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

Exclusion — the series

7 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. a centretrue measurediminutionbounded depthstraight linesperspectivehandscrollisometricdimetrictrimetriccavaliercabinetelevationmilitaryfilled means the system keeps itmeasured from each system's own projectionno row is filled in both of the first two

    A centre and a measure are exclusive

    Eight drawing systems, measured on five questions, with the pinhole as a row rather than the header. Exactly one has a centre of projection and it is exactly the one with no true measure — and loosening the measure test by a hair lets it in, which is what says the boundary is real.

    part 1 · choices
  2. a centretrue measurediminutionbounded depthstraight linesperspectivehandscrollisometricdimetrictrimetriccavaliercabinetelevationmilitaryfilled means the system keeps itmeasured from each system's own projectionno row is filled in both of the first two

    Each system answers its own question

    A comparison in which every system wins its own column proves nothing if the columns were chosen after the systems. The test that makes it a result is whether any system wins something it was not designed for — and two of them do.

    part 2 · choices
  3. the ratio along a receding line15.6%0% parallelthe depth range in the last tenth69.0%10% lineara square metre, near against far53.5% larger0% parallelthe floor of the far room6.2 points0 parallelwhat it costs, and what the other systems have insteadmeasured by the same computationthe price of a station point

    What perspective gave up

    The field ends by turning its own battery on the system it has been comparing everything against. Four quantities a pinhole destroys that the other systems keep, each measured by the same computation as the systems it is set against, and each the price of the one thing perspective has and they do not.

    part 3 · choices
  4. an edge, read with the best single ruler for the pictureperspective39.5% outhandscroll39.2% outisometric0% outdimetric16.7% outtrimetric15.9% outcavalier0% outcabinet16.7% outelevation33.3% outmilitary0% out400 boxes, square3 of 9 exact

    A yes in the table is a price

    The comparison table says isometric, cavalier, the elevation and the plan oblique all keep measure. Priced on four hundred boxes, with each picture handed its own best ruler, the four charge 0%, 0%, 33.3% and 0% for an edge — and a pinhole charges 39.5%, only 6.2 points more than the elevation it is filed against. Turn the boxes and three of the four yeses cost something; only the plan oblique's stays free.

    part 4 · choices
  5. 456711.502how far the ground runs out (m, log scale)page spent drawing it (px², log scale)cavalierpinholehandscrollcrossed slitspinhole 431,233 px² · cavalier 13.3 million px²crossed slits 43,300 px²

    A page is bounded by a divide, not a centre

    A pinhole draws the whole of an infinite ground in a bounded patch of page — each doubling of distance half the one before — while a handscroll spends the same page on every doubling and an isometric drawing spends three quarters of its page on the last one. It is tempting to credit the centre. A crossed-slits camera, whose rays miss any common point by 0.46 m, is bounded too: what does it is dividing by depth in both directions of the page.

    part 5 · choices
  6. a centretrue measurediminutionbounded depthstraight linesperspectivehandscrollisometricdimetrictrimetriccavaliercabinetelevationmilitarycrossed-slitsfilled means the system keeps it10 rowsthe last is filled in neither of the first two

    The tenth row has neither

    A crossed-slits camera divides by depth in both page directions and its rays miss any common point by 0.354 m. Put on the comparison table it prices 38.8% on length, 69.9% on area and 58.2% on angle against a pinhole's 39.5%, 70.8% and 60.9%, and its midpoint drift is 15.6% — the pinhole's own figure. It keeps a true scale in no direction at all, and it bows a straight run of ground by 1.11 px, which no row with a centre does. Giving up the point buys nothing and costs a third thing besides.

    part 6 · choices
  7. 78.510.51421421051050∞78.510.51421421051050∞where the horizontal slit sits (m)where the vertical slit sits (m)8 with a centre, 17 with a measurenone with both

    The exclusion is two conditions, not ten rows

    Ten systems have been measured and none has both a centre and a true measure. Ten is not a proof. Swept across the whole two-slit family — eighty-one members, both parameters run out to infinity — a centre appears at exactly the eight members whose slits sit at one finite distance, a measure at exactly the seventeen with a slit at infinity, and at none of them both. The case the two conditions appear to leave open is closed by the rays themselves: one divide is a slit, and eight page points use 6.02 m of it.

    part 7 · choices

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