There are an infinite number of projection methods, each having a unique effect on the final resolution. For example:
Non-adaptive: e.g. ERP, CMP. ERP benefits from mathematical simplicity, the spatial resolution of ERP images increase towards the poles. CMP avoids the singularity of ERP, but it sacrifices adjacency. Also, CMP still results in a suboptimal resolution distribution, with resolution increasing towards the corners of the cube and away from the forwards viewing direction.
Adaptive: e.g. Pyramid projection
J(\theta, \phi, 1) is the Jacobian Matrix of projection function f(\theta, \phi, 1). The resolution after mapping can be calculated as Equ. 1.
Therefore, some projection function can be derived by solving for the Jacobain given a resolution function.
To compare the performance of different projections, this paper proposes two metric: resolution and uniformity (the coherence of horizontal and vertical resolutions). Besides, they uses three weighted function: 1) forward: forward direction 2) fovea: viewport 3) empirical patterns