Square heightfields are fine for many purposes, but eventually some applications need spherical
surfaces like the earth.
one possibility: apply the same kind of RTIN approach as the conventional
CLOD algorithms to a spherical tessellation composed of right triangles, e.g.
the tetrakishexahedron (vrml),
basically a cube with its faces split into 4 right triangles, though it
could also be thought of as a tetrahedron with each face split into 6 equal
right triangles
however, the triangles do not remain perfect right triangles after the
first subdivision
space simulator for the real planets of the solar system
has paging and CLOD for the planet elevations and textures!
he describes: "I have multiple-level texture and elevation blocks. The
bottom level is 256x128, after that all tiles are 254x254 + a 1 pixel border.
I use separate passes for the color and bumpmapping, which are loaded/generated
in a background thread. Mapping is cylindrical, and all tiles are optional
(you can leave out high-detail tiles at the poles, for instance)."
"The algorithm is ROAM with a octahedron mesh. The vertex
coordinates are generated from the texture coordinates. The first 5 or so
levels are precomputed in a 128KB tree. Vertex coords are float, tex coords
are integer."
T.
Gerstner. Multiresolution Compression and Visualization of Global Topographic
Data (.pdf)
academic paper describing a ROAM-like tessellation of the globe based
on regular geographic coordinates
oceans are depressed to preserve coastlines
a global error values allows decimation (compression) of the whole dataset
before runtime, the tree structure allows high-resolution insets (their
example uses the city of Bonn)
"a quadtree layout of regular shaped quadratic meshes [..] capable
to generate everything on the fly, best for procedural generated
planetary bodies, but it is capable for real planets too."
A planetary rendering demo (closed source) which shows spherical LOD,
bump mapping, noise detail texture, atmospheric glow. Demo datasets
of Mars and Earth.
Apparently last updated in 2003, no current contact for author.
Spherical Earth, Continuous LOD and Paging of Elevation and Texture
Very little software is yet capable of doing all of these things together.
Here are the currently known implementations:
There
are many schemes for subdividing and indexing feature on a sphere. Not
directly related to LOD, but more likely useful for other operations such as
optimized geographical queries.