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Show HN: A WebGL-based Complex Expression Parser and Plotter
- BenoitP 11y agoVery nice! I have spend the last hour trying to display the Poincaré disk[1], but to no avail. I have z * ( cos(1.57 * (a^2+b^2+1)^(1/2)) / sin(1.57 * (a^2+b^2+1)^(1/2)) ), which project the coordinates to the infinite on a circle. But this is only a fancy zoom, straight lines are not projected to circles. [1]https://en.wikipedia.org/wiki/Poincar%C3%A9_disk_model https://en.wikipedia.org/wiki/Poincar%C3%A9_disk_model
- BenoitP 11y agoI also have this: ((i-(z)/10000)/(i+(z)/10000))^(50000) which is sort of like the Poincaré half plane
- marcosscriven 11y agoFrom the docs: "It's important to note that When rendering with these infinitely-tiled images, the mapping that is rendered is actually the inverse of the function given. This is because it is prohibitively expensive to compute images of the function itself. (In fact, we are rendering a kind of "pull-back".) Specifically, when rendering a pixel in the image, the location of that pixel in the complex plane is passed to your function, which produces a complex value. That transformed value specifies a location in the original image. This procedure is fast, but plots the inverse of the function given. So, if you want to plot e.g. log(z), then you should instead put in e^z."
- brandonpelfrey 11y agoYeah, this seemed kind of "unfortunate" when I started this project, but it still turned out to be an interesting/fun toy. The issue is that when you compute where f(z) sends each point in the complex plane to, you would need to color in the pixel corresponding to that transformed point. f() is user-defined, so it could be a very weird function that could cover some portions of the image we're trying to draw but not others, etc. Moreover, even if I had some kind of procedure for determining which x's to sample so f(x) lay inside the image we're trying to draw, it's not amenable to GLSL. This is typically referred to scatter vs. gather-type operations.
- arcatek 11y agoNote that you can apparently use the `t` variable to express time. Ex: t*z
- brandonpelfrey 11y agoI should probably try to find a way to make it clearer what all can be done, or make it more obvious where the documentation is ("t" is mentioned there.)
- Keyframe 11y agoHeh nice, here's a rotozoomer: http://brandonpelfrey.github.io/complex-function-plot/?expression=eippXigxK3QpK3oqdA== http://brandonpelfrey.github.io/complex-function-plot/?expre... edit: a nicer rotozoom: http://brandonpelfrey.github.io/complex-function-plot/?expression=KHoqNCkqaV4oMSt0KSsoeipwaSkqdA== http://brandonpelfrey.github.io/complex-function-plot/?expre...
- VikingCoder 11y agoz ^ z I love thinking about this, as it goes negative.