Analytic equation of elliptic-like figure

[pslarsen]

I have to implement the following figure in a programme I am writing but I actually don’t know if there exists an analytical equation describing it. Before I had my problem propagation like a rectangular box, but this might give a better approximation. For your information I am writing a programme to describe fracture propagations in oil reservoirs at work. Do some of you guys know if it can be obtained and if yes - what it is? If no, why not? Generally assume that radius R1, R2, R3 and R4 are all different from each other. I was thinking about separating it into four sub problems and use the fact that I am looking for a function that has to be perpendicular to each radius, but I don’t want to spend a lot of time on this if there is a generally known formula.

Thx,
Peter.

PS: Note that the outer elliptical line is wrong but just there to illustrate the problem!

 

[LCKurtz]

You could use piecewise sections of ellipses. That would at least satisfy your perpendicularity condition. Here's an example: