Years later my boss was telling me how satisfied he was that he could throw any problem in my general direction and it would be gone in no time. There is nothing like the risk of losing his work permit to motivate a young guy to work himself down to a crisp, all for peanuts.
First take a sample in each corner of the pixel to be rendered (s1 s2 s3 s4), then compute:
coverage=0.5 + (s1+s2+s3+s4)/(abs(s1)+abs(s2)+abs(s3)+abs(s4))/2
Relative to the standard method it is expensive to calculate. But for a modern GPU it is still a very light workload to do this once per screen pixel.
It is indeed scale invariant but I think you can do better, you should have enough to make it invariant to any linear transformation. The calculation will be more complex but that is nothing compared to evaluating the SDF
You should be pretty close though. For a linear function you can just calculate the distance to the 0 line, which is invariant to any linear transformation that leaves that line where it is (which is what you want). This is just the function value divided by the norm of the gradient. Both of which you can estimate from those 4 points. This gives something like
dx = (s2 - s1 + s4 - s3)
dy = (s3 - s1 + s4 - s2)
f = (s1+s2+s3+s4)/4
dist = f / sqrt(dx*dx + dy*dy)You don't technically need 4 reads per pixel either, for instance you can process a 7x7 group with a 64-count thread group. Each thread does 1 read, and then fetches the other 3 values from its neighbours and calculates the average. Then the 7x7 subset of the 8x8 write their values.
You could integrate this into the first pass too, but then there would be duplication on the overlapped areas of each block. Depending on the complexity of the first pass, it still might be more efficient to do that than an extra pass.
Knowing that it's only the edges that are shared between threads, you could expand the work of each thread to do multiple pixels so that each thread group covers more pixels the reduce the number of pixels sampled multiple times. How much you do this by depends on register pressure, it's probably not worth doing more than 4 pixels per thread but YMMV.
Is this intentional? To me this is an opiniated (aka artistic preference) feature preserving method not the perfect one.
Btw the common visualization has a source and an author:
https://iquilezles.org/articles/distfunctions2d/ https://www.shadertoy.com/playlist/MXdSRf
I'm not grasping what you're referring to here.
Having some weird mid-length discontinuity in the edge direction for me. Not just perceptually.
Maybe I’m misunderstanding something here or have a different idea what the goal of that exercise is, but I would expect some pixels to turn near white near the center towards that gap sector.
The following stackexchange answer addresses that question rather well: https://gamedev.stackexchange.com/a/130933/3355 As you see, dFdx and dFdx are not exactly derivatives, these are discrete screen-space approximations of these derivativities. Very cheap to compute due to the weird execution model of pixel shaders running in hardware GPUs.
On the other hand, if you want something that looks roughly the same no matter which color you use, counteracting such oddities of perception is certainly unavoidable.
By the way, since the article mentions ellipse distance approximations, the fastest way to approximate distance to an ellipse is to use a trick I came up with based on a paper from 1994 [1]: https://github.com/servo/webrender/blob/c4bd5b47d8f5cd684334... Unless it's changed recently, this is what Firefox uses for border radius.