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

Picture surface — where it appears

3 essays name this object, across 3 fields. What follows is each of them, and the objects they name alongside it.
plane — bend 0.0%cylinder — bend 6.0%stereographic — bend 3.5%equidistant — bend 4.5%equal-area — bend 5.1%equirect. — bend 5.7%120° across in every panelsame scene, same angle, six surfaces

No picture surface keeps everything

A picture has to be cast onto something, and every candidate surface destroys something different. Six of them are measured here on the same three properties, and the corner of the plot where a surface pays nothing is empty — not because nobody has thought of one, but because a theorem says there is none.

curved · surface flat picture plane — straight lines stay straightcylindrical picture surface — even stretch, bowed linesone scene, two picture surfacesneither is the distorted one

When the picture surface is not flat

A flat picture plane keeps straight lines straight and stretches the edges without bound. A cylindrical one spreads the stretch evenly and bends every straight line that is not through the axis. Neither is the distorted one — they are answers to different questions, and the choice decides what a wide view can be.

viewing · surface 15°30°45°60°85°the rim: 48.61° from straight upbeyond it: the bottom, reflected45° of sky0.469460° of sky0.370275° of sky0.211485° of sky0.0738area scalen = 1.333, so the rim is at asin(1/n) = 48.61°area scale 0.563 at the centre, 0.0738 at 85°

The sky inside a cone

From under water the whole sky — every direction out to the horizon — arrives inside a cone of 48.61°. Outside it the surface is a mirror. That cone is a picture surface, and it has a distortion no surface in the curved field has — an area scale that runs to zero.

refraction · snellwindow

Named alongside it

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

AnisotropyArea scaleConformalEquirectangularFisheyeHorizonBeltramiCritical angleCylindrical projectionEdge stretchGnomonicPanorama

All concepts