Interpolation between intersecting curves

Hello,

For a project I have to do an interpolation between two curves. I have datapoints for both curves:

first curve (x1,y1):

x1=[0.155,0.16,0.165,0.17,0.175,0.18,0.185,0.19,0.195,0.2,0.205,0.21,0.215,0.22,0.225,0.23,0.235,0.24,0.245,0.25,0.255,0.26,0.265,0.27,0.275,0.28,0.285,0.29,0.295,0.3,0.305,0.31,0.315,0.32,0.325,0.33,0.335,0.34,0.345,0.35,0.355,0.36,0.365,0.37,0.375,0.38,0.385,0.39,0.395,0.4,0.405,0.41,0.415,0.42,0.425,0.43,0.435,0.44,0.445,0.45,0.455,0.46,0.465,0.47,0.475,0.48,0.485,0.49,0.495,0.5,0.505,0.51,0.515,0.52,0.525,0.53,0.535,0.54,0.545,0.55,0.555,0.56,0.565,0.57,0.575,0.58,0.585,0.59,0.595,0.6,0.605,0.61,0.615,0.62,0.625,0.63,0.635,0.64,0.645,0.65,0.655,0.66,0.665,0.67,0.675,0.68,0.685,0.69,0.695,0.7,0.705,0.71,0.715,0.72,0.725,0.73,0.735,0.74,0.745,0.75,0.755,0.76,0.765,0.77,0.775,0.78,0.785,0.79,0.795,0.8,0.805,0.81,0.815,0.82,0.825,0.83,0.835,0.84,0.845,0.85,0.855,0.86,0.865,0.87,0.875,0.88,0.885,0.89,0.895,0.9,0.905,0.91,0.915,0.92,0.925,0.93,0.935,0.94,0.945,0.95,0.955,0.96,0.965,0.97,0.975,0.98,0.985,0.99,0.995,1];

y1=[0.749,0.743,0.736,0.729,0.723,0.717,0.708,0.7,0.693,0.686,0.679,0.675,0.671,0.667,0.663,0.658,0.653,0.648,0.643,0.638,0.633,0.63,0.626,0.623,0.619,0.616,0.612,0.609,0.606,0.603,0.6,0.597,0.594,0.591,0.588,0.585,0.582,0.579,0.577,0.574,0.571,0.569,0.567,0.564,0.562,0.56,0.558,0.556,0.553,0.551,0.55,0.549,0.547,0.546,0.545,0.543,0.542,0.541,0.539,0.538,0.537,0.536,0.535,0.534,0.534,0.533,0.532,0.531,0.53,0.53,0.529,0.529,0.528,0.528,0.527,0.526,0.526,0.525,0.525,0.524,0.524,0.524,0.524,0.524,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.524,0.525,0.525,0.526,0.526,0.527,0.527,0.528,0.529,0.529,0.53,0.531,0.532,0.532,0.533,0.534,0.534,0.535,0.536,0.537,0.538,0.538,0.539,0.54,0.541,0.542,0.542,0.543,0.544,0.545,0.546,0.546,0.547,0.548,0.549,0.55,0.551,0.552,0.553,0.553,0.554,0.555,0.556,0.557,0.558,0.559,0.56,0.561,0.562,0.562,0.563,0.564,0.565,0.566,0.567,0.568,0.569,0.57,0.571,0.572,0.572];

and second curve (x2,y2):

x2=[0.305,0.31,0.315,0.32,0.325,0.33,0.335,0.34,0.345,0.35,0.355,0.36,0.365,0.37,0.375,0.38,0.385,0.39,0.395,0.4,0.405,0.41,0.415,0.42,0.425,0.43,0.435,0.44,0.445,0.45,0.455,0.46,0.465,0.47,0.475,0.48,0.485,0.49,0.495,0.5,0.505,0.51,0.515,0.52,0.525,0.53,0.535,0.54,0.545,0.55,0.555,0.56,0.565,0.57,0.575,0.58,0.585,0.59,0.595,0.6,0.605,0.61,0.615,0.62,0.625,0.63,0.635,0.64,0.645,0.65,0.655,0.66,0.665,0.67,0.675,0.68,0.685,0.69,0.695,0.7,0.705,0.71,0.715,0.72,0.725,0.73,0.735,0.74,0.745,0.75,0.755,0.76,0.765,0.77,0.775,0.78,0.785,0.79,0.795,0.8,0.805,0.81,0.815,0.82,0.825,0.83,0.835,0.84,0.845,0.85];

y2=[0.695,0.694,0.692,0.691,0.69,0.689,0.688,0.686,0.685,0.684,0.683,0.682,0.681,0.68,0.678,0.677,0.675,0.674,0.673,0.671,0.67,0.669,0.667,0.666,0.665,0.663,0.662,0.661,0.66,0.659,0.658,0.657,0.656,0.655,0.654,0.653,0.652,0.651,0.65,0.649,0.649,0.648,0.647,0.646,0.645,0.644,0.643,0.642,0.641,0.641,0.641,0.64,0.64,0.64,0.639,0.639,0.639,0.638,0.638,0.638,0.637,0.636,0.636,0.635,0.634,0.633,0.633,0.632,0.632,0.632,0.632,0.632,0.632,0.632,0.632,0.632,0.632,0.632,0.632,0.631,0.631,0.631,0.631,0.631,0.631,0.631,0.631,0.631,0.631,0.63,0.631,0.631,0.631,0.631,0.631,0.631,0.631,0.632,0.632,0.632,0.633,0.633,0.633,0.634,0.634,0.635,0.636,0.636,0.637,0.638];

The curve with points (x1,y1) are fuel consumption points of an aircraft engine with Bypass-ratio of 13. The curve with points (x1,y1) are fuel consumption points of an aircraft engine with Bypass-ratio of 8.5. I need to interpolate the curves to obtain a bypass-ratio of 12. So I'm not looking for mid-value of both curves, but it should ten more towards the (x1,y1) points.

I tried some stuff like interpolating the individual curves first, to obtain a nicer set of data, but then I get stuck on interpolating between the curves.

Hope someone can help,

PS: sorry for the ugly and long data set

Mikel

Answer 1

[Ameer Hamza]

Try this

x1=[0.155,0.16,0.165,0.17,0.175,0.18,0.185,0.19,0.195,0.2,0.205,0.21,0.215,0.22,0.225,0.23,0.235,0.24,0.245,0.25,0.255,0.26,0.265,0.27,0.275,0.28,0.285,0.29,0.295,0.3,0.305,0.31,0.315,0.32,0.325,0.33,0.335,0.34,0.345,0.35,0.355,0.36,0.365,0.37,0.375,0.38,0.385,0.39,0.395,0.4,0.405,0.41,0.415,0.42,0.425,0.43,0.435,0.44,0.445,0.45,0.455,0.46,0.465,0.47,0.475,0.48,0.485,0.49,0.495,0.5,0.505,0.51,0.515,0.52,0.525,0.53,0.535,0.54,0.545,0.55,0.555,0.56,0.565,0.57,0.575,0.58,0.585,0.59,0.595,0.6,0.605,0.61,0.615,0.62,0.625,0.63,0.635,0.64,0.645,0.65,0.655,0.66,0.665,0.67,0.675,0.68,0.685,0.69,0.695,0.7,0.705,0.71,0.715,0.72,0.725,0.73,0.735,0.74,0.745,0.75,0.755,0.76,0.765,0.77,0.775,0.78,0.785,0.79,0.795,0.8,0.805,0.81,0.815,0.82,0.825,0.83,0.835,0.84,0.845,0.85,0.855,0.86,0.865,0.87,0.875,0.88,0.885,0.89,0.895,0.9,0.905,0.91,0.915,0.92,0.925,0.93,0.935,0.94,0.945,0.95,0.955,0.96,0.965,0.97,0.975,0.98,0.985,0.99,0.995,1];
y1=[0.749,0.743,0.736,0.729,0.723,0.717,0.708,0.7,0.693,0.686,0.679,0.675,0.671,0.667,0.663,0.658,0.653,0.648,0.643,0.638,0.633,0.63,0.626,0.623,0.619,0.616,0.612,0.609,0.606,0.603,0.6,0.597,0.594,0.591,0.588,0.585,0.582,0.579,0.577,0.574,0.571,0.569,0.567,0.564,0.562,0.56,0.558,0.556,0.553,0.551,0.55,0.549,0.547,0.546,0.545,0.543,0.542,0.541,0.539,0.538,0.537,0.536,0.535,0.534,0.534,0.533,0.532,0.531,0.53,0.53,0.529,0.529,0.528,0.528,0.527,0.526,0.526,0.525,0.525,0.524,0.524,0.524,0.524,0.524,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.523,0.524,0.525,0.525,0.526,0.526,0.527,0.527,0.528,0.529,0.529,0.53,0.531,0.532,0.532,0.533,0.534,0.534,0.535,0.536,0.537,0.538,0.538,0.539,0.54,0.541,0.542,0.542,0.543,0.544,0.545,0.546,0.546,0.547,0.548,0.549,0.55,0.551,0.552,0.553,0.553,0.554,0.555,0.556,0.557,0.558,0.559,0.56,0.561,0.562,0.562,0.563,0.564,0.565,0.566,0.567,0.568,0.569,0.57,0.571,0.572,0.572];
ratio1 = 13;

x2=[0.305,0.31,0.315,0.32,0.325,0.33,0.335,0.34,0.345,0.35,0.355,0.36,0.365,0.37,0.375,0.38,0.385,0.39,0.395,0.4,0.405,0.41,0.415,0.42,0.425,0.43,0.435,0.44,0.445,0.45,0.455,0.46,0.465,0.47,0.475,0.48,0.485,0.49,0.495,0.5,0.505,0.51,0.515,0.52,0.525,0.53,0.535,0.54,0.545,0.55,0.555,0.56,0.565,0.57,0.575,0.58,0.585,0.59,0.595,0.6,0.605,0.61,0.615,0.62,0.625,0.63,0.635,0.64,0.645,0.65,0.655,0.66,0.665,0.67,0.675,0.68,0.685,0.69,0.695,0.7,0.705,0.71,0.715,0.72,0.725,0.73,0.735,0.74,0.745,0.75,0.755,0.76,0.765,0.77,0.775,0.78,0.785,0.79,0.795,0.8,0.805,0.81,0.815,0.82,0.825,0.83,0.835,0.84,0.845,0.85];
y2=[0.695,0.694,0.692,0.691,0.69,0.689,0.688,0.686,0.685,0.684,0.683,0.682,0.681,0.68,0.678,0.677,0.675,0.674,0.673,0.671,0.67,0.669,0.667,0.666,0.665,0.663,0.662,0.661,0.66,0.659,0.658,0.657,0.656,0.655,0.654,0.653,0.652,0.651,0.65,0.649,0.649,0.648,0.647,0.646,0.645,0.644,0.643,0.642,0.641,0.641,0.641,0.64,0.64,0.64,0.639,0.639,0.639,0.638,0.638,0.638,0.637,0.636,0.636,0.635,0.634,0.633,0.633,0.632,0.632,0.632,0.632,0.632,0.632,0.632,0.632,0.632,0.632,0.632,0.632,0.631,0.631,0.631,0.631,0.631,0.631,0.631,0.631,0.631,0.631,0.63,0.631,0.631,0.631,0.631,0.631,0.631,0.631,0.632,0.632,0.632,0.633,0.633,0.633,0.634,0.634,0.635,0.636,0.636,0.637,0.638];
ratio2 = 8.5;

% first interpolating signal1 to be of same length as signal2
x1_new = x2; % same x values as x2
y1_new = interp1(x1, y1, x1_new);

ratiox = 12;
x3 = x2; % same x values as x1_new and x2
y3 = interp1([ratio1 ratio2], [y1_new; y2], ratiox);

hold on
plot(x1_new, y1_new, 'DisplayName', 'ratio=13');
plot(x2, y2, 'DisplayName', 'ratio=8.5');
plot(x3, y3, 'DisplayName', 'ratio=12'); % values at ratio=12
legend

Answer 2

[David Hill]

f=fit(x1',y1','poly5');
g=fit(x2',y2','poly5');
x=min(x2):.01:max(x2);
h=1/4.5*(g(x)-f(x))+f(x);%only good for minimum x-range established by data (x2)