Rendering transparent geometry is problematic in real-time graphics as the most function for blending transparent geometry together requires perfect sorting of all geometry. This can be extremely problematic, especially for intersecting geometry where it might be impossible to correctly sort it. Therefore, a number of new algorithms that attempt to approximate or reproduce the result of sorted blending in an order-independent manner has been developed lately.
Fourier Opacity Mapped Order-Independent Transparency (FOMOIT) is a new algorithm which constructs an approximated visibility function for each pixel and stores it using Fourier series. It then uses these functions to calculate a weighted sum of colors for each pixel. Neither the visibility function nor the weighted sum requires the geometry to be sorted.
FOMOIT has better quality compared to Weighted Blended Order-Independent Transparency (WBOIT). Compared to Adaptive Order-Independent Transparency (AOIT), Fourier Opacity Mapped Order-Independent Transparency has a number of advantages. FOMOIT uses hardware functions that are more widely available, and can easily be tweaked to have better performance and memory usage at minimal quality loss. It can therefore be especially useful on older and/or weaker computers.
FOMOIT suffers from a few limitations and artifacts in certain cases. The first problem lies in the dependence on a tight depth range of the scene. This makes FOMOIT unfit for certain types of real-time graphics that require a wide depth range. The second problem is self-occlusion of geometry, which can cause incorrect weights to be calculated, resulting in color bleeding. We propose a workaround for this problem, but further research is encouraged in this area.
Our conclusion is that FOMOIT can, as long as the limitations of the algorithm are respected, produce higher quality results than AOIT while providing better hardware compatibility, performance and memory usage, and even in cases where AOIT provides better visual quality, FOMOIT can be used as a lower quality fallback for older and weaker computers.