Concept

Polyconic — where it appears

A projection giving every parallel its own cone, so that each is drawn at true scale and none of the classical properties holds anywhere. It was the United States' standard for much of the nineteenth century and it fails both the conformality and the equal-area tests.

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

American polyconic. The graticule of the American polyconic projection at 30° of longitude and 15° of latitude. a different tangent cone for every parallel — true to scale along all of them, and along the central meridian. It is neither conformal nor equal-area.

The projections that gave up being one thing

The polyconic is built from a different cone for every parallel, which means it is built from no cone at all. It preserves nothing the usual tests look for, it has an exact property neither of them measures, and its sheets do not fit together — a defect discovered in the field rather than at the drawing board.

families · Families

Which way Sinusoidal stretches the ground. The major axis of Tissot's indicatrix at 180 points, drawn as a stroke rather than an ellipse because the argument is the orientation. Longer strokes mark more elongated indicatrices. The direction departs from the graticule by up to 44.4°, so the scale "along the meridian" is not the scale along the direction that is actually stretched most.

Distortion has a direction

Tissot's indicatrix is an ellipse, an ellipse has an orientation, and the orientation is never reported. On most projections it is not along the meridian, on a conformal one it does not exist at all, and both facts are computable from the same four derivatives as everything else.

distortion · Tissot

Named alongside it

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

Anisotropy Bearing Cone Conformality Cylinder Developable surface Graticule Invariant Jacobian Principal direction Principal scale factors Shape distortion

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