Series

Anamorphreach — the series

4 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. ground line — right from anywherefaint: intended · solid: seendeparture (mm) against height (m)01.38the error map is an elation, with the ground line as its axisno characteristic ratio — nothing off the axis is fixed250 mm sidewayszero on the axis, 212.5 mm at the top

    Where the anamorph still works

    A picture correct from one point raises an obvious question that nobody answers with a number — how far may the eye move. The answer here is exact rather than approximate: a wrong viewpoint composes the intended picture with a central collineation whose axis is the line the picture stands on, so the error is zero along that line and grows linearly upward, and a step sideways costs precisely as much as the same step upward.

    part 4 · viewing
  2. no single viewpoint — the rays miss by no distance at all — the rays are parallel4 pictures on 3 kinds of face

    A flight that has ends

    A real staircase has three families of faces and the rule proposed last round predicted three pictures. It supports four, because a picture is fixed by a direction and the flight's two sides point opposite ways — one kind of face that no single direction reaches both of. The rule counts words and the object counts orientations.

    part 4 · viewing
  3. toward the designup10 mm14 mm across36 mm along the sight line

    The room the eye may stand in

    An anamorph is correct from one point, and one point is not a thing a person can occupy. Fix a tolerance on the picture and the set of eye positions that meet it is a solid — for a design 1.8 m wide and a ten-millimetre tolerance it is 36 mm long, 14 mm across and 31 cubic centimetres altogether, a spindle pointing along the line of sight. Ten times the tolerance is a thousand times the room.

    part 5 · viewing
  4. 00.2500.5000.75012345how high the eye is (m)share of the object, and share of the design that landsof the object's surfaceof the design that landsa corridor with a doorway, 7 facesbest surface share 100% at 2.5 m

    The eye that reaches the most

    A higher eye buys the faces occlusion was hiding and loses design off the far end of the object, so "the best eye" is not a question with an answer until somebody says which of the two they are paying for. On three objects the answer is as high as possible; on a corridor with a doorway in it the two quantities cross and the best height is two and a bit metres.

    part 6 · viewing

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