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

Dual quadric — where it appears

The set of planes tangent to a quadric surface, written as a symmetric 4×4 matrix. Pushing it through a camera gives the dual of the outline directly, which is why the image of any quadric is three matrix products with no sampling in them.

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

Also named here as polar plane, quadric — the same set of essays touches all of them, so they are one junction rather than several.

correct from 8 cm, at 160 mm widestretch 1.358 · centres 4.28 px

The ball at the edge of the frame

A ball photographed near the edge of a wide picture is not drawn as a circle. It is an ellipse, longer along the radius from the centre of the picture than across it, and the centre of that ellipse is not the image of the centre of the ball. Both are properties of the flat sheet the picture is on, and an exact pinhole produces both.

foundations · quadric 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.

Camera matrixConicContour generatorDemonstrationPolar planeQuadricAdjugatecentre of projectionDegeneracyDual conicEdge stretchfield of view

All concepts