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	Spline (mathematics) - Wikipedia, the free encyclopedia
		In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees.
		Splines are a popular representation of curves in these subfields because of the simplicity of their construction, their ease and accuracy of evaluation, and their capacity to approximate complex shapes through curve fitting and interactive curve design.
		Spline functions for interpolation are normally determined as the minimizers of suitable measures of roughness (for example integral squared curvature) subject to the interpolation constraints.
	en.wikipedia.org /wiki/Cubic_spline (2312 words)

	B-spline - Wikipedia, the free encyclopedia
		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 spline is contained in the convex hull of its control points.
	en.wikipedia.org /wiki/B-spline (610 words)

	PlanetMath: cubic spline interpolation
		The set of cubic splines on a fixed set of knots, forms a vector space for cubic spline addition and scalar multiplication.
		Cubic splines are frequently used in numerical analysis to fit data.
		This is version 3 of cubic spline interpolation, born on 2003-06-11, modified 2003-06-12.
	planetmath.org /encyclopedia/CubicSplinInterpolation.html (486 words)

	Interpolation - Wikipedia, the free encyclopedia
		Spline interpolation uses low-degree polynomials in each of the intervals, and chooses the polynomial pieces such that they fit smoothly together.
		For instance, the natural cubic spline is piecewise cubic and twice continuously differentiable.
		Like polynomial interpolation, spline interpolation incurs a smaller error than linear interpolation and the interpolant is smoother.
	en.wikipedia.org /wiki/Interpolation (1046 words)

	Mathcad Library
		Cubic splines are a common method of approximating a curve.
		A spline is simply a polynomial function that approximates a set of points, and a cubic spline is a third order polynomial.
		The word spline comes from a drafting tool used to do just this; a spline is a thin, elastic rod which can be weighted so that it follows any curve the drafter wishes to draw.
	www.mathcad.com /library/LibraryContent/MathML/complex_splines.htm (1486 words)

	Cubic Spline Interpolation
		Another alternative is spline interpolation, which encompasses a range of interpolation techniques that reduce the effects of overfitting.
		We seek to fit a cubic polynomial on the interval [1, 2] and another cubic polynomial on the interval [2, 3].
		The cubic spline, along with the three points upon which it is based, is shown in Exhibit 1.
	www.riskglossary.com /articles/cubic_spline.htm (371 words)

	Natural Cubic Spline (Site not responding. Last check: 2007-10-31)
		This applet computes a Cubic Spline between each of the nodes (Black Circles).
		To experiment with Cubic Splines select a node with your mouse and drag the node to the desired location.
		Cubic splines are the most popular spline functions.
	www.math.utah.edu /~wright/applets/spline/spline.html (274 words)

	GameDev.net -- Defeating Lag With Cubic Splines
		This article will attempt to explain a technique for eliminating the "jerk" of lag by employing the power of cubic splines in a dead-reckoning algorithm.
		Before jumping straight into cubic splines, a brief description of dead reckoning is required.
		Cubic splines are a kind of dead reckoning that creates a smooth transition between two data points.
	www.gamedev.net /reference/programming/features/cubicsplines (198 words)

	Monotonic Cubic Spline Interpolation (ResearchIndex)
		Interpolating cubic splines are popular for fitting data because they use low-order polynomials and have C 2 continuity, a property that permits them to satisfy a desirable smoothness constraint.
		3 On monotone and convex spline interpolation (context) - Costantini - 1986
		2 Co-monotone interpolating splines of arbitrary degree: A loc..
	citeseer.ist.psu.edu /223645.html (483 words)

	BSpline Library: Cubic B-Spline
		The first column is the X value, the second is the spline evaluation at that point, and the third is the evaluation of the spline's first derivative.
		The spline algorithm first removes the mean from the input data to improve the matrix calculations, and the mean is added back in when evaluating the spline at any point.
		This is a C++ implementation of a cubic b-spline least squares and derivative constraint algorithm.
	www.atd.ucar.edu /~granger/bspline/doc/index.html (761 words)

	SPLINE - Interpolation and Approximation of Data (Site not responding. Last check: 2007-10-31)
		SPLINE is a library of C++ routines, using double precision arithmetic, for constructing and evaluating spline functions.
		Also included are a set of routines that return the local "basis matrix", which allows the evaluation of the spline in terms of local function data.
		SPLINE is also available in a FORTRAN90 version and a MATLAB version.
	www.scs.fsu.edu /~burkardt/cpp_src/spline/spline.html (678 words)

	Spline
		Compare the cubic spline of the previous example to a Bezier spline.
		The spline graphics primitive has an option allowing the control points to be shown.
		The rendering of the splines uses an adaptive algorithm, similar to that of the
	documents.wolfram.com /teachersedition/Teacher/Graphics/Spline.html (301 words)

	Cubic Splines
		The natural spline is the curve obtained by forcing a flexible elastic rod through the points but letting the slope at the ends be free to equilibrate to the position that minimizes the oscillatory behavior of the curve.
		It is useful for fitting a curve to experimental data that is significant to several significant digits.
		A practical feature of splines is the minimum of the oscillatory behavior they possess.
	math.fullerton.edu /mathews/n2003/CubicSplinesMod.html (228 words)

	SPLINE - Interpolation and Approximation of Data (Site not responding. Last check: 2007-10-31)
		SPLINE is a FORTRAN90 library, using double precision arithmetic, for setting up and evaluating splines.
		NMS is a FORTRAN90 library which includes a package for the computation of piecewise cubic Hermite splines.
		PPPACK is Carl de Boor's library of piecewise polynomial functions, including, in particular, cubic splines.
	www.scs.fsu.edu /~burkardt/f_src/spline/spline.html (707 words)

	Cubic Spline Quadrature
		Then integrate the natural cubic spline for a quadrature method.
		Investigate cubic spline quadrature for approximating the integral
		Use cubic spline quadrature to approximate the value of the integral.
	math.fullerton.edu /mathews/n2003/SplineQuadMod.html (161 words)

	cubic-spline.html
		To do spline interpolation, we need a series of knots and a pair of slopes.
		All we really care about is the coefficients for the cubic polynomials which make up our splines.
		between the cubic polynomials and solve for the unknown coefficients.
	www.cis.rit.edu /~njs8030/coding/maple_html/cubic-spline.html (376 words)

	Spline Interpolation Demo (Site not responding. Last check: 2007-10-31)
		When we string these curves together, we set the second and first derivatives at the endpoints of each piecewise cubic curve equal to that of the adjacent cubic curve's second and first derivatives thus providing for a continuous second derivative.
		The term "relaxed" is used because the endpoints of the cubic spline have their second derivative equal to zero.
		The construction of the relaxed cubic spline was done using Bezier curves as the piecewise cubic curves, thus four control points for each Bezier curve are needed.
	www.math.ucla.edu /~baker/java/hoefer/Spline.htm (234 words)

	Cubic - maths interpolation - C / C++ Numerical Component
		A cubic spline is a piecewise cubic polynomial such that the function, its derivative and its second derivative are continuous at the interpolation nodes.
		The natural cubic spline has zero second derivatives at the endpoints.
		It is the smoothest of all possible interpolating curves in the sense that it minimizes the integral of the square of the second derivative.
	www.codecogs.com /d-ox/maths/interpolation/cubic.php (348 words)

	Monotonic Cubic Spline Interpolation (Site not responding. Last check: 2007-10-31)
		This paper describes the use of cubic splines for interpolating monotonic data sets.
		Interpolating cubic splines are popular for fitting data because they use low-order polynomials and have $C^2$ continuity, a property that permits them to satisfy a desirable smoothness constraint.
		Comparisons among the different techniques are given, and superior monotonic cubic spline interpolation results are presented.
	csdl.computer.org /comp/proceedings/cgi/1999/0185/00/01850188abs.htm (208 words)

	Spectral Analysis with Cubic Splines (Site not responding. Last check: 2007-10-31)
		In 1993, a new method was developed for finding the periodicity of stellar light curves using cubic splines.
		The technique is similar in philosophy to the "minimum string length" approach and is therefore insensitive to the actual light curve shape.
		Application of cubic splines to the spectral analysis of unequally spaced data
	www-personal.umich.edu /~akerlof/cubic-spline (325 words)

	I was asked to elaborate on the odd form of the cubic spline equation: (Site not responding. Last check: 2007-10-31)
		Well, how about we now ensure that our family of four cubic equations (remember there are four intervals, and thus, four functional forms of Eq.1) have continuous first derivatives at the internal three points. We can do this because they are cubic.
		We will define a NATURAL CUBIC SPLINE as one where the double prime terms are 0.0 at the endpoints.
		Still would be a cubic spline. Just like in the book, but the results would be slightly off.
	kahuna.sdsu.edu /~impellus/cubice.htm (1270 words)

	Cubic Spline Interpolation (ResearchIndex)
		An introduction into the theory and application of cubic splines with accompanying Matlab m-file cspline.m Introduction Real world numerical data is usually difficult to analyze.
		To this end, the idea of the cubic spline was developed.
		Using this process, a series of unique cubic polynomials are fitted between each of the data points, with the stipulation that the curve obtained be...
	citeseer.ist.psu.edu /261352.html (184 words)

	Guru's Lair Cubic Spline & Bezier Curves Library (Site not responding. Last check: 2007-10-31)
		Cubic Splines (some of which are called Bezier curves) are the
		spline through four data points, all of which are on the curve.
		Cubic spline Basis Functions are a powerful but little understood
	www.tinaja.com /cubic01.asp (764 words)

	Curve Fit/X Curve Fitting Example Software - Cubic Spline BSplines (Site not responding. Last check: 2007-10-31)
		This method enables the usual cubic spline model to be extended to the case where, instead of fitting a spline model through all data points (knots), which could result in a very "wriggly" curve, allows a smooth curve to be fit to the data.
		Unlike polynomial models however, which can perform poorly on some data sets, since each data point can affect the polynomial over the whole range of the data, the smoothed cubic spline model retains the flexible approximation capabilities of regular spline models coupled with the smoothing characteristics of the Reinsch algorithm.
		A weight matrix C is returned, which can then be used in the corresponding cubic spline method.
	windale.com /curvefitx.php (935 words)

	Cubic Spline Curve
		The diagram shows a geometric construction for a cubic spline curve.
		It is tangent to AB at A. It lies inside the convex hull of A,B,C,D. (The convex hull is the smallest convex polygon containing the points)
		In fact the curve is a cubic in t.
	www.saltire.com /applets/advanced_geometry/spline/spline.htm (139 words)

	Recovering Event Histories by Cubic Spline Interpolation
		The problem is illustrated by the inconsistent age at marriage schedules published by two recent U.S. censuses.
		This paper develops a general method for fixing problems of this kind by using cubic spline interpolation.
		We use the method to adjust U.S. age at marriage data, thus resolving a large proportion of the discrepancy between 1960 and 1970 censuses.
	repositories.cdlib.org /ucsbecon/bergstrom/1988A (157 words)

	About "Cubic Spline Demo" (Site not responding. Last check: 2007-10-31)
		A Java applet (Beta) demonstrating the approximating capabilities of the Natural Cubic Spline Algorithm.
		The red line represents the given function 1.0 -------------------- (x0.3sqrt(0.5x + 7)) Select any combination of x values and hit the button labelled "Fit it!" The applet calculates the spline interpolant from the (x,f(x)) pairs and plots the result.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /library/view/6540.html (68 words)

	Building cubic B-spline
		The problems with a single Bezier spline range from the need of a high degree curve to accurately fit a complex shape, which is inefficient to process.
		To overcome the problems, a piecewise curve is used.
		Therefore the order of the curve is not dependent on the number of control points.
	www.ibiblio.org /e-notes/Splines/B-spline.htm (288 words)

	More on Cubic Spline Math (Site not responding. Last check: 2007-10-31)
		% The length of a cubic spline is not obvious, and I have yet to prove a
		2 3 3 7.5 7 7 8 4 grabcoeffs % input the spline
		% spline having a loop 2 0.5 8.01 {dup find3y} for
	www.tinaja.com /text/bezmath.html (2163 words)

	SPLINE - Interpolation and Approximation of Data (Site not responding. Last check: 2007-10-31)
		SPLINE includes some simple routines for setting up and evaluating interpolating and approximating splines.
		SPLINE is a C version of a subset of the FORTRAN SPLINE collection.
		SPLINE_CUBIC_VAL evaluates a cubic spline at a specific point.
	orion.math.iastate.edu /burkardt/c_src/spline/spline.html (138 words)

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