# interpolation and splines
# subtopics
* [bezier curves](splines/bezier-curve.html)
* [catmull-rom splines](splines/catmull-rom-spline.html)

# links
* [curved paths](https://www.redblobgames.com/articles/curved-paths) in the context of game development with much useful information and links
* [comparison of interpolation methods](http://paulbourke.net/miscellaneous/interpolation/)
* [interactive introduction to splines](https://www.ibiblio.org/e-notes/Splines/Intro.htm) examples and comparisons
* [interpolation](http://danceswithcode.net/engineeringnotes/interpolation/interpolation.html) by d. rose
* [slides with a comparison between curve and spline functions](https://www.cs.cmu.edu/afs/cs/academic/class/15462-f11/www/lec_slides/lec06.pdf)
* [tinyspline](https://tinyspline.org/) software library. ansi c, mit license, nurbs, b-splines and bezier curves. no api overview except for the header file, always generic for any number of dimensions with many heap memory allocations
* [circular arc interpolation](https://observablehq.com/@jrus/circle-arc-interpolation)
* on wikipedia
  * [cubic hermite spline](https://en.wikipedia.org/wiki/Cubic_Hermite_spline)
  * [interpolation](https://en.wikipedia.org/wiki/Interpolation)
  * [spline interpolation](https://en.wikipedia.org/wiki/Spline_interpolation)
* cubic splines
  * [article](https://timodenk.com/blog/cubic-spline-interpolation/) by timo denk, with an accompanying online [tool](https://tools.timodenk.com/cubic-spline-interpolation) and its javascript [code](https://github.com/Simsso/Online-Tools/blob/master/src/page/logic/cubic-spline-interpolation.js)
  * [cubic spline program](https://stackoverflow.com/questions/7642921/cubic-spline-program) on stackoverflow
  * [on wikiversity](https://en.wikiversity.org/wiki/Cubic_Spline_Interpolation)
  * [scipy](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.CubicSpline.html) natural cubic splines with scipy
  * [smoothing with cubic splines](https://www.semanticscholar.org/paper/SMOOTHING-WITH-CUBIC-SPLINES/afbeeab7a657e3ab2181c7645626061be84fafe8) by d.s.g. pollock
  * [spherical linear interpolation / slerp](https://en.wikipedia.org/wiki/Slerp)

# notes
* b-splines seem to have the highest continuity in general, but go only through the first and last point
* natural cubic splines seem to have the highest continuity while going through all points
* nurbs seem to be a generalisation of b-splines which seem to be a generalisation of bezier curves
* hermite and catmull-rom interpolation seem to be variations of cubic interpolation
* interpolation, curve fitting and splines: interpolation goes at least to start and end points, curve fitting approximates a curve between values, splines combine interpolation piecewiese
* gsl can do only one and two dimensional interpolation
* energy-minimising curve fitting might be a topic of interest
* exponential interpolation ((x ** (- 1 t)) (x ** t))