shaunlebron
commented
6 years ago Hey thanks for your interest :)
However simple the projection, the math always comes out not really retaining that simplicity at a glance. Some projections I understood, but there were a ton of projections I was trying out without understanding how to derive them (I just pulled them from wikipedia and other projection libraries). Sometimes the math is impenetrable because they are by nature a compression of context that is hard to unpack. But the math isn't so important to understand as it is to learn how to apply them—via the forward/inverse coordinate mapping that I made sure was documented well here:
https://github.com/shaunlebron/blinky/tree/master/game/lua-scripts/lenses#lenses
If you are still interested in the math, the panini paper shows how it is derived:
So that's where the variable names came from:
- dscr = discriminant
- clon = cosine of longitude
- S = (not mnemonic)
The stereographic projection math is on wikipedia.
Regarding the equivalence of Panini and Stereographic, they are only equivalent in 2D (in the top-down diagrams). To clarify, both projection methods do the same thing shown below—but Panini does it for a cylinder, and Stereographic does it for a sphere. And if you take a horizontal slice at the center of a sphere and a cylinder, both slices are equal to the same circle, which is why they're equivalent in 2D, but they're formulas are different in 3D.
jokoon
18107
Hello,
First I want to thank you from working on this, it's really fascinating work and I want to thank you for sharing it. I having eye-ing it for a long time now.
I'm very interested in using the pannini projection in my project (170 degrees seems like a sufficient result), and I'd like to better understand how that shader works.
I've read the small summary here http://shaunlebron.github.io/visualizing-projections/ and I understand how it works. In blinky you talk about lenses and globes, but I still don't understand the low level details and I cannot connect the theory from the practice and the shader code.
In http://shaunlebron.github.io/visualizing-projections/ you state that pannini == stereographic, yet you have different functions for stereographic and pannini (stereographic_inverse, stereographic_forward, and panini_forward, panini_ray).
Variable names are not always self-descriptive (dscr, c, clon, S).
I guess I should start to use some paper and draw better geometry diagrams?
Your work would be much more valuable if you took a slight amount of time adding more comments about that code and its math. Sorry about asking to take time from your own!