Added Panini Projection to pt_projection

[RandomDude4]

Added the Panini projection, specifically the "cylindrical stereographic" version with the parameter D = 1.0

D can be any value in order to seamlessly scale between projections: D = 0 gives the rectilinear projection D = +inf should give the "cylindrical orthographic projection"

More info in this paper on why Panini is natural for the human eye: http://dx.doi.org/10.2312/COMPAESTH/COMPAESTH10/009-016

Question: Perhaps the Panini and Stereographic projections should be given a lower pt_projection values, as these are the most useful next to rectilinear? Cylindrical, mercator, etc. are just for demonstration, but very disorienting to use in an actual game.

[apanteleev]

Thanks, I'll give it a try. One thing stands out: it's spelled Pannini (double N). :)

Perhaps the Panini and Stereographic projections should be given a lower pt_projection values, as these are the most useful next to rectilinear?

Ok, sure.

[RandomDude4]

One thing stands out: it's spelled Pannini (double N). :)

When I saw your comment I couldn't believe that I had been misspelling it all this time!? But after checking online, both Unity and Unreal Engine documentation spell it "Panini" with one "n", (fyi: they have only implemented it as a post process, not natively like here, so in their case it results in a blurred image) https://docs.unity3d.com/Packages/com.unity.render-pipelines.universal@7.1/manual/Post-Processing-Panini-Projection.html https://docs.unrealengine.com/4.26/en-US/RenderingAndGraphics/PostProcessEffects/PaniniProjection/

But you are right that the name of the original painter Gian Paolo Pannini (1691-1765), which the projection is named after, does have the double "nn". Let me know which version you prefer, and I will update the code and documentation accordingly.

Do you have a preferred order of the projections in pt_projection? Rectilinear and Pannini are probably the most commonly found in gaming, stereographic is also popular as far as I know. The others are rarely used when playing games, more for texture mapping etc.

This is a suggestion: pt_projection 0 -> rectilinear pt_projection 1 -> panini pt_projection 2 -> stereographic pt_projection 3 -> cylindrical pt_projection 4 -> equirectangular pt_projection 5 -> mercator

[apanteleev]

Regarding the spelling - indeed, I see the single-N and double-N versions used interchangeably in various sources. I don't have a strong preference, but since both Unity and Unreal use the single-N version, let's do the same.

Your suggestion for the projection order looks good.

[RandomDude4]

I renumbered all the cases according to the suggestion above. I also noticed a redundant "default:" case in main.c that I removed.