Download
cs 175 week 9 b splines definition algorithms n.
Skip this Video
Loading SlideShow in 5 Seconds..
CS 175 – Week 9 B-Splines Definition, Algorithms PowerPoint Presentation
Download Presentation
CS 175 – Week 9 B-Splines Definition, Algorithms

CS 175 – Week 9 B-Splines Definition, Algorithms

1 Vues Download Presentation
Télécharger la présentation

CS 175 – Week 9 B-Splines Definition, Algorithms

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

  1. CS 175 – Week 9B-SplinesDefinition, Algorithms

  2. Overview • the de Boor algorithm • B-spline curves • B-spline basis functions • B-spline algorithms • uniform B-splines and subdivision

  3. The De Boor Algorithm • modify the de Casteljau algorithm • start with different blossom values • gives approximating limit curve • down recurrence gives another polynomial basis • neighbouring curve segments join smoothly

  4. B-Spline Curves • piecewise polynomial • Cn- continuous at -fold knots • local control • affine invariance • local convex hull property • interpolate n-fold control point • interpolate control point at n-fold knot • variation diminishing

  5. Knot Insertion • add local detail > refine curve • increase degree • refine knot vector • add one knot • replace n-1 c.p.’s with n new c.p.’s • Boehm’s algorithm • one level of de Boor’s algorithm • conversion to piecewise Bézier

  6. B-Spline Basis Functions • recursive definition • piecewise polynomial • Cn- continuous at -fold knots • compact support • partition of unity • non-negativity • basis for all piecewise polynomials • recursive formula for derivative

  7. Uniform B-Splines • knots are equally spaced • basis functions are just shifted • convolution theorem • subdivision • insert all “mid-knots” • n=2 > Chaikin’s corner cutting • general n > Lane-Riesenfeld