texture mapping

Spherical Texture mapping

Submitted by admin on Fri, 2007-03-30 18:43.

Spherical Textures
courtesy of vterrain.org



There are many ways to apply a texture map to a sphere.  It is an important process because of applications such as texture-mapping the entire surface
of the earth.

  • naive approach: directly map latitude-longitude onto sphere
    • source: a single rectangular texture with a proportion of 2x1
    • uv mapping: u goes from 0 to 1 around the equator, v goes from 0 to 1 from pole to pole
    • pro: simple, most data sources are already in this format
    • con: wastes the majority of the texture resolution at the poles, where
      it is usually least needed
    • BlueMarbleViewer uses this approach
  • cubic mapping
    • source: 6 textures corresponding to sides of a cube surrounding the sphere
    • uv mapping is projected (e.g. with Gnomonic Projection) from the surface of the sphere to the sides of the cube
    • pro: more evenly distribution of texels than the naive approach
    • con:
      • the projection is a non-linear warp, making the computation difficult
      • still has wide variation in ratio of texels/surface area
  • Omnitect mapping
    • like cubic mapping, uses four equatorial textures and two polar
    • however, the equatorial textures use a direct lat-lon mapping, and the poles are treated specially by joining four spherical right triangles of the top and bottom latitudes
    • pro: takes advantage of simple direct lat-lon mapping for most of the non-polar surface
    • con
      • complicated special cases for the tile boundaries
      • two types of mapping with different requirements for subdivision and projection
    • detail: see slides on global tiling system
  • icosahedral mapping
    • like cubic mapping, but using an icosahedron
    • source: pairs of the icosahedron's faces can be joined into quads, for 10 square source textures
    • uv mapping: uv is simply (0,0), (1,0), (0,1) at the corners of each triangular face
    • pro:
      • less distortion than other approaches, evenly distributed texels/surface area
      • elegant system of identical regular triangles
    • con:
      • rendering must explicitly store and draw all 20 faces of the icosahedron
      • more tile boundaries to deal with
    • when applied to the earth with boundaries arranged to avoid breaking land masses, this is known as Buckminster Fuller's Dymaxion Projection
    • this is now implemented in the VTP software
      • a pre-processing utility projects a conventional earth texture map onto 20 faces (10 square texture maps)
      • at runtime, spherical icosahedron is created, with one mesh per face, in Enviro
  • octahedral
  • Aasgaard's map projection
    • developed for the SINTEF Virtual Globe, Rune Aasgaard's map projection page has a great PowerPoint presentation illustrating the approach, example source code of the transformation, and other supporting documents
    • basically maps a quadtree onto a Mercator-like projection, with the depth
      of the tree's branches decreasing towards the poles
    • benefit is that the texels stay close to square
    • disadvantage is that the poles behave badly (distortion, wasted texture memory) which is often not a problem since they are "small and usually insignificant"
    • published academically as "Projecting a Regular Grid onto a Sphere or Ellipsoid", Rune Aasgaard, in: "Advances in Spatial Data Handling", Dianne Richardson and Peter van Oosterom (eds.), Springer-Verlag 2002, pp 339-350

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