0.0127101,0.0127772,0.0136188,0.013876,0.0139232,0.0139421,0.0149886,0.015104,0.0152948,0.0153545,0.0155167,0.015642,0.0168527,0.0173993,0.017488,0.0175471,0.0181454];

y5 = [0,1.00E-04,0.00022,0.0002489,0.0003969,0.0004566,0.0004931,0.0005463,0.0005648,0.0005992,0.0006584,0.0006806,0.0007686,0.0007744,0.0007831,0.0008563,0.0009153,0.0010211,0.0010907,0.00111,0.0012128,0.0012502,0.0012988,0.0013787,0.0013815,0.0014949,0.0014972,0.0017449,0.0018736,0.0019831,0.0020233,0.0020536,0.0022654,0.0023013,0.0023648,0.0023736,0.0023754,0.0028436,0.0028757,0.0029503,0.0029842,0.0033201,0.0036535,0.0038019,0.0038349,0.0039231,0.004027,0.0045444,0.0046125,0.0048235,0.0048992,0.0051622,0.0051989,0.0056406,0.005772,0.0057961,0.0058057,0.0063438,0.0064049,0.0065075,0.00654,0.0066292,0.006699,0.0073962,0.0076961,0.0077429,0.0077739,0.0080807];

y = [y1(:),y2(:),y3(:),y4(:),y5(:)]; % much better!

A = [0.5;0.6;0.7;0.8;0.9];

C = compose("A = %g",A);

plot(x,y)

hold on

% example for angle = 40 and A = 0.63

yq = interp2(A,x,y,0.63,40)

plot(40,yq,'*k')

legend(C{:},'A = 0.63')

x = [0 7.1702 9.1995 9.5716 11.3641 12.0744 12.5141 13.1736 13.4104 13.867 14.7294 15.1015 16.9448 17.0631 17.2322 18.3484 19.0079 20.0395 20.699 20.885 21.9673 22.4408 23.1342 24.2334 24.2672 25.3495 25.3664 26.9053 27.6494 28.3427 28.6302 28.867 31.336 31.8095 32.5197 32.6043 32.6212 35.5418 35.7159 36.1218 36.3078 38.1838 40.0113 40.7892 40.9583 41.401 41.9053 44.1496 44.425 45.2706 45.575 46.6573 46.8129 48.7542 49.3461 49.4549 49.4983 51.9051 52.1702 52.6082 52.7452 53.1172 53.4047 56.1781 57.4295 57.6325 57.7678 59.1375];

A = [0.5 0.6 0.7 0.8 0.9];

y1 = [0 0.0020385 0.0029971 0.0031692 0.0039805 0.0043153 0.0045343 0.0048942 0.0050347 0.0053227 0.0058919 0.0061278 0.0073044 0.0073855 0.0075032 0.0083247 0.0088284 0.0096041 0.0100713 0.0102005 0.010981 0.0113609 0.0119703 0.0130149 0.0130479 0.0141152 0.0141319 0.0156525 0.0163877 0.0170739 0.0173591 0.0175943 0.0201634 0.0206939 0.0215118 0.0216106 0.0216304 0.0251692 0.0253869 0.0258977 0.0261335 0.0285498 0.0309047 0.0319193 0.032142 0.03273 0.0334105 0.036545 0.0369321 0.0381116 0.0385328 0.0400127 0.040223 0.0428361 0.0436564 0.0438095 0.0438708 0.0473963 0.0477901 0.0484244 0.0485977 0.0491639 0.0495916 0.0537516 0.0556341 0.0559395 0.0561431 0.0582054];

y2 = [0 0.0012683 0.0021179 0.0022702 0.0030119 0.0033161 0.0035092 0.0038069 0.0039163 0.0041315 0.0045528 0.0047406 0.0057299 0.0057969 0.0058935 0.0065504 0.0069509 0.0075884 0.0079984 0.0081139 0.0087828 0.0090767 0.009513 0.0102275 0.0102501 0.0109859 0.0109976 0.0120843 0.0126222 0.0131294 0.0133411 0.0135161 0.0153693 0.0157302 0.0162751 0.0163402 0.0163533 0.0186568 0.0187971 0.0191247 0.0192751 0.0208039 0.0223233 0.0229833 0.0231281 0.0235096 0.0239475 0.0259189 0.0261606 0.0268967 0.027159 0.0280794 0.0282105 0.0298293 0.0303207 0.0304111 0.0304473 0.0324635 0.0326876 0.0330586 0.0331748 0.0334911 0.0337359 0.0361113 0.0371869 0.0373614 0.0374777 0.0386548];

y3 = [0 0.0006766 0.0012771 0.0013806 0.0018907 0.0021204 0.002306 0.0026193 0.0027171 0.0028934 0.0032128 0.0033498 0.0040542 0.0041021 0.0041712 0.0046468 0.0049396 0.0054045 0.0056995 0.0057817 0.0062531 0.006458 0.0067599 0.0072545 0.0072702 0.0077953 0.0078038 0.0085914 0.008973 0.0093259 0.0094717 0.0095916 0.0108428 0.0110848 0.0114515 0.0114956 0.0115044 0.0131414 0.0132431 0.0134797 0.0135881 0.01468 0.0157464 0.0162024 0.0163018 0.0165625 0.0168602 0.0181916 0.018355 0.0188555 0.0190349 0.0196682 0.0197587 0.0208751 0.0212111 0.0212726 0.0212972 0.0226611 0.0228141 0.0230691 0.0231495 0.0233696 0.0235414 0.0252623 0.026059 0.0261885 0.0262749 0.0271481];

y4 = [0 0.0001386 0.0003101 0.0003914 0.0007895 0.0009534 0.0010573 0.0012172 0.0012758 0.0013909 0.001615 0.0017137 0.0022114 0.0022435 0.0022893 0.0025888 0.0027614 0.0030217 0.0031838 0.0032293 0.0034972 0.0036189 0.0038069 0.0041348 0.0041454 0.0044929 0.0044984 0.0049984 0.0052326 0.005448 0.0055372 0.0056109 0.0064064 0.0065684 0.0068176 0.0068478 0.0068538 0.0079593 0.0080295 0.0081951 0.0082722 0.0090844 0.0098947 0.0102295 0.0103015 0.0104889 0.010701 0.0116406 0.0117567 0.0121153 0.0122452 0.0127101 0.0127772 0.0136188 0.013876 0.0139232 0.0139421 0.0149886 0.015104 0.0152948 0.0153545 0.0155167 0.015642 0.0168527 0.0173993 0.017488 0.0175471 0.0181454];

y5 = [0 1.00E-04 0.00022 0.0002489 0.0003969 0.0004566 0.0004931 0.0005463 0.0005648 0.0005992 0.0006584 0.0006806 0.0007686 0.0007744 0.0007831 0.0008563 0.0009153 0.0010211 0.0010907 0.00111 0.0012128 0.0012502 0.0012988 0.0013787 0.0013815 0.0014949 0.0014972 0.0017449 0.0018736 0.0019831 0.0020233 0.0020536 0.0022654 0.0023013 0.0023648 0.0023736 0.0023754 0.0028436 0.0028757 0.0029503 0.0029842 0.0033201 0.0036535 0.0038019 0.0038349 0.0039231 0.004027 0.0045444 0.0046125 0.0048235 0.0048992 0.0051622 0.0051989 0.0056406 0.005772 0.0057961 0.0058057 0.0063438 0.0064049 0.0065075 0.00654 0.0066292 0.006699 0.0073962 0.0076961 0.0077429 0.0077739 0.0080807];

y = [y1; y2; y3; y4; y5]

figure

plot(x, y.')

hold on

plot(40, 0.02, 'bo') % example for angle = 40 and A = 0.63

legend("A = "+A)

title('Coefficient')

ylabel('K_c')

xlabel('angle')

% query point:

xq = 40;

Aq = 0.63;

% interpolated y value:

yq = interp2(x,A,y,xq,Aq)

plot(xq,yq,'rx','HandleVisibility','off') % 'HandleVisibility','off' to avoid showing in the legend