How is the isoline in a 2D contour calculated inside 'contourc' function?

Hello Matlab experts,

My questions is about using contourc function to get a isoline in a 2D contour. For example,

iso_line = contourc(x,y,function_of_x_y,[0.5 0.5]);

I assume that the algrithme is interploilating the function_of_x_y on meshgrids(x,y) to get the isoline at 0.5. My question is what is the interpolation function? is it a linear interpolation? Does the uniform or non-uniform grids affect the 2D iso_line matrix?

Thanks in advance.

Bin

[darova]

I think MATLAB detects intersected faces first

Then calculate intersection of plane and each face

[Steven Lord]

I don't believe we document exactly how contourc generates the contours. Can you say a little more about why you're interested in this information?

[Bin Jiang]

Thanks for the reply, Steven. You are right, and Matlab does not give the details about this, and this may involve coding patent. The reason why I want to know is whether I should add spatial weight to each data point if the iso_line is calculated based on non-uniform grids? I may verifiy this confusion by comparing the results with uniform and non-uniform grids. I will try this firstly by myself, and thanks again.

[Bin Jiang]

Thanks for the reply and detailed answering, Darova. Your hypothesis is sound. I am wondering how matlab calculate the intersection. I suppose that Matlab interpolates this orginal mesh to finer mesh, and then approximate the isoline.

[darova]

It calculates plane-to-plane intersection

Two equations of plane:

Simplified to get line:

Then it checks if the line lies on both planes

[Bin Jiang]

Thanks again for the further explanation. Follow you thoughts, if we take a simpler 2D case as shown in the below code,

iso_line = contourc(x,y,function_of_x_y,[0.5 0.5]);

the two planes you mentioned are the [x y] plane and a plane of function_of_x_y at given value (actually a line in 2D or a plane parallel to the isoline), am I right? Matlab get the intersection of the line with local elementary 2D plane [dx dy], and these intersections are the data point of the iso-line. I think I understand the procedure better than before. Cheers.

[darova]

[Bin Jiang]

Thanks for the clarification. The figure looks more understandable now.