Octahedron Map

Since the sphere is a 2-manifold rather than a 3-manifold, a bijection can be formed between the points on the sphere and the 2D texture coordinates.

Real-Time Rendering Fourth Edition / 10.4.4 Other Projections

L1 (Manhattan) norm

Applications

Point Light Shadow Mapping

// TODO

Normal Representation

// Real-Time Rendering Fourth Edition / 16.6 Compression and Precision
// Evidently, a bijection can be formed between the unit vectors and the points on the sphere. And thus, the projector functions can be used to compress the normals to 2D coordinates.

"Octahedral Encoding" of "3.8.3 Spherical Parameterizations" of PBR Book V4

References

[Engelhardt 2008] Thomas Engelhardt, Carsten Dachsbacher. "Octahedron Environment Maps." VMV 2008.
[Meyer 2010] Quirin Meyer, Jochen Sussmuth, Gerd Sussner, Marc Stamminger, Gunther Greiner. "On Floating-Point Normal Vectors." Computer Graphics Forum 2010.
[Cigolle 2014] Zina Cigolle, Sam Donow, Daniel Evangelakos, Michael Mara, Morgan McGuire, Quirin Meyer. "A Survey of Efficient Representations for Independent Unit Vectors." JCGT 2014.