Let's say that I have a multiply connected curve defined implicitly. For example:
How can we find the area of from the rectangle ?
So, if we can calculate the area of a filled figure than it's all done. There is a function for that kind of evaluations?
P.S. I wrote myself a program which detects where the changes from a connected component to another is made by fimplicit data points and I made a loop that sums all the areas of the polygons created using the [k,v]=boundary(Points,1) command.
I have the areas precision up to 4 decimal places, but I cannot solve the problems that appear on the corners of the rectangle , because boundary don't have them included in the points obtained from fimplicit. To be more precis, if I have the area that my code gives is not the area of a quarter of a circle, but the area of that sector minus the area of the triangle determined by it.
Also I have to mention that the integral method fails (it has too little precision). I mean that we can use the formula