How to find the coordinate of the point on (180) contour line when y(max)?

How to find the coordinate of the point on (180) contour line when y(max)?

Code of the contour line:

clear

x = 0:0.1:3;

y = -2:0.1:3;

[X,Y] = meshgrid(x,y);

Z = 1000*(X.*exp(-X.^2-Y.^1));

contour(X,Y,Z,[90 180],'ShowText','on')

Answer 1

[John D'Errico]

Easy.

1. Use contourc to find that specific contour. It will be a piecewise linear curve.
2. Find the point where y is maximum. That will also tell you the x coordinate at that point.

[Stephen23]

Extracting and working with the data from the CONTOURC output matrix is rather... tedious and fiddly.

There are several wrappers on FEX to make it easier to work with that data, e.g. :

https://www.mathworks.com/matlabcentral/fileexchange/38863-extract-contour-data-from-contour-matrix-c

Answer 2

[Matt J]

You could do the calculus, or use the Symbolic toolbox to help you.

syms x y z(x,y)

z=1000*(x.*exp(-x.^2-y.^1));
G=gradient(z);

assume(x>0);

xy_max=solve([G(1)==0, z==180]), %location of max point

xy_max = struct with fields:
    x: 2^(1/2)/2
    y: - log((9*2^(1/2))/50) - 1/2