The Dansēji (or Danseiji; /dɑn.ˈseɪ.dʒi/; literally "Elastic Earth") projections are the optimal map projections, in the most literal sense of the word. Each one is represented by a fine mesh of vertices that represent an elastic spherical surface. That surface is allowed to come to rest, thus reducing the distortions of size and shape throughout the mesh.
For a more complete explanation, see this blog post. For the newer map projections based on the same principle, see my repository for the Elastic projections.
All of the source code and output data files are released to the public domain (see LICENSE for more information). The Dansēji projections are defined by the CSV files found in output/. An example Python script using these to create SVG maps can be found in src/example/.
Each Dansēji projection is created, in theory, with an inifintely thin spherical shell of an elastic material, representing the Earth's surface, which is then constrained into a plane. The initial configuration is either an equatorial Hammer projection, for a more conventional map, or an oblique azimuthal equidistant projection, for a more optimal one. This surface is then deformed in order to mimimize the elastic potential energy under a Neo-Hookean model. In practice, I do this using finite element analysis and an L-BFGS scheme.