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geometrycomputational-geometryellipse

How can I calculate the area of a slice of a superellipse?

Say I have a superellipse with a given width, height and eccentricity (n). I want to create x horizontal slices of equal height. How can I calculate the area of each slice?

I don't even need exact values for the specific project I'm working on, only close approximations.

Solution

  • You can make integral for area of superellipse slice like this (4) and integrate it numerically in needed range instead of 0..a

    enter image description here

    I think that for approximation simple method of midpoint rectangles is enough:

    for slice interval y0..y1 choose number of sub intervals n, step h = (y1-y0)/n and calculate function value (y instead of x) in points y0 + h/2 + h*i, i = 0..n-1, then sum these values and multiply sum by y1-y0.