Egg-Shaped Curves (2007)(nyjp07.com)
nyjp07.com
Egg-Shaped Curves (2007)
https://nyjp07.com/index_egg_E.html
5 comments
Rendering nerds will know and love Eric Veach's classic glass egg renders from his thesis (e.g. page 362): https://graphics.stanford.edu/papers/veach_thesis/thesis.pdf
A true classic.
We containerized an egg, scaled to a dozen on k8s, rewrote the chicken in Rust, and still couldn’t crack PMF—turns out all we needed was a shell script.
Anyone else into pink flamin' eggs? https://www.youtube.com/watch?v=VHzVHmmHHPk&t=65s
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Related reading:
Eggquations https://matheminutes.blogspot.com/2013/03/eggquations.html
Mathematically Designing an Egg https://konfou.xyz/docs/mathematically-designing-an-egg.pdf
Equation of Egg Shaped Curve II (Egg Shaped Curve proposed by Mr. Itou) https://nyjp07.com/index_egg_by_Itou_E.html
Anyone else into pink flamin' eggs? https://www.youtube.com/watch?v=VHzVHmmHHPk&t=65s
---
Related reading:
Eggquations https://matheminutes.blogspot.com/2013/03/eggquations.html
Mathematically Designing an Egg https://konfou.xyz/docs/mathematically-designing-an-egg.pdf
Equation of Egg Shaped Curve II (Egg Shaped Curve proposed by Mr. Itou) https://nyjp07.com/index_egg_by_Itou_E.html
I know I'm weird but I love posts like this. I keep thinking there should be a paper for solving any closed form curve but haven't found it yet. (Symmetric curves are 'easy' but asymmetric like the egg get complicated fast. Solving a bowling pin (for example) would be interesting)
I'm partial to the piriform curve [1], which I call the "gumdrop curve." I had a lot of fun trying to make a game where the characters were gumdrops. I could change either parameter (width or height) while keeping area constant, so I could have procedural animations of them stretching to give the impression of falling from a great height and such. (Keeping area constant is a basic principle in making animations believable.)
I didn't end up finishing the game but I learned a lot about programming UIs and using canvas-like interfaces.
If you turn up such a paper I'd love to take a look. It does seem like something that you could solve with gradient descent once you've guessed the right family of curves (eg Lissajous curves).
[1] https://mathworld.wolfram.com/PiriformCurve.html
If you turn up such a paper I'd love to take a look. It does seem like something that you could solve with gradient descent once you've guessed the right family of curves (eg Lissajous curves).
[1] https://mathworld.wolfram.com/PiriformCurve.html