Concept

Mirror — where it appears

A reflecting surface, which is a second camera when flat and a projection from nowhere at all when curved.

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

eyethe best fit — no ray goes through itno single viewpoint — the rays miss by 2.46 mmover 20 cm of a 2.00 m ball

A curved mirror has no eye

A flat mirror is a second camera — reflect the eye in the plane and every line of sight passes through the reflected point, to 2.8e-12 mm. Curve the mirror and the point is gone. Over 20 cm of a mirror ball two metres across, the lines of sight miss their own best-fitting point by 2.8 mm, and by 52.9 mm on a ball half a metre across. What replaces the eye is not a worse eye; it is nothing.

mirrors · curvedmirror
00.2500.5000.7501050100150angle of the direction from the camera's own axis (degrees)where it lands in the picture, as a fraction of the picture's radiusequisolidequidistantorthographica ball 24 cm across, camera 24 radii offequal-area within 0.82% · equidistant 21.5%

A mirror ball is an equal-area fisheye

Photograph a mirror ball from far enough away and its rule is ρ = R·sin(θ/2), which is the equal-area fisheye — not an approximation to it, the rule. Measured, the departure falls from 4.27% of the picture's radius at 3 radii to 0.01% at 2000, while the next-best named rule stays 21% out at every distance. And the ball reflects 100.0% of the directions there are, which no designed surface does.

mirrors · mirrorball
eye, on the axisa cone 29 cm across and 22 cm highthe design lies from 0.17 m to 0.47 m out

The cone that reads the floor

A conical mirror standing on a design turns it into a picture, and the map it performs is exact, one-to-one, and not a projectivity — a homography fitted to four of the marks returns those four to 7e-13 mm and puts the rest 2480 mm away, on a design 369 mm wide. The reason is that the cone turns the annulus inside out: the middle of the picture comes from the far edge of the floor and the rim from the near one.

mirrors · conemirror

Named alongside it

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

Reflectioncentre of projectionPicture planeRay tracingAnamorphosisArea scaleAstigmatismCausticCentral collineationConeDevelopableEquidistant

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