
Review of Short Phrases and Links 
This Review contains major "Splines" related terms, short phrases and links grouped together in the form of Encyclopedia article.
Definitions
 Splines are piecewise defined polynomials and provide more flexibility than ordinary polynomials when defining simple and smooth functions.
 Splines are very useful for modeling arbitrary functions, and are used extensively in computer graphics.
(Web site)
 When the Bspline is uniform, the basis Bsplines for a given degree n are just shifted copies of each other.
(Web site)
 Cubic Bsplines with uniform knotvector is the most commonly used form of Bspline.
(Web site)
 De Boor's work at GM resulted in a number of papers being published in the early 60's, including some of the fundamental work on Bsplines.
(Web site)
 The use of splines for modeling automobile bodies seems to have several independent beginnings.
(Web site)
 Interpolating and smoothing splines.
(Web site)
 Representation of piecewise polynomial diminishing splines.
(Web site)
 Finite element thin plate splines in density estimation.
 For the rest of this section, we focus entirely on onedimensional, polynomial splines and use the term "spline" in this restricted sense.
 In the mathematical study of polynomial splines the question of what happens when two knots, say t i and t i +1, are moved together has an easy answer.
 Given a knot vector , a degree n, and a smoothness vector for , one can consider the set of all splines of degree having knot vector and smoothness vector .
 Representations and names For a given interval * and a given extended knot vector on that interval, the splines of degree n form a vector space.
 A comprehensive spline curve function library for creating and evaluating splines in Excel, VB and VBA. Free download of evaluation copy.
(Web site)
 This is the essence of De Casteljau's algorithm, which features in Bzier curves and Bzier splines.
 SPLINES The term spline comes from drafting, where splines were flexible strips guided by points on a paper, used to draw curves.
 For a representation that defines a spline as a linear combination of basis splines, however, something more sophisticated is needed.
 It is a linear combination of Bsplines basis curves.
 Fast evaluation of radial basis functions: methods for twodimensional polyharmonic splines.
 This new edition features expanded presentation of Hermite interpolation and Bsplines, with a new section on multiresolution methods and Bsplines.
(Web site)
 These are most often used with n = 3; that is, as Cubic Hermite splines.
 Cardinal splines are specified by a set of control points and a tension parameter.
 To model smooth curves, we can implement Bezier splines, which are mathematically defined from a set of control points.
 The space of all natural cubic splines, for instance, is a subspace of the space of all cubic C^2 splines.
 Birkhoff ( Garrett Birkhoff (19111996)) was quick to recommend the use of cubic splines for the representation of smooth curves.
(Web site)
 Runge's function is nicely interpolated using splines however, and cubic splines are the most common interpolation method in this family.
(Web site)
 An introduction to splines for use in computer graphics and geometric modeling.
 Discrete Bsplines and subdivision techniques in computeraided geometric design and computer graphics.
 The most used method for this splines are nonuniform Bsplines ( NURBS) and Bezier's splines.
 NonUniform Rational BSplines (NURBS) curves and surface are parametric functions which can represent any type of curves or surfaces.
(Web site)
 With the advent of computers, polynomials have been replaced by splines in many areas in numerical analysis.
 Through the advent of computers splines have gained importance.
 Arcs of two cubics suffice to construct a basis of cardinal splines.
 In Cardinal splines, each segment is a 3rd degree spline with each polynomial in Hermite form (also see this).
Splines
 The literature of splines is replete with names for special types of splines.
 This was done for differentiable splines of degree at least four defined on domains divided into subrectangles with one diagonal.
(Web site)
 The input can include not only straight line segments, but also circles, circular arcs, Bezier curves, and interpolated splines.
(Web site)
Categories
 Topology > Topological Spaces > Manifolds > Curves
 Computer Science > Algorithms > Numerical Analysis > Interpolation
 Information Technology > Computer Science > Algorithms > Numerical Analysis
 Information > Information Technology > Computer Science > Algorithms
 Glossaries > Glossary of Numerical Analysis /

Books about "Splines" in
Amazon.com


