Bouncing Balls, Round Two: Logarithms?!

In this video we'll build the second easing function for a bounce. While I was building the first (with a loop, check link below) I became convinced that there must be a smarter way to do this. The way I came up with uses a logarithm, which gives us an infinite number of bounces, for the price of one! Logarithms are often a bit mysterious to people and therefore quickly forgotten after high school. In this video I hope to give you an intuition about how you can leverage a logarithm to do stuff that could otherwise get quite costly.

========== Timetable =================

0:00 - Intro 1:37 - Problems with Loops 3:01 - Intro to Logarithms 6:30 - Visualizing in ShaderToy 8:30 - Drawing Parabola 10:50 - Changing the Base 13:00 - Attenuate Bounces 16:15 - Undoing Deformation 21:45 - Start at the Top 24:50 - Bonus Time 27:02 - Outro

========== Social Media Links ==========

Twitter: @The_ArtOfCode Facebook: https://www.facebook.com/groups/theartofcode/ Patreon: https://www.patreon.com/TheArtOfCode ShaderToy: https://www.shadertoy.com/user/BigWIngs PayPal Donation: https://paypal.me/theartofcode FX Hash (NFTs): https://www.fxhash.xyz/u/The%20Art%20of%20Code

========== If you want to follow along ==========

Start point (if you want to follow along): https://www.shadertoy.com/view/NlXyzS End point: https://www.shadertoy.com/view/7lByDz

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

Let's get Bouncy! (loop version): ShaderToy for complete beginners: https://youtu.be/u5HAYVHsasc Writing a ray marcher: https://youtu.be/PGtv-dBi2wE ... https://www.youtube.com/watch?v=IKVM4DAQ840