Concept

Equidistant projection — where it appears

The fisheye whose picture radius is proportional to the angle off axis, which measures angles off the paper with a ruler and preserves neither shape nor area.

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

02468020406080angle off the optical axis (degrees)area scale, relative to the centreplanecylinderstereographicequidistantequal-areaequirect.measured by differencing on the spherethe plane leaves the frame

Every fisheye is a different rule

The word "fisheye" names a shape of lens and not a projection. There are several, they disagree with each other by tens of per cent at the frame edge, and each is the right answer to a different question — one is a protractor, one is a counting instrument, one preserves shape. Which one a lens implements is a fact about that lens, and it is rarely printed on the barrel.

curved · fisheye
fitted conic: a circle to 1e-9stereographicdashed: the fit, not the samples

The arcs a curvilinear drawing uses

The taught way to draw a very wide view by hand is to run every straight edge of the world as a circular arc. That recipe has been repeated for sixty years without a surface attached to it, and it turns out to name one exactly — fitting a general conic to the image of a straight line returns a circle to nine decimal places under stereographic projection and returns nothing like a circle under any other surface this site has.

curved · curvilinear
planeevery linecylinderone parameter · parallelno meeting pointstereographicone parameter · concurrentthey meet to 1e-12equirect.one parameter · parallelno meeting point3 of 4 keep a curvethe signature has three values, not eight

The lines a surface leaves alone

Only the plane draws every straight line straight, which this site has measured and which gets read as though a curved surface bent everything. It does not. Every curved picture surface here keeps a one-parameter family of world lines exactly straight, and the family is a curve on the sphere of lines rather than a region of it — so a grid of samples finds none of it, which is what the first version of this measurement reported.

curved · straightfamily

Named alongside it

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

AnisotropyArea scaleBeltramiConformalDemonstrationEqual area projectionfield of viewGnomonicPicture surfaceStereographic projectionStraight familyCanopy photography

All concepts