>>13194394>>13196512>>13197437>>13198682these examples are all equally terrible.
they assume euclidian space in 3d without curvature. let me explain.
>>13196512this example probably shows it best.
the curvature is fine to start. what you then need to do, is project that 3d plane back on to 2d plane. that means there is "more space" around the sphere in 2d.
but, you'll say, that's obvious, but no, it isn't. it's the mesh that throws everything off. see, we start with squares, quadrilaterals with 4 equidistant sides. but as we approach the sphere, they aren't equidistant anymore in the picture.
to keep distances the same, the deformation would have to be displayed differently, making it better to understand conceptually.
in short, straight lines don't "snap back", but bend.
