A.2.3.1 General

26.1183GPPRelease 17TSVirtual Reality (VR) profiles for streaming applications

Tools: ARFCN - Frequency Conversion for 5G NR/LTE/UMTS/GSM

The 3D XYZ coordinate system as shown in Figure A.1 can be used to describe the 3D geometry of ERP and CMP projection format representations. Starting from the center of the sphere, X axis points toward the front of the sphere, Z axis points toward the top of the sphere, and Y axis points toward the left of the sphere.

Figure A.1: 3D XYZ coordinate definition

Note: The text in this Annex is based on JVET output document (JVET-H1004: Algorithm descriptions of projection format conversion and video quality metrics in 360Lib (Version 5)) with simplifications to only two projection types which are used in the present document and further fixes regarding misalignments. C++ implementation of the concepts described by this annex is available in 360Lib Software: available at: https://jvet.hhi.fraunhofer.de/svn/svn_360Lib.

The coordinate system is specified for defining the sphere coordinates azimuth (ϕ) and elevation (θ) for identifying a location of a point on the unit sphere. The azimuth ϕ is in the range [−π, π], and elevation θ is in the range [−π/2, π/2], where π is the ratio of a circle’s circumference to its diameter. The azimuth (ϕ) is defined by the angle starting from X axis in counter-clockwise direction as shown in Figure A.1. The elevation (θ) is defined by the angle from the equator toward Z axis as shown in Figure A.1. The (X, Y, Z) coordinates on the unit sphere can be evaluated from (ϕ, θ) using following equations:

X = cos(θ)*cos(ϕ)

Y = cos(θ)*sin(ϕ)

Z = sin(θ)

Inversely, the longitude and latitude (ϕ, θ) can be evaluated from (X, Y, Z) coordinates using:

ϕ = tan^-1(Y/X)

θ = sin^-1(Z/(sqrt(X²+Y²+Z²)))

A 2D plane coordinate system is defined for each face in the 2D projection plane. Where Equirectangular Projection (ERP) has only one face, Cubemap Projection (CMP) has six faces. In order to generalize the 2D coordinate system, a face index is defined for each face in the 2D projection plane. Each face is mapped to a 2D plane associated with one face index.