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

Pushbroom — the ladder

4 distinct arguments against one idea, from the one that introduces it to the one that assumes the rest.
  1. the eye's trackthe eye at x = -10.5 mevery point is drawn by the one position of the eye that is level with itplan — the eye's track and the scans it makes28 m of travel

    A scroll is a camera that moves

    A Chinese handscroll is not a picture with a wandering viewpoint or a picture with no viewpoint. It is the image of an eye that travels along a track and records one vertical line at a time, and that object has an exact geometry — orthographic along the roll, perspective across it.

    rung 1 · scroll
  2. a receding straight line, and the chord it is not9.59 px of sagthe control — the same line at constant depth0e+0 pxno single viewpoint — the rays miss by 6.1 ma straight line's image is a hyperbola

    A straight line in a scroll is a hyperbola

    Under a pushbroom the image of a straight world line is a Möbius function of the paper coordinate, which is a rectangular hyperbola. It is straight exactly when the line holds its depth — so a curve in a handscroll is a depth signal rather than a stylistic one, and the sag is computable in pixels.

    rung 2 · scroll
  3. the best point, missed by 8.57 m27 m of the eye's trackno single viewpoint — the rays miss by 8.57 mthe eyes are a track, not a point

    The centre a scroll does not have

    Fit a common point to the rays of one section of a handscroll and it misses by metres. The miss is not a residual to be tightened — it is exactly the standard deviation of the eye's own track, it grows linearly with how much is unrolled, and it goes to zero only for a section of no width.

    rung 3 · scroll
  4. along the rollthe two midpoints coincide — 0e+0 pxone mark, drawn twiceacross itthey separate by 21.9%the image of the midpointthe midpoint of the imageno single viewpoint — the rays miss by 6.9 m21.9% of the receding segment

    A map along, and a picture across

    The midpoint of a segment lying along a scroll's length images to the midpoint of its image, exactly. The midpoint of a receding one lands 22% of the way off. One projection, two answers — and the direction that keeps measure keeps something a perspective picture never offers.

    rung 4 · scroll

All ladders