Describe B-splines - Githubissues

AudioSceneDescriptionFormat / splines

Python package for creating interpolating splines (for position and rotation)

https://splines.readthedocs.io/

MIT License

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Describe B-splines #11

Open mgeier opened 1 year ago

mgeier commented 1 year ago

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 lies within the convex hull of the control points (like Bézier)
starting point for NURBS
generalization of Bezier splines: "If n = p (i.e., the degree of a B-spline curve is equal to n, the number of control points minus 1), and there are 2(p + 1) = 2(n + 1) knots with p + 1 of them clamped at each end, this B-spline curve reduces to a Bézier curve."

mgeier commented 1 year ago

The basis matrix for a uniform cubic B-spline is shown (without derivation) in:

Clark, James H. “Parametric Curves, Surfaces and Volumes in Computer Graphics and Computer-Aided Geometric Design.” Technical Report. Computer Systems Laboratory, Stanford University, November 1981. http://i.stanford.edu/pub/cstr/reports/csl/tr/81/221/CSL-TR-81-221.pdf.

mgeier commented 1 year ago

The basis matrix is also shown in:

Barsky, Brian A. “End Conditions and Boundary Conditions for Uniform B-Spline Curve and Surface Representations.” Computers in Industry, Double Issue- In Memory of Steven Anson Coons, 3, no. 1 (March 1, 1982): 17–29. https://doi.org/10.1016/0166-3615(82)90028-8.

For a more detailed derivation we are referred to:

Barsky, B.A. (1983) A Study of the Parametric Uniform B-spline Curve and Surface Representations. Technical Report UCB/CSD-83-118. EECS Department University of California, Berkeley. Available at: https://www2.eecs.berkeley.edu/Pubs/TechRpts/1983/5671.html.