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Home > Art, Film & Photography > Splines: Bzier Curve, B-Spline, Non-Uniform Rational B-Spline, Spline, Cubic Hermite Spline, Spline Interpolation, Polyharmonic Spline
Splines: Bzier Curve, B-Spline, Non-Uniform Rational B-Spline, Spline, Cubic Hermite Spline, Spline Interpolation, Polyharmonic Spline

Splines: Bzier Curve, B-Spline, Non-Uniform Rational B-Spline, Spline, Cubic Hermite Spline, Spline Interpolation, Polyharmonic Spline


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About the Book

Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Bzier Curve, B-Spline, Non-Uniform Rational B-Spline, Spline, Cubic Hermite Spline, Spline Interpolation, Polyharmonic Spline, Thin Plate Spline, Sculpted Prim, de Boor's Algorithm, Monotone Cubic Interpolation, Smoothing Spline, Interpolation, Kochanek-bartels Spline, Bzier Spline, Perfect Spline, Hermite Spline. Excerpt: In the mathematical subfield of numerical analysis, a B-spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. A fundamental theorem states that every spline function of a given degree, smoothness, and domain partition, can be represented as a linear combination of B-splines of that same degree and smoothness, and over that same partition. The term B-spline was coined by Isaac Jacob Schoenberg and is short for basis spline. B-splines can be evaluated in a numerically stable way by the de Boor algorithm . Simplified, potentially faster variants of the de Boor algorithm have been created but they suffer from comparatively lower stability. In the computer science subfields of computer-aided design and computer graphics the term B-spline frequently refers to a spline curve parametrized by spline functions that are expressed as linear combinations of B-splines (in the mathematical sense above). A B-spline is simply a generalisation of a Bzier curve, and it can avoid the Runge phenomenon without increasing the degree of the B-spline. Definition Given m real values ti, called knots, with a B-spline of degree n is a parametric curve composed of a linear combination of basis B-splines bi, n of degree n . The P i are called control points or de Boor points . There are m n-1 control points and they form a convex hull . The m-n-1 basis B-splines of degree n can be defined using the Cox-de Boor recurs...


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Product Details
  • ISBN-13: 9781155494296
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • No of Pages: 94
  • Spine Width: 6 mm
  • Weight: 150 gr
  • ISBN-10: 1155494296
  • Publisher Date: 04 May 2010
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Bzier Curve, B-Spline, Non-Uniform Rational B-Spline, Spline, Cubic Hermite Spline, Spline Interpolation, Polyharmonic Spline
  • Width: 229 mm


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