Knot insertion and deletion algorithms for B-spline curves and surfaces
Society for Industrial and Applied Mathematics, 1993 - Art - 197 pages
New approaches to knot insertion and deletion are presented in this unique, detailed approach to understanding, analyzing, and rendering B-spline curves and surfaces. Computer scientists, mechanical engineers, and programmers and analysts involved in CAD and CAGD will find innovative, practical applications using the blossoming approach to knot insertion, factored knot insertion, and knot deletion, as well as comparisons of many knot insertion algorithms. This book also serves as an excellent reference guide for graduate students involved in computer aided geometric design.
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Chapter 1 An Introduction to Blossoming
Chapter 3 Factored Knot Insertion
5 other sections not shown
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additions/subtractions affine combinations Aided Geom algorithms for B-spline B-spline coefficients B-spline curves basis functions Bezier curves blossom segment blossom values Boehm's algorithm Boehm's knot insertion Boor algorithm Boor-Fix column oriented computation counts condition number control polygon cubic curves curves and surfaces derivatives discrete B-spline divided differences division triangle dual functionals factored knot insertion factored versions formula forward differencing geometrically continuous given homogeneous de Boor homogeneous polynomial inserting knots integer intersection knot insertion algorithm knot insertion techniques knot sequence knot vector Lemma linear Lyche matrix methods modification monomial basis monomial form multilinear blossom multiplications Newton dual basis Newton dual form numerical stability old control vertices original control vertices Oslo algorithm Oslo triangle piecewise polynomial polynomial curve progressive basis progressive curves progressive schemes progressive sequence proof R. N. Goldman recursive evaluation algorithm result row oriented Sablonniere's algorithm sketching spline start-up stroke tensor product tetrahedron Theorem transformation variant vertex