How to find the range of a contour along each dimension of a plane with least possible error?
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I have a matrix of data which I plotted as a contour using the contour function. The y-axis of the plot is taken as log of the variable, i.e. I used:
The resulting plot has an irregular shape. By "irregular" I mean that it's not a nice smooth elliptical or rectangular shape, it's quite jagged at places and not evenly spread everywhere. I am posting one such plot below.
Here, I want to find out the left most point and the right most point of this contour to find the range along x-axis. Similarly, I want to find the bottom most point and the top most point of this contour to find the range along y-axis. Obviously for such shape, the x coordinates of the y_bottom and y_top will be different; y coordinates of the x_left and x_right will be different.
So, how do I find out the four points? One way is to do it by observation and select the points myself to note down the values, but there is a chance of error there. How to find it exactly with code?
Also I have another minor doubt: since I have used log2 of the y data, is there any way to minimize approximation error that I should be careful about?