splines
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AudioSceneDescriptionFormat
Python package for creating interpolating splines (for position and rotation)
Delbourgo R, Gregory JA. C 2 rational quadratic spline interpolation to monotonic data. IMA J Numer Anal 1983;3:141-52. Gregory JA, Delbourgo R. Piecewise rational quadratic interpolation to monotonic data. IMA...
According to http://denkovacs.com/2016/02/catmull-rom-spline-derivatives/ this is supposed to be possible.
Make third derivative continuous between first and second segment. See De Boor, A Practical Guide to Splines, revised edition, page 43. There's already a work-in-progress branch for that: https://github.com/mgeier/splines/tree/not-a-knot
Cardinal splines are Catmull-Rom splines with an additional *tension* parameter. This is very similar to Kochanek-Bartels splines, which also have a *tension* parameter (plus *continuity* and *bias*). So it might...
* sames smoothness as natural splines, not interpolating (only approximating) but local control * "B" stands for "basis". Why? * control points are called "de Boor" control points? * curve...
See Foley, Thomas A., and Gregory M. Nielson. „Knot Selection for Parametric Spline Interpolation“. In Mathematical Methods in Computer Aided Geometric Design. Academic Press, 1989. https://doi.org/10.1016/B978-0-12-460515-2.50023-8
See Fang, Jing-Jing, and Chia-Lien Hung. “An Improved Parameterization Method for B-Spline Curve and Surface Interpolation.” Computer-Aided Design 45, no. 6 (June 1, 2013): 1005–28. https://doi.org/10.1016/j.cad.2013.01.005. This mentiones "Foley" parameterization,...
See also #11. https://en.wikipedia.org/wiki/Non-uniform_rational_B-spline knots, control points, weights Like B-splines, NURBS are *approximating* splines, i.e. the curve typically does not pass through its control points. X3D provides NurbsCurve, NurbsCurve2D, NurbsCurveInterpolator...
They are already mentioned several times in the text because they are often confused with Catmull-Rom splines. The relevant paper is already part of the references: https://github.com/AudioSceneDescriptionFormat/splines/blob/f993a797ee7c530608258ed0a6b98999829e499a/doc/references.bib#L80-L89
β-splines are B-splines with "tension" and "bias", developed by Barsky.
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Python package for creating interpolating splines (for position and rotation)