Intersection of Two Implicit Curves over a domain

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Rodrigo
Rodrigo 2013-5-8
评论： Sudhanshu Verma 2020-11-19
I have two implicit equations, one circle and one ellipse. I would like to know if there is a function or a way to find an intersection belonging to a given domain. Consider, for example:
circ = @(x,y) x^2+y^2-4 elp = @(x,y) ((x-2))^2+((y+2)/4)^2-1
There are two points of intersection (approximately):
P1 ~ (1.00 , -1.73) P2 ~ (1.46 , 1.37)
So I would like to know how to find P1, knowing it lies somewhere between: X: (0.8 , 1.2) Y: (-2 , -1)
OBS: I have no problems with numeric approximations, especially if it is not computationally intensive.
Thanks

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采纳的回答

Teja Muppirala
Teja Muppirala 2013-5-9
This sort of problem can be solved easily using FSOLVE
circ = @(x,y) x^2+y^2-4
elp = @(x,y) ((x-2))^2+((y+2)/4)^2-1
fsolve(@(X)[circ(X(1),X(2)); elp(X(1),X(2))],[1 -1.5])
This returns
ans =
1.0023 -1.7307
  2 个评论
Ankit Singh
Ankit Singh 2017-3-13
Can we use this without having to enter the probable range, i.e. [1 -1.5]? Also can this method be used for 2 ellipses?
Sudhanshu Verma
Sudhanshu Verma 2020-11-19
But there are 2 point of intersection, how would you find the second one

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更多回答（1 个）

Rodrigo
Rodrigo 2013-5-9
that was just what i needed! thanks!

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