BSpline

create and evaluate b-splines

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Declaration

classdef BSpline < handle

Overview

The BSpline

Topics

• Initialization
  • BSpline create a new BSpline instance
• Primary attributes
  • K order of polynomial
  • S degree of the polynomial (S=K-1)
  • domain min and max value of the independent variable
  • tKnot knot points
  • xi coefficients (Mx1)
• Spline evalutation
  • C piecewise polynomial coefficients
  • Xtpp splines at the points tpp
  • evaluateFromPPCoefficients Returns the value of the function with derivative D represented by PP coefficients C at locations t.
  • matrix returns the basis splines of order K evaluated at point t, given knot points tKnot.
  • ppCoefficientsFromSplineCoefficients Returns the piecewise polynomial coefficients in matrix C from spline coefficients in vector m.
  • t_pp piece-wise polynomial break points
• Operations
  • cumsum indefinite integral of a BSpline
  • diff differentiation of a BSpline
  • feval value of BSpline
  • mtimes multiplication (.*)
  • plus addition (+)
  • power (.^)
  • roots of BSpline for its domain
  • sqrt square-root of a BSpline
  • valueAtPoints evaluate the spline (and its derivatives) at arbitrary points t
• Utility
  • pointsOfSupport this function assumes that the spline are terminated at the
• Other
  • splineCoefficientsDidChange
  • subsref Subscript overload
  • tKnotDidChange

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