provide some readme text

README.md

@@ -2,15 +2,38 @@ Sub-Projects
 ------------
 
 Sub-projects in this repository:
-- The "earth" project for experimenting with texture mappings
+- Experiments with texture mappings
   ([source](./earth/), [web app](https://hcschuetz.github.io/sphere-texturing/earth/dist/))
-- the "map transformations" project experimenting with shape and texture
-  transformations
+- A presentation on map/texture transformations
   ([source](./map-transformations/),
   [web app](https://hcschuetz.github.io/sphere-texturing/map-transformations/dist/))
 
 
 Texture Layouts For Spheres
 ===========================
 
-TODO (long/lat sphere vs. icosphere vs. octasphere)
+
+The most common way to render a sphere is based on the latitude/longitude grid
+as it is used for the earth:
+Select two opposite points on the sphere as the "poles",
+a bunch of equidistant "meridians", and a bunch of equidistant "parallels".
+Introduce a vertex at each intersection of a meridian and a parallel
+and connect neighboring vertices.
+This divides the sphere into a set of quadrangles.
+Dividing each quadrangle along one of its diagonals
+gives a triangulation of the sphere.
+
+The natural texture for such a "lat/long sphere" is a map with a
+[equirectangular projection](https://en.wikipedia.org/wiki/Equirectangular_projection).
+This is easy to implement and good enough for many applications.
+But while the distance between meridians gets smaller and smaller near the poles
+on the sphere,
+the meridians have a constant distance on the map.
+This leads to some drawbacks:
+- Equirectangular maps are heavily distorted.
+- Texture memory is wasted.
+- Triangles around the poles are degenerated on the sphere
+  and thus the corresponding parts of the texture/map are not rendered.
+
+To avoid these drawbacks
+this project investigates texture mappings based on octaspheres and icospheres.