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

The eye that moves

A handscroll is drawn by an eye that travels, imaging one line at a time — orthographic along the roll and perspective across it, so a mile of river holds its scale while a single pavilion still recedes. Its rays miss their own best centre by metres, and the miss is exactly the length of track you unroll.
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.

 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.

 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.

 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.

 a rotating eye — the panorama2e-15 ma projectiona translating eye — the scroll7.97 mnot oneboth of these draw a straight world line as a curverms miss of the least-squares centreone of them is a projection

A scroll is not a panorama

Both draw straight world lines as curves, and one of them is a projection. A rotating eye keeps its centre exactly however far it turns; a translating eye has none at all. Curvature and centrelessness are independent properties, and conflating them is the standard mistake about both objects.

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