Concept

Panini projection — where it appears

A one-parameter family of picture surfaces projecting onto a cylinder from a point behind its axis, keeping verticals straight at every setting.

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

d = 0d = 0.5d = 1d = 2d = 4d = 0straight48.06° angle×17.80 aread = 0.54.81% bend23.08° angle×4.66 aread = 17.21% bend16.84° angle×2.65 aread = 29.61% bend23.13° angle×1.57 aread = 411.54% bend32.71° angle×1.73 areaa general straight line · worst angle · area range, over the field130° acrossangular minimum at d = 1.00

One parameter between two surfaces

Wide architectural views are usually made on a projection with a number attached to it — a family running from the flat plane at one end toward the cylinder at the other, with everybody using the value one. That value has never been given a geometric defence. Measured across the family on this site's own battery, the worst angular error over the field has a minimum, and the minimum is at 1.04.

curved · panini
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.

AnisotropyConformalCylindrical projectionDemonstrationPicture surfaceStereographic projectionStraight familyArea scaleBeltramiCube mapDegeneracydegrees of freedom

All concepts