Analytic equation of elliptic-like figure

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SUMMARY

The discussion centers on the need for an analytical equation to model fracture propagation in oil reservoirs using an elliptic-like figure. Peter, the original poster, seeks a formula that accommodates different radii (R1, R2, R3, R4) and maintains perpendicularity to each radius. He considers breaking the problem into four sub-problems but prefers to avoid unnecessary time investment if a known formula exists. The suggestion of using piecewise sections of ellipses is proposed as a potential solution to meet the perpendicularity condition.

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This discussion is beneficial for engineers, researchers, and programmers involved in modeling fracture propagation in oil reservoirs, as well as those interested in analytical geometry and numerical methods.

pslarsen
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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!
 

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

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