Not sure if this is super relevant to the course, but seeing this slide knowing all of the previous content we've covered (namely sampling and frequency domain) reminded me of sinc interpolation (something I learned about in EE120 last semester)! I was wondering if we'd ever discuss this kind of interpolation in this class, since the topic seems relevant in the context of sampling and frequencies :D
GarciaEricS
One thing I was wondering about is how "smooth" this really is. By that I mean, is how many derivatives of the function does it take for the derivatives to not be continuous. From what I found here:
It seems like second derivatives are continuous but third derivatives are not continuous. This is interesting, because it still looks smooth. I guess smoothness is really only noticeable up to second derivatives.
lycorisradiatu
This slide reminds me of a really relevant video I saw earlier: https://www.youtube.com/watch?v=vD5g8aVscUI. It introduces the smooth transition function in one dimension.
aidangarde
One thing I was thinking about with smooth interpolation is how the cost function is derived. Some combination of computing power and time, space complexity, and how valuable accuracy and smoothness are in the resulting geometry. I wonder how there are ways to predict how many polynomials are needed for interpolation without explicitly solving it for each problem.
RishSharma7
This slide presentation (https://www.mpp.mpg.de/~caldwell/fs06/Lecture3.pdf) was really helpful for me to further understand the benefits of interpolation, and how different degrees of specificity result in different types of curves. I noticed that this particular analysis of the topic delved into Data Smoothing and Lagrange Polynomials. Not sure if I missed it somewhere, but will we be discussing these a lot in class (and possibly using them for our final projects)?
Not sure if this is super relevant to the course, but seeing this slide knowing all of the previous content we've covered (namely sampling and frequency domain) reminded me of sinc interpolation (something I learned about in EE120 last semester)! I was wondering if we'd ever discuss this kind of interpolation in this class, since the topic seems relevant in the context of sampling and frequencies :D
One thing I was wondering about is how "smooth" this really is. By that I mean, is how many derivatives of the function does it take for the derivatives to not be continuous. From what I found here:
https://stackoverflow.com/questions/58897691/why-does-the-second-derivative-of-a-cubic-spline-look-so-jaggy
It seems like second derivatives are continuous but third derivatives are not continuous. This is interesting, because it still looks smooth. I guess smoothness is really only noticeable up to second derivatives.
This slide reminds me of a really relevant video I saw earlier: https://www.youtube.com/watch?v=vD5g8aVscUI. It introduces the smooth transition function in one dimension.
One thing I was thinking about with smooth interpolation is how the cost function is derived. Some combination of computing power and time, space complexity, and how valuable accuracy and smoothness are in the resulting geometry. I wonder how there are ways to predict how many polynomials are needed for interpolation without explicitly solving it for each problem.
This slide presentation (https://www.mpp.mpg.de/~caldwell/fs06/Lecture3.pdf) was really helpful for me to further understand the benefits of interpolation, and how different degrees of specificity result in different types of curves. I noticed that this particular analysis of the topic delved into Data Smoothing and Lagrange Polynomials. Not sure if I missed it somewhere, but will we be discussing these a lot in class (and possibly using them for our final projects)?