How to create an irrgular mesh?

Hi, I’m working on an inverse obstacle problem recently and I occurred a problem about generating mesh.

Here is the domain image, where the yellow area represents the obstacle and the blue area represents the domain I want to generate mesh on.
Taking the mathematical method, the yellow area denotes the set {x | f(x) > 0}, where f(x) is a function defining on the whole domain.
That is, there’s no explicit expression of the yellow area, and I can only identify it by its definition.

The question is, how can I generate mesh on the blue area?

Any idea will be helpful, and I truly appreciate that.