Math for Game Programmers: Fast and Funky 1D Nonlinear Transformations

In this 2015 GDC tutorial, SMU Guildhall's Squirrel Eiserloh takes a dive into the world of 1D nonlinear transformations to help game programmers make better games.

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[graphics_travelers]

Shame, he should have more time for these kind of presentations. His work is priceless.

[awoidf]

What a legend
He doesn't even waste time to tell me what his name is. So I had to go back and look it up to look up his other talks.

[thiagooliveira]

Quadradic is 2nd degree... because it comes from quadrado(square). Thats not a bad nomenclature, the confusion is caused by english mixing germanic and latin words...

[Dspectre]

the more i rewatch this, the more valuable it appears to be to me.

[seditt]

Dude, this is great for figuring various jump arcs for a 2D(or 3D I guess) Platformer inorder to implement Variable Gravity. You just implement where you are in _dt in the jump over all and you would get your perfect Gravity value so your player moves in whatever arch you define. Very nice talk.Simple and easy enough that a cave man like me could understand it.

[KKomalShashank]

Squirrel Eiserloh was my game programming professor at SMU Guildhall. He was the best teacher I ever had. The most amazing person, who explained complex concepts in such a cool, interesting and easy-to-understand manner. Everyone has their No. 1 teacher that they remember fondly for the rest of their lives. For me, that teacher is Squirrel Eiserloh.

[primevst]

you guys should check out the 'tunable normalized sigmoid function'. It can represent most of these shapes with just a change in a constant. Can be very usefull

[cdanek]

Small error in the BellCurve6 tween - you need to Flip(SmoothStop3) instead of just using SmoothStop3 otherwise you get a cumulative function (an S curve looking thing).

[davidpike]

Excellent talk, especially when you pause it and code it live as well. Thank you!

[youtubehandlesux]

What great timing this got recommended to me. Just finished programming almost all the linear transformation stuff for my game and a non-linear tutorial appears

[brianviktor]

Excellent! I was exactly looking for some of these functions, and the performance update on power with mix is really nice to know. I am doing procedural generation for creating galaxies, and I needed something very specific (the Arch namely). The added toolkit will be very helpful in general, as I use all sorts of such functions a LOT. Plus now I know inserting 2 inverse-functions (1-x) is actually not obscene.

[KimboKG]

12:05 didn't noticed this last time I watched. Now I understood the purpose of this talk.

[DobinSergei]

Congratulations 🎉 You have discovered Modulation.

[gurkiratsinghbajwa]

13:14 I think it should be opposite for higher powers (say >4). pow(x, n) function will do the calculation in O(logn) time but x*x*..x will do it in O(n) time.

[hanflingch]

Smoothstart2.2's relative error compared to x^2.2 just explodes as it narrows zero and is even for like 0.2 15% off. This wrecks total havoc with your color reproduction, in particular given the fact that the x^2.2 is already a quite poor approximation to the sRGB gamma transfer function, which already suffers huge relative errors.

[synystersocks]

lovely accurate, effective efficient math for curves, thanks ^^ its hard to find better concepts than old dated ones ^^

[markemerson]

like the math but i really expected to see some code with the math applied to some game examples. example, vectors, lerping, shooting projectiles, closest neighbor etc etc..

[ffs]

It is surprising how much personality non-mathematicians often attach to such abstract concepts as multiplication or power functions. This is an interesting perspective on how to achieve fast and ‘good-looking’ transformations, but I am slightly worried about the attachment to particular cases for educational purposes and not recommending any general ideas as further reading or at least references. I would be happy to hear some remarks about division vs multiplication (powers are expensive, but what about reciprocals?) because this basic operation enriches the non-linear set a lot.

[jerrygreenest]

14:18 in Russian "quadrat[ic]" means "a square", so for us it doesn't actually sound weird, since X quadratic means literally "X squarish".
I don't really know why it's called quadratic in English though, - since you call a square "square", not "a quadrat" like we do, so you should be actually calling it:

x² = x squarish
x³ = x cubic
etc...

[shanmukhag]

Really good channel. Happy that I followed you guys, good work GDC.