How to get the accurate coordinate value of the point on a fitted contour? And how to integrate along the contour?

Hello!

I am in trouble with processing data with matlab.

The mesh is two dimensional and each grid point has its function value f.

In matlab, the iso-surface of f=0 can be fitted with the command 'contour';

Then the question is,

1) Given an x coordinate value, how to get the accurate y coordinate value of the point on the fitted contour?

2) In order to get the accurate length of the total contour, how to integrate along the contour?

dx=dy=0.001m

For a random x coordinate value, for example x=0.00875, how to get the corresponding y coordinate value on the contour f=0？

And how to get the accurate length of the total red contour line?

==============================================================================

Data=load('shuju.dat');

x=Data(:,1);

y=Data(:,2);

f=Data(:,5);

xx=reshape(x,301,43);

yy=reshape(y,301,43);

ff=reshape(f,301,43);

v=[0,0];

contour(xx,yy,ff,v,'r','LineWidth',2);

xlabel('x/m');

ylabel('y/m');

========================================================================

Thanks!

Answer 1

[Roger Stafford]

You can obtain a two-row matrix, C, from your call to 'contour' which contains x,y coordinates for points along contours:

   C = contour(xx,yy,ff,v,'r','LineWidth',2);

It is called a "contour matrix".

For 2) to integrate along the contour, just use as arclengths the euclidean linear distance between successive points as contained in C. For the format of C see the site:

   http://www.mathworks.com/help/matlab/ref/contour-properties.html#prop_ContourMatrix

If the contour takes a jump as appears to happen in your case, you can eliminate all segments whose lengths are larger than some predetermined amount.

For 1) it would be a matter of finding corresponding y values for an x value which lies within some segment of the contour as given in C. In your case there will be more than one y for some x's.

[Ren Zetian]

Thanks!

Another question, maybe similar to 1).

How can I get the accurate f value at a certain point(x,y)? Can this be solved by using interp function?

Since my final aim is to know whether the certain point(x,y) is before or after the f=0 surface, that is, whether the f value at a certain point(x,y) is positive or negative.

Thanks!

[Roger Stafford]

Yes, you could use matlab's 'interp2' with your original meshgrid for that purpose. See

   http://www.mathworks.com/help/matlab/ref/interp2.html

[Ren Zetian]

Thanks a lot !!

Answer 2

[Ren Zetian]

Some details are added, thanks!

Answer 3

[Ren Zetian]

Some details are added, thanks!