Useful functions for game designers - Cosine Interpolation

While working on a previous video about Lagrange interpolation, I figured that it would be an interesting exercise to go over some other kinds of interpolation. In this video we go over piecewise linear, and cosine interpolations.

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Starting point:

End Point:

========== Other videos to watch ==========

Linear interpolation:

Lagrange interpolation:

Or using smooth minimums:

Or using Hermite interpolation (smoothstep):

[Haykke]

"but first lemme just take a sip of tea"
*proceeds to grab a jug of tea*
this man is truly built different

[jeffcummings]

Your teaching takes me into a mathematical world where the equations are as easy to manipulate as play doh! Thank you so much for sharing!

[roberth]

Nice! The advantage of Cosine over Lagrange Interpolation is that new points can be added by only touching the last point and adding a cosine function to it.

[robotics_and_stuff]

This was very helpful! I have used this to make smooth motions in the UI system I’m working on. Thanks a lot!

[daviddawkins]

Excellent. I like the way you derive these from scratch, very cleverly done. I'd prefer quieter music, it's quite distracting

[GonzoGonschi]

thanks a lot buddy, that you make this nerd wisdom accessible for all us mortals

[gchinmayvarma]

Beautiful Beautiful!!!
Bezier interpolation, using things like Lerp() is also another beautiful way for a value x to approach another value y! It makes it smooth and i use it almost everywhere in UI design ( for example a text appearing form bottom to the center of the screen) !
Its great to see someone making such great vids! love ur vids

[kolosso]

I love this series your doing, man! If I ever need a curvy line I'll know where to come back to

[Enherj]

Great stuff! More interpolations, please, including Bezier.

[hualee]

Great stuff! More interpolations, please! Newton interpolation, piecewise linear interpolation, Hermite interpolation, and cubic spline interpolation

[CodAv]

That's actually a great interpolation for some kind of node editor, as in Blender, where you connect outputs to inputs on rectangular shapes (nodes). Looks best in such applications if lines end in a 90° angle to the box's border.

[piranha]

You would make such a great math teacher!

[SayHelloToGrux]

Hello, BigWIngs! Great video as usual, thank you so much! Can you please recommend any useful books on applied mathematics for programmers to continue exploring such a thing! Thank you!

[Adeith]

I love these videos. Could you also look at the natural spline, where the second derivative is zero at the points. It has a really nice look to it.

[SheepyPeka]

learning about these small things is really cool and I get to learn more really cool techniques at a good pace from you .w.
keep up the great work yo>

[Scy]

Can you do a video on bezier curve as well? Not sure if it applies to 3d graphics a lot, but it is useful in some structural and graphic design at least.

[bubu]

"let me take a sip of tea" takes out a 2 liter glass of tea 💀

[adrianshawuk]

This is great but the music is very loud at the start.
I'm enjoying your shader stuff too. Subscribed

[gabitheancient]

that's very cool, didn't know about that

[AlexSmolyankin]

Very nice. I'm wondering can this interpolation be implemented for surface in 3D?