Smooth Interpolation Function in One Dimension | Smooth Interpolation Function E1

Comments · 457

• KR

  @krause-314 · 4 years ago · pinned

  Is there a name for this kind of interpolation so that I can search more about?

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• ED

  @edgelernt4021 · 4 years ago

  <a href="https://www.youtube.com/watch?v=vD5g8aVscUI&amp;t=476">7:56</a> “It is too big to fit in the margin” - Pierre de Fermat has entered the chat

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• XA

  @Xammed · 4 years ago

  The subtle humor in this is incredible

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• KA

  @kallethoren · 4 years ago

  The &quot;Can we do any better?&quot; with Lara Croft got me good

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• OF

  @offscript1675 · 4 years ago

  Safe to say, I’m confused

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• PI

  @PitumanLife118 · 2 years ago

  bro really performed surgery on functions

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• TE

  @TechSY730 · 4 years ago (edited)

  Good stuff.<br>Kind of gives insight as to why finding an &quot;analytic&quot; continuation (but for this video not really as we are only dealing with reals, but more generally) can be difficult. Why &quot;infinitely differentiable&quot; is such a constraining condition.<br><br>(Hopefully) Constructive criticism:<br><br>I found myself losing track of which &quot;Greek letter function&quot; was modeling what parts of our goal.<br><br>Like it would be helpful to have a line like &quot;φ will be the continuous step function used to interpolate&quot; or something when you defined the function.<br>Same for the ψ function too.<br><br>If you did already describe it, there was enough time between when you stated it and performing the proofs and derivations (<a href="https://www.youtube.com/watch?v=vD5g8aVscUI&amp;t=510">8:30</a> ish) that it deserved having a reminder at that point.

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• JO

  @joluju2375 · 4 years ago

  I had to play the video twice to finally understand that the solution you expose is what is known as &quot;crossfading&quot; in audio engineering, and that most of the video is devoted to how to easily build a decent S-shape transition signal. I appreciate when ideas and intentions come first in plain language, and the maths come after, it&apos;s more easy for me to follow. However, I subscribed to your channel. Please, keep the pace slow, and the music down ! &nbsp; &nbsp;:D

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• LU

  @LukePalmer · 4 years ago

  Very beautiful technique. &nbsp;I also love that that function e^(-1/x) is bonkers in the complex plane so this argument totally breaks down on the complexes.

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• WY

  @wyrmhero4275 · 4 years ago

  This video is just mindbowing, never thought that there would even be a way to construct truly smooth interpolation. Also, your visuals and presentation is really great, loved it. Keep going!

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• AL

  @AlexanderVulpes · 4 years ago

  This is really surprising! When I first saw the title I figured smooth transitions would be impossible, but here we are lol

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• AV

  @AvesNova · 4 years ago

  Thank you so much! This has been in the back of my mind for a while now. Great explanation.

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