Concept

Conic fit — where it appears

Solving for the six coefficients of a general conic through sampled points, which returns a circle, an ellipse or a line without being told which to expect.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

fitted conic: a circle to 1e-9stereographicdashed: the fit, not the samples

Stereographic keeps every angle, and only stereographic

One surface in the family preserves shape exactly — every right angle stays a right angle and both its arms are magnified equally, to the last bit the arithmetic has. It also sends every circle in the world to a circle in the picture, which the site's existing conic fit can be pointed at and asked to confirm without being told what it is looking at.

curved · conformal
fitted conic: a circle to 1e-9stereographicdashed: the fit, not the samples

The arcs a curvilinear drawing uses

The taught way to draw a very wide view by hand is to run every straight edge of the world as a circular arc. That recipe has been repeated for sixty years without a surface attached to it, and it turns out to name one exactly — fitting a general conic to the image of a straight line returns a circle to nine decimal places under stereographic projection and returns nothing like a circle under any other surface this site has.

curved · curvilinear
horizonthe horizon does not cut the circle — the pair is complexrectified from the two points aloneangles: 2.2e-13°ratios: 5.6e-15length: —circle of radius 1.05 ma dash is a quantity two points cannot buy

The two points a picture hides

The stratification rung says a photograph of a plane is projective, becomes affine when the vanishing line is known, and becomes metric with one more fact. The one more fact has a size and a shape: it is two points, complex conjugates on the vanishing line, and a rectification built from those two and nothing else returns every world angle to a tenth of a picodegree and every ratio of lengths to five parts in a quadrillion — and refuses to name a length.

foundations · circularpoints

Named alongside it

The objects these essays reach for when they reach for this one.

AnisotropyCircle preservingConformalDemonstrationfield of viewStereographic projectionAbsolute conicArea scaleBeltramiCircular pointsConicdegrees of freedom

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