Analytic equation of elliptic-like figure

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In summary, the speakers are discussing the implementation of a figure in a program, but they are unsure if there is an analytical equation for it. The figure represents fracture propagation in oil reservoirs and has four different radii. They consider using piecewise sections of ellipses to satisfy the perpendicularity condition.
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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
 

FAQ: Analytic equation of elliptic-like figure

What is an analytic equation of an elliptic-like figure?

An analytic equation of an elliptic-like figure is a mathematical equation that describes the shape of an ellipse, which is a type of elliptic-like figure. It is typically written in the form of x^2/a^2 + y^2/b^2 = 1, where a and b represent the semi-major and semi-minor axes of the ellipse, respectively.

How is an analytic equation of an elliptic-like figure different from other equations?

An analytic equation of an elliptic-like figure is different from other equations because it is used specifically to describe the shape of an ellipse. Other equations may describe different shapes, such as circles or hyperbolas.

What is the significance of an analytic equation in studying elliptic-like figures?

An analytic equation is significant in studying elliptic-like figures because it allows for a precise and mathematical representation of the figure's shape. This can help in analyzing and understanding its properties and behavior.

Can an analytic equation be used to find the area of an elliptic-like figure?

Yes, an analytic equation can be used to find the area of an elliptic-like figure. The formula for the area of an ellipse is given by πab, where a and b are the semi-major and semi-minor axes of the ellipse, respectively.

Are there any limitations to using an analytic equation to describe an elliptic-like figure?

Yes, there are some limitations to using an analytic equation to describe an elliptic-like figure. The equation assumes that the figure is a perfect ellipse, which may not always be the case in real-world situations. Additionally, the equation does not account for any irregularities or imperfections in the shape of the figure.

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