If you drift randomly from the north pole, where do you touch land?
#cartography #geo #spatial #interpolation #wos
https://observablehq.com/@visionscarto/spherical-wos

The approx() function in R

Post: https://www.spsanderson.com/steveondata/posts/2023-08-17/

#R #RStats #OpenSource #Interpolation

In the course of rewriting Chapter 5 of my two books #MATLAB and #Python Recipes for Earth Science, the chapter on #interpolation is also being rewritten. Here is a pre-release version of the opening example, open for your comments: http://mres.uni-potsdam.de/index.php/2023/06/27/interpolating-unevenly-spaced-data-with-matlab/

But is it good enough? Looking up some real world data on the effect I'm looking for, it looks like my noise is still *way* too big. My effect is .1mm/s^2 or smaller. Ugh. My noise is still 10x that.

So far all of these methods have used just velocity to recover acceleration. Now I'm #learning Hermite and cubic spline #interpolation to use both pos and vel and maybe reduce my error even more.

The smooth elset is for a high-e orbit For Reasons which also means the hard part is perigee.

My first naive method was to subtract adjacent velocities. That's awful.

Learning some #numerical methods, I then tried (v(t+1) - v(t-1))/2t. That gives me a 25 mm/s^2 residual acc. Meh.

Lagrange #interpolation gives me 5 mm/s^2. Getting somewhere.

Going back to central diffs but using t-2, t-1, t+1, t+2 I do even better at 1.5 mm/s^2 residual.

'Fundamental limits and algorithms for sparse linear regression with sublinear sparsity', by Lan V. Truong.

http://jmlr.org/papers/v24/21-0543.html

#sparse #sparsity #interpolation

#Interpolation is an excellent example of achieving and balancing the original intent of #IntellectualProperty rights—protecting and awarding musicians for their artistic contributions—while also encouraging new creative and transformative works.  https://www.project-disco.org/intellectual-property/interpolation-and-how-it-has-reintroduced-new-audiences-to-past-music/

#interpolation of #Neanderthal sites suggests possible #undiscovered #ArchaeologicalSites in #Iran :) Hope they're right and find stuff there!

#Archaeology #migration #ancientPeople #Europe #Asia #MiddleEast

#ComputerModeling #QGIS #climateData #archaeologicalData

https://phys.org/news/2023-03-european-neanderthal-migration-hints-hidden.html

Interpolation Can Provably Preclude Invariance https://arxiv.org/abs/2211.15724
#Overfitting to the point of #interpolation can hinder invariance-inducing objectives: One cannot assume a #DeepLearninig model with an invariance penalty will indeed achieve any form of #invariance… suggests that “benign overfitting,” in which models generalize well despite interpolating, might not favorably extend to settings in which #robustness or #fairness are desirable.

I'm googling #interpolation methods for use with #ephemerides because I'm working with potentially maneuvering #satellite data

I clicked on a likely-looking link: https://www.astro.com/astrowiki/en/Interpolation

The mix of #science and #astrology is amazing: "Interpolation is also necessary to calculate the positions of the house cusps..."

These guys trained Stable Diffusion with spectrograms to generate music and even do img2img or rather sound2sound. So clever! Check out their typewriter to jazz interpolation, very cool 😊

https://www.riffusion.com/about

#stablediffusion #ai #gan #sound #synth #aiart #machinearning #interpolation #spectrogram

Here's a neat little function that fits a cubic curve to the unit interval. You can get many family favorites with just two extra slope parameters! 🤌

Hermite Step: https://shadertoy.com/view/msBXzy

#math #interpolation #shadertoy

Here's a neat little function that fits a cubic curve to the unit interval. You can get many family favorites with just two extra slope parameters! 🤌

Hermite Step: https://shadertoy.com/view/msBXzy

#math #interpolation #shadertoy

In #paleoclimate time series amplitude of spectral peaks usually varies with time. Evolutionary power spectral analysis such as the FFT-based spectrogram and wavelet power spectral analysis helps. These methods, however, require #interpolation of the time series to a grid of evenly-spaced times. Instead we can use the Lomb-Scargle Method for unevenly-spaced spectral analysis, computed for a sliding window, to map changes of the #cyclicities through time.

http://mres.uni-potsdam.de/index.php/2020/06/26/evolutionary-lomb-scargle-power-spectral-analysis-with-matlab/

I implemented (hopefully #monotone) #cubic #interpolation, as well as linear and step modes, for #zoom depth #animation in my #zoomasm tool for assembling #fractal animations from exponential strip keyframes. Much smoother than the piecewise linear that was the only option before (no more speed discontinuities at waypoints, unless you want them).