Visual Plane
every picture states the point it is correct from
Concept

Dual conic — where it appears

The set of lines tangent to a conic, written as a symmetric 3×3 matrix in line coordinates. It is the object a solid's outline naturally is, because what an eye sees of a surface is which lines graze it rather than which points lie on it.

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

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 correct from 18 cm, at 160 mm wideoutline from the duals · ellipse

Every quadric has one outline

The curve where a solid turns away from the eye is the section of the solid by one plane — the eye's polar plane — and the outline is three matrix products with no sampling in them. It works for a ball, a dish and a hyperboloid, and it fails for a cone, whose dual outline collapses to a single point and forgets which two lines pass through it.

foundations · quadric

Named alongside it

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

ConicDemonstrationAbsolute conicAdjugateCamera matrixCircular pointsConic fitContour generatorDegeneracydegrees of freedomDual quadricGround plane rectification

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