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Reflection mapping 158
Cube mapping
Cube mapping and other polyhedron mappings address the severe
distortion of sphere maps. If cube maps are made and filtered correctly,
they have no visible seams, and can be used independent of the
viewpoint of the often-virtual camera acquiring the map. Cube and
other polyhedron maps have since superseded sphere maps in most
computer graphics applications, with the exception of acquiring
image-based lighting.
Generally, cube mapping uses the same skybox that is used in outdoor
renderings. Cube mapped reflection is done by determining the vector
that the object is being viewed at. This camera ray is reflected about
the surface normal of where the camera vector intersects the object.
This results in the reflected ray which is then passed to the cube map
to get the texel which provides the radiance value used in the lighting
calculation. This creates the effect that the object is reflective.
HEALPix mapping
HEALPix environment mapping is similar to the other polyhedron
mappings, but can be hierarchical, thus providing a unified framework
for generating polyhedra that better approximate the sphere. This
allows lower distortion at the cost of increased computation [1] .
History
Precursor work in texture mapping had been established by Edwin
Catmull, with refinements for curved surfaces by James Blinn, in 1974.
[2] Blinn went on to further refine his work, developing environment
mapping by 1976. [3]
Gene Miller experimented with spherical environment mapping in
1982 at MAGI Synthavision.
Wolfgang Heidrich introduced Paraboloid Mapping in 1998 [4] .
Emil Praun introduced Octahedron Mapping in 2003 [5] .
Mauro Steigleder introduced Pyramid Mapping in 2005 [6] .
Tien-Tsin Wong, et al. introduced the existing HEALPix mapping for rendering in 2006 [1] .
A diagram depicting an apparent reflection being
provided by cube mapped reflection. The map is
actually projected onto the surface from the point
of view of the observer. Highlights which in
raytracing would be provided by tracing the ray
and determining the angle made with the normal,
can be 'fudged', if they are manually painted into
the texture field (or if they already appear there
depending on how the texture map was obtained),
from where they will be projected onto the
mapped object along with the rest of the texture
detail.
Example of a three-dimensional model using
cube mapped reflection