DEGREE REDUCTION OF B-SPLINE CURVES

  • Published : 2001.09.01

Abstract

An algorithmic approach to degree reduction of B-spline curves is presented. The new algorithms are based on the blossoming spline curves are obtained by the generalized least square method. The computations are carried out by minimizing the $L_2$ distamce between the two curves.

Keywords

References

  1. Mathematical programming in statistics T.S.Arthanari;Y.Dodge
  2. Knot Insertion and Deletion Algorithms for B-spline Curves and Surface An Introduction to Blossoming P.J.Barry;R.N.Goldman(ed.);T.Lyche(ed.)
  3. Mathematical Method in Computer Aided Design Ⅱ Best approximations of parametric curve by spline W.L.F.Degen;T.Lyche(ed.);L.L.Schumaker(ed.)
  4. Topology J.Dugundji
  5. Comput. Aided Des. v.18 The definition and computation of a metric on plane curves J.D.Emery
  6. NURBS Curves and Surfaces : from projective geometry to practical use G.Farin
  7. Bull. Australian Math. Soc. v.56 The Distance for $B\'{e}zier$ Curves and Degree reduction B.G.Lee;Y.Park
  8. J. KSIAM v.4 The Degree elevation of B-spline curves and its matrix representation B.G.Lee;Y.Park
  9. Comput. Aided Geom. Des. v.14 A simple, efficient degree rasing algorithm for B-spline curves W.Liu
  10. Comput. Aided Des. v.26 Software-engineering approach to degree elevation of B-spline curves L.Piegl;W.Tiller
  11. Comput. Aided Des. v.27 Algorithm for degree reduction of B-spline curves L.Piegl;W.Tiller
  12. The NURBS Book L.Piegl;W.Tiller
  13. Comput. Aided Geom. Des. v.2 Degree elevation of B-spline curves H.Prautzsch
  14. Comput. Aided Geom. Des. v.8 A fast algorithm to raise the degree of B-spline curves H.Prautzsch;B.Piper
  15. Technical report, Digital Systems Research Center Blossoming : a connect-the-dots approach to splines L.Ramshaw
  16. Comput. Aided Geom. Des. v.6 Blossoms are polar forms L.Ramshaw
  17. Linear Regression Analysis S.R.Searle