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.
- 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.
- When the B-spline is uniform, the basis B-splines for a given degree n are just shifted copies of each other.
- Cubic B-splines with uniform knot-vector is the most commonly used form of B-spline.
- 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 B-splines.
- The use of splines for modeling automobile bodies seems to have several independent beginnings.
- Interpolating and smoothing splines.
- Representation of piecewise polynomial diminishing splines.
- Finite element thin plate splines in density estimation.
- For the rest of this section, we focus entirely on one-dimensional, 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.
- This is the essence of De Casteljau's algorithm, which features in B--zier curves and B--zier 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 B-splines basis curves.
- Fast evaluation of radial basis functions: methods for two-dimensional polyharmonic splines.
- This new edition features expanded presentation of Hermite interpolation and B-splines, with a new section on multi-resolution methods and B-splines.
- 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 (1911-1996)) was quick to recommend the use of cubic splines for the representation of smooth curves.
- Runge's function is nicely interpolated using splines however, and cubic splines are the most common interpolation method in this family.
- An introduction to splines for use in computer graphics and geometric modeling.
- Discrete B-splines and subdivision techniques in computer-aided geometric design and computer graphics.
- The most used method for this splines are nonuniform B-splines ( NURBS) and Bezier's splines.
- Non-Uniform Rational B-Splines (NURBS) curves and surface are parametric functions which can represent any type of curves or surfaces.
- 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).
- 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.
- The input can include not only straight line segments, but also circles, circular arcs, Bezier curves, and interpolated splines.
- 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 /
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