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### DefinitionsUpDw('Definitions','-Abz-');

1. Splines are piecewise defined polynomials and provide more flexibility than ordinary polynomials when defining simple and smooth functions.
2. Splines are very useful for modeling arbitrary functions, and are used extensively in computer graphics. (Web site)

### B-SplineUpDw('B-SPLINE','-Abz-');

1. When the B-spline is uniform, the basis B-splines for a given degree n are just shifted copies of each other. (Web site)
2. Cubic B-splines with uniform knot-vector is the most commonly used form of B-spline. (Web site)
3. 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. (Web site)

### SplineUpDw('SPLINE','-Abz-');

1. The use of splines for modeling automobile bodies seems to have several independent beginnings. (Web site)
2. Interpolating and smoothing splines. (Web site)
3. Representation of piecewise polynomial diminishing splines. (Web site)
4. Finite element thin plate splines in density estimation.
5. For the rest of this section, we focus entirely on one-dimensional, polynomial splines and use the term "spline" in this restricted sense.

### KnotUpDw('KNOT','-Abz-');

1. 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.
2. 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 .
3. 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.

### CurveUpDw('CURVE','-Abz-');

1. A comprehensive spline curve function library for creating and evaluating splines in Excel, VB and VBA. Free download of evaluation copy. (Web site)
2. This is the essence of De Casteljau's algorithm, which features in B--zier curves and B--zier splines.
3. SPLINES The term spline comes from drafting, where splines were flexible strips guided by points on a paper, used to draw curves.

### BasisUpDw('BASIS','-Abz-');

1. For a representation that defines a spline as a linear combination of basis splines, however, something more sophisticated is needed.
2. It is a linear combination of B-splines basis curves.
3. Fast evaluation of radial basis functions: methods for two-dimensional polyharmonic splines.

### HermiteUpDw('HERMITE','-Abz-');

1. This new edition features expanded presentation of Hermite interpolation and B-splines, with a new section on multi-resolution methods and B-splines. (Web site)
2. These are most often used with n = 3; that is, as Cubic Hermite splines.

### Control PointsUpDw('CONTROL_POINTS','-Abz-');

1. Cardinal splines are specified by a set of control points and a tension parameter.
2. To model smooth curves, we can implement Bezier splines, which are mathematically defined from a set of control points.

### Cubic SplinesUpDw('CUBIC_SPLINES','-Abz-');

1. The space of all natural cubic splines, for instance, is a subspace of the space of all cubic C^2 splines.
2. Birkhoff ( Garrett Birkhoff (1911-1996)) was quick to recommend the use of cubic splines for the representation of smooth curves. (Web site)
3. Runge's function is nicely interpolated using splines however, and cubic splines are the most common interpolation method in this family. (Web site)

### Computer GraphicsUpDw('COMPUTER_GRAPHICS','-Abz-');

1. An introduction to splines for use in computer graphics and geometric modeling.
2. Discrete B-splines and subdivision techniques in computer-aided geometric design and computer graphics.

### NurbsUpDw('NURBS','-Abz-');

1. The most used method for this splines are nonuniform B-splines ( NURBS) and Bezier's splines.
2. Non-Uniform Rational B-Splines (NURBS) curves and surface are parametric functions which can represent any type of curves or surfaces. (Web site)

### AdventUpDw('ADVENT','-Abz-');

1. With the advent of computers, polynomials have been replaced by splines in many areas in numerical analysis.
2. Through the advent of computers splines have gained importance.

### CardinalUpDw('CARDINAL','-Abz-');

1. Arcs of two cubics suffice to construct a basis of cardinal splines.
2. In Cardinal splines, each segment is a 3rd degree spline with each polynomial in Hermite form (also see this).

### SplinesUpDw('SPLINES','-Abz-');

1. The literature of splines is replete with names for special types of splines.
2. This was done for differentiable splines of degree at least four defined on domains divided into subrectangles with one diagonal. (Web site)
3. The input can include not only straight line segments, but also circles, circular arcs, Bezier curves, and interpolated splines. (Web site)

### CategoriesUpDw('Categories','-Abz-');

1. Topology > Topological Spaces > Manifolds > Curves
2. Computer Science > Algorithms > Numerical Analysis > Interpolation
3. Information Technology > Computer Science > Algorithms > Numerical Analysis
4. Information > Information Technology > Computer Science > Algorithms
5. Glossaries > Glossary of Numerical Analysis /
6. Books about "Splines" in Amazon.com  Short phrases about "Splines"   Originally created: March 20, 2008.   Links checked: July 30, 2013.   Please send us comments and questions by this Online Form   Please click on to move good phrases up.
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