MATLAB: How to interpolate missing range between curves

interpolationmissing datasets

Hi, I have the x and y values for the depicted curves, but I want to connect the ends/beginnings of the curves with each other to have only one line. How can I interpolate the missing ranges? I have read some posts in this community but I don't understand how to apply the solutions to my case. I would be thankful if someone can give a suitable example.

Best Answer

Hello Ince,

I am assuming that you have each of the x and y values for each line stored in a separate variable (and for this example, that they are all row vectors). If you are simply looking to plot it all as a continuous line, you can just do this:

xAll = [x1 x2 x3 x4 x5];
yAll = [y1 y2 y3 y4 y5];
plot(xAll, yAll)

to simulate linear interpolation (since it'll just draw a line between the last point of one section and the first point of the next).

From the image, it looks like the end of one section occurs at the same x-value as the beginning of the next. This means that traditional interpolation doesn't really make sense, as if you were to try to interpolate at that x-value, the answer could be any y-value between the endpoints. Of course, interpolating at that y-value and getting the correct x-value is valid, but you can do that without anything special.

So if you're trying to do more than just draw a continuous line, can you explain in more detail what you are trying to do with this interpolation?

-Cam

Related Solutions

MATLAB: How to solve multiple equations dependent on each other

Since you depend on your previous answers, you can simply loop through the equations and store the answers.

x = ones(1,10); % also contains your initial x
y = ones(1,10); % just to preallocate y as well
for i=1:9              % loop 9 times
  y(i) = 2*x(i) + 5;   % calculate the y-value

  x(i+1) = 2*y(i) + 5; % calculate the 'next' x-value

end
y(10) = 2*x(10) + 5;   % finish off by calculating the final y-value

If you only care about the final value, this suffices:

x = 1;
for i=1:9
  y = 2*x + 5; % calculate the y-value
  x = 2*y + 5; % calculate the 'next' x-value
end
y = 2*x + 5;

MATLAB: Using fsolve over a range of equations.

Solve the equations once and then plug in the values.

for z = 100:105
  x1=velprof(z,y1);
  x2=velprof(z,y2);
  x3=velprof(z,y3);
  x4=velprof(z,y4);
  c = [ (((x3*y4-x4*y3)*x2^2+(-x3^2*y4+x4^2*y3)*x2+x3*x4*y2*(-x4+x3))*x1^3+((-x3*y4+x4*y3)*x2^3+(-x4^3*y3+x3^3*y4)*x2+y2*x3*x4^3-x3^3*x4*y2)*x1^2+((x3^2*y4-x4^2*y3)*x2^3+(x4^3*y3-x3^3*y4)*x2^2+x3^2*x4^2*y2*(-x4+x3))*x1-x3*x2*x4*y1*(-x4+x3)*(x2-x4)*(x2-x3))/((-x4+x3)*(x2-x4)*(x2-x3)*(x1-x4)*(x1-x3)*(x1-x2)), ...
  (((-y2+y1)*x4^2+(y2-y4)*x1^2-x2^2*(y1-y4))*x3^3+((-y1+y2)*x4^3+(y4-y2)*x1^3+x2^3*(y1-y4))*x3^2+((y3-y2)*x1^2+x2^2*(y1-y3))*x4^3+((y2-y3)*x1^3-x2^3*(y1-y3))*x4^2+x1^2*x2^2*(y3-y4)*(x1-x2))/((-x4+x3)*(x2-x4)*(x2-x3)*(x1-x4)*(x1-x3)*(x1-x2)), ...
  (((y4-y3)*x2+(y2-y4)*x3-x4*(y2-y3))*x1^3+((y3-y4)*x2^3+(y4-y2)*x3^3+x4^3*(y2-y3))*x1+((-y1+y4)*x3+x4*(y1-y3))*x2^3+((y1-y4)*x3^3-x4^3*(y1-y3))*x2-x3*x4*(-x4+x3)*(x3+x4)*(-y2+y1))/((-x4+x3)*(x2-x4)*(x2-x3)*(x1-x4)*(x1-x3)*(x1-x2)), ...
  (((y3-y4)*x2+(y4-y2)*x3+x4*(y2-y3))*x1^2+((y4-y3)*x2^2+(y2-y4)*x3^2-x4^2*(y2-y3))*x1+((y1-y4)*x3-x4*(y1-y3))*x2^2+((-y1+y4)*x3^2+x4^2*(y1-y3))*x2+x3*x4*(-y2+y1)*(-x4+x3))/((-x4+x3)*(x2-x4)*(x2-x3)*(x1-x4)*(x1-x3)*(x1-x2)) ];
  disp(z)
  disp(c)
end

Best Answer

Related Solutions

MATLAB: How to solve multiple equations dependent on each other

MATLAB: Using fsolve over a range of equations.

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