Concept

Buffer — where it appears

The set of points within a stated distance of a place, which is a disc on the sphere and is not a cell in any scheme. Answering a query about one costs more than the ratio of its area to a cell's, because the cells it overlaps have to be tested rather than merely counted.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

"Within 0.01°" on the ground, at five latitudes. The same condition drawn at five latitudes, all at one scale. A degree of latitude is a fixed distance — 1106 metres here, varying by less than one per cent from equator to pole — while a degree of longitude collapses as cos φ, from 1113 metres to 289 at 75°. So the "circle" is an ellipse of 3.86:1 there, and it encloses 26 per cent of the ground the same condition covers on the equator. Even on the equator it is not round: M is smaller than N by the flattening, so the shape is 6694 parts per million shorter north–south than east–west.

A degree is not a unit of length

"Within 0.01 degrees" is a condition anybody can write and no instrument can measure. On the ground it is an ellipse — 1,106 metres north–south and 558 east–west at 60° — and even on the equator it is not a circle, because the meridian's radius of curvature is smaller than the parallel's by the flattening.

applied · Dataset

Everywhere within 200 km of the route from London to Tokyo. The shortest route between the two places, and the set of places within 200 kilometres of it, with both edges computed on the sphere and then projected. On the ground the set holds 3.949 million square kilometres — the band 3.823 and the two end caps 0.126, which between them make one disc of the corridor's own width. Drawn in Mollweide the corridor is visibly wider at one end than the other, and the ground it stands for is not.

A corridor has a width the page cannot keep

Buffering a line is the most-run operation in spatial analysis and the corridor it produces is a reach set with two failures nobody separates: stroked on the page, one width covers 190 to 471 kilometres of ground along a single route; computed in closed form, the formula stops being the area at a width the route's own length fixes, and eventually claims more ground than the sphere has.

paths · Reach

A 6° query against a cube scheme, and the cells it fetches. The cells of a tangent-warped cube scheme at level 5, with the 29 cells a query of 6° radius touches shaded. The disc's own area is 16.84 cells; the count is 29, because every cell the disc's boundary crosses is fetched as well as every cell inside it. In Hilbert order those cells form six contiguous ranges of identifiers, which is six range scans, and the span from the lowest to the highest covers 91 cells against the 29 wanted. Drawn in Mollweide, with the mesh shown only near the query.

A query is a disc, and a disc is not a cell

Everything a cell system does is an address lookup except the one question anybody actually asks it: find everything within five kilometres of here. That is a disc, and the number of cells it fetches is not its area divided by a cell's — at the radii a query is really made at, it is three to seventeen times that.

applied · Cells

Named alongside it

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

Tolerance Address Aggregation Anisotropy Area Boundary Cell Closed form Convention Corridor Coverage Cut locus

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