Projecting a Regular Grid onto a Sphere or Ellipsoid

Abstract

This paper presents a new map projection intended for mapping regular Level-ofDetail structures like quad-trees, wavelets or Lindstrom/ROAM triangulations on a spherical/ellipsoidal earth. The projection maps the squares of regular structures to near-squares on the globe, even near the poles. The projection gives simple equations, visually pleasing graphic output and works well with familiar algorithms and data structures.

Global isolation by distance despite strong regional phylogeography in a small metazoan

“…For all sequences of known geographic origin decimal longitudes and latitudes were recorded with the aid of virtual Globe [50]. The distance between locations in kilometers was calculated with the following formula:…”

“…Distances between field sites were estimated using the great arc formulae for calculating distances on a spheroid, with a value of 6371.01 km as the mean radius of the Earth [ 49 ]. For all sequences of known geographic origin decimal longitudes and latitudes were recorded with the aid of virtual Globe [ 50 ]. The distance between locations in kilometers was calculated with the following formula:…”

Computations on an Ellipsoid for GIS

“…Aasgaard [1] describes a level of detail approach for tessellating the globe that produces identifiable vertical strips with boundaries along longitude lines. Within the strips, the tessellation -while fairly good from an aspect ratio perspective -has a fairly irregular topology.…”