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Asked: 2026-05-18T07:06:00+00:00

Suppose you have an arbitrary closed curve (endpoint returns relatively close to first point)

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Suppose you have an arbitrary closed curve (endpoint returns relatively close to first point) generated through a bunch of dataset coordinates, how do you find the centerpoint and the boundaries of the resulting shape?

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  1. Editorial Team

    There are two possible interpretations (perhaps more) for your question.

    The first one was already addressed by @AakashM, and we may depict it in the following plot:
    alt text

    Where the red square is the “boundary”.
    I’ll cite @AakashM here, because I understand his remark VERY important:“(I note that for you to have a closed curve, you need the endpoint to be not just ‘close to’, but coincident with the first point)”

    As for the centerpoint, you have at least two “natural ways” for calculating it with this definitions:

    1. Centerpoint = Middle Point of the Red Square
    2. Centerpoint = { Mean of x coordinates of your curve, Mean of y coordinates of your curve}

    Both of them may serve as a center point, but the results will be different.

    The other way of dealing with the problem is finding the Convex Hull of your curve, as depicted below:

    alt text

    If you google for it, you will find algorithms for finding the Convex Hull, a nice introduction is here.

    Again, you have two “natural ways for calculating the centerpoint:

    1. Centerpoint = { Mean of x coordinates of your curve, Mean of y coordinates of your curve}
    2. Centerpoint = { Mean of x coordinates of the CH points, Mean of y coordinates of the CH points}

    HTH!

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