The viewer is closer for the circle and farther for the square. That makes sense to me because the straight lines are the projection of the curve to the axis of planes while the circle projects the curve to the base of a cone. My first guess. Interesting to see it diagramed.
2D projections are one hell of a drughttps://twitter.com/josepjulien/status/1147615756487729153 …
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Four planes at right angles to each other cut a cone parallel to the axis of the cone. The intersections are the four hyperbola. Viewed from one side at the apex of the cone the lines project to the cones base a circle formed by a plane cutting the cone perpendicular to the axis.
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From the others side you see the lines projected along the planes forming a square. Notice the slight concave lines. The camera lens diameter is smaller than the diagonal of the square. The farther the camera moves from the figure the lines become straighter.
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is this where you need topological data analysis
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Squaring the circle.
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