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

Cubemap — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. leftfrontrightbackupdownacross the left/front seam: 1.80°, with each side straight to 7e-16corner area ×5.196anisotropy √3 = 1.7321 there

    Six flat pictures of everything

    There is one way to photograph the whole sphere and keep every straight line straight, and it is to stop using one surface. Six flat pictures at ninety degrees cover everything, each of them a perfect pinhole, and the price is paid entirely at the seams — where a straight line does not bend but kinks, by an angle that reaches 45 degrees and is exactly zero for the lines lying in the seam's own plane.

    part 3 · curved
  2. 42.0°27.3°13.5°13.5°27.3°42.0°leftfrontrightbackupdownmidpoint: 0°7 straight lines, at 60° to the seamworst 42.04° · midpoint 0°

    The kink at a seam

    A cube map is six flat pictures, so every great circle is drawn exactly straight inside a face — to 3e-15 of its chord — and breaks at the join. The break is a kink and not a bend, it is exactly zero at a seam's midpoint whatever the slant, and it is bounded by 2·atan(½) = 53.130° at the corner.

    part 4 · curved

All series