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	Spline (mathematics) - Wikipedia, the free encyclopedia
		Splines are a popular representations for 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.
		Smoothing splines may be viewed as generalizations of interpolation splines where the functions are determined to minimize a weighted combination of the average squared approximation error over observed data and the roughness measure.
	www.wikipedia.org /wiki/Cubic%20spline (2279 words)

	Spline (mathematics)
		In the picture, the curve that passes through A, B, C, and D is an interpolating spline (specifically, a linear spline) and the curve that passes through A and D, but not B and C, is an approximating spline (specifically, a Bézier spline).
		An important characteristic of splines is that they are given by polynomials, but only piecewise: different polynomials may be used in different parts of a curve.
		The simplicity of representation and the ease with which a complex spline's shape may be computed make splines popular representations for curves in computer science, predominantly in computer graphics but also for other kinds of interpolation, such as smoothing of digital audio.
	www.brainyencyclopedia.com /encyclopedia/s/sp/spline__mathematics_.html (365 words)

	Spline (mathematics) - Encyclopedia, History, Geography and Biography
		In the mathematical subfield of numerical analysis a spline is a special curve defined piecewise by polynomials.
		In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results even when using low degree polynomials, thus avoiding Runge's phenomenon.
		The simplicity of representation and the ease with which a complex spline's shape may be computed make splines popular representations for curves in computer science, predominantly in computer graphics.
	www.arikah.net /encyclopedia/Spline_curve (412 words)

	Spline (mathematics) -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		The term spline comes from the flexible (A flexible strip (wood or rubber) used in drawing curved lines) spline devices used by shipbuilders and draftsmen to draw smooth shapes.
		In (additional info and facts about interpolating) interpolating problems, (additional info and facts about spline interpolation) spline interpolation is often preferred to (additional info and facts about polynomial interpolation) polynomial interpolation because it yields similar results even when using low degree polynomials, thus avoiding (additional info and facts about Runge's phenomenon) Runge's phenomenon.
		The simplicity of representation and the ease with which a complex spline's shape may be computed make splines popular representations for curves in (The branch of engineering science that studies (with the aid of computers) computable processes and structures) computer science, predominantly in (The pictorial representation and manipulation of data by a computer) computer graphics.
	www.absoluteastronomy.com /encyclopedia/s/sp/spline_(mathematics).htm (523 words)

	Citations: Cardinal Spline Interpolation - Schoenberg (ResearchIndex)
		The mth order B spline is given by the m fold convolution of the unit pulse function p(t) 1 for t [0, 1) 0 otherwise with itself.
		Schoenberg I. Cardinal spline interpolation, CBMS-NSF Vol 12, SIAM Philadelphia.
		One particular spline function is the B spline (basic spline) so called because translates of this function form a basis for the space of spline functions.
	citeseer.ist.psu.edu /context/267497/0 (2610 words)

	Cardinal Spline (Site not responding. Last check: 2007-10-08)
		A Cardinal Spline is a series of individual curves between points joined to form a larger curve.
		The spline is specified by an array of points and a tension parameter.
		A Cardinal Spline passes smoothly through each point in the array; there are no sharp corners and no abrupt changes in the tightness of the curve.
	www.geomet-cmm-software.com /KB10083.htm (1176 words)

	COMP259: Final Project (Site not responding. Last check: 2007-10-08)
		A Cardinal spline is calculated for each DOF (degree of freedom) that a particular model has.
		The blue curve is also a Cardinal Spline but the only points that takes in consideration are the endpoints (frame 0 and last frame), and the any point that has been changed by the user, more precisely the difference between the original point and the changed point.
		Cardinal Spline option will play out the motion by using just the ordinary cardinal spline which is usually not enough to get anything good.
	www.cs.unc.edu /~krstic/comp259/finalProject/final/final.html (1192 words)

	Spline Filters
		Cardinal Spline Filters: Stability and Convergence to the Ideal Sinc Interpolator
		The authors provide an interpretation of polynomial spline interpolation as a continuous filtering process.
		However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from Elsevier.
	bigwww.epfl.ch /publications/aldroubi9201.html (228 words)

	Cardinal Splines in GDI+ (Site not responding. Last check: 2007-10-08)
		A cardinal spline is a sequence of individual curves joined to form a larger curve.
		The formulas for mathematical splines are based on the properties of flexible rods, so the curves produced by mathematical splines are similar to the curves that were once produced by physical splines.
		To draw a cardinal spline, you need an instance of the Graphics class, a Pen, and an array of Point objects The instance of the Graphics class provides the DrawCurve method, which draws the spline, and the Pen stores attributes of the spline, such as line width and color.
	msdn2.microsoft.com /library/4cf6we5y(en-us,vs.80).aspx (532 words)

	A New Approach to Semi-Cardinal Spline Interpolation - Bejancu (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		In the present paper, we propose a new construction for the Lagrange functions of semi-cardinal spline interpolation, based on a radial basis and Fourier transform approach.
		Polyharmonic Spline Interpolation on a Semi-Space Lattice - Bejancu, Jr.
		4 splines Polyharmoniques Cardinales: Interpolation (context) - Rabut - 1990
	citeseer.ist.psu.edu /bejancu00new.html (432 words)

	Almost Cardinal Spline Interpolation (ResearchIndex)
		When the interpolation points and the knots of the interpolating splines are characterized by a periodic behavior, the interpolating problem is called Cardinal Interpolation.
		This work extends known results on Cardinal Interpolation to the "almost cardinal" case, where the interpolation is cardinal except for a finite number of interpolation points and knots.
		5 Oscillation Matrices and Cardinal Spline Interpolation (context) - Micchelli - 1978
	citeseer.ist.psu.edu /75586.html (248 words)

	Spline (mathematics) - Enpsychlopedia (Site not responding. Last check: 2007-10-08)
		A one-dimensional spline, $S(t)$ , is an example of a piecewise function.
		The space of all natural cubic splines, for instance, is a subspace of the space of all cubic $C^2$ splines.
		It is commonly accepted that the first mathematical reference to splines is Schoenberg's paper [S], which is probably the first place that the word "spline" is used in connection with smooth, piecewise polynomial approximation.
	www.grohol.com /psypsych/Spline_curve (2576 words)

	Sampling Theory and Spline Interpolation (Site not responding. Last check: 2007-10-08)
		In the spline method, the signal is reconstructed using sample-weighted cardinal splines as opposed to sample-weighted sinc functions.
		This means that cardinal splines can be used for signal reconstruction from samples just as sinc functions are used.
		This is because the support of the cardinal splines is more compact than that of the sinc function.
	cnx.rice.edu /content/m11126/latest (464 words)

	Cardinal B-Splines
		The most important ones are symmetry, limited range where the function is nonzero, and the fact that the sum of the function evaluated for all integers is one.
		The spline function was not giving correct results, so this graph allowed us to see exactly where the function was incorrect.
		This property is important because we multiply the Cardinal B-Spline value by the charge of a particle and then make use of its values at integer valued mesh points.
	www.challenge.nm.org /archive/03-04/FinalReports/26/node15.html (274 words)

	How to: Draw Cardinal Splines (Site not responding. Last check: 2007-10-08)
		A cardinal spline is a curve that passes smoothly through a given set of points.
		To draw a cardinal spline, create a Graphics object and pass the address of an array of points to the DrawCurve method.
		In a closed cardinal spline, the curve continues through the last point in the array and connects with the first point in the array.
	msdn2.microsoft.com /library/554h284b(en-us,vs.80).aspx (552 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		As this monograph shows, the purpose of cardinal spline interpolation is to bridge the gap between the linear spline and the cardinal series.
		The author explains cardinal spline functions, the basic properties of B-splines, including B- splines with equidistant knots and cardinal splines represented in terms of B-splines, and exponential Euler splines, leading to the most important case and central problem of the book-- cardinal spline interpolation, with main results, proofs, and some applications.
		The Basis Property of B-splines; The Exponential Euler Splines; Cardinal Spline Interpolation; Cardinal Hermite Interpolation; Other Spaces and Semi-Cardinal Interpolation; Finite Spline Interpolation Problems; Semi-Cardinal Interpolation and Quadratures with General Boundary Conditions; Extremum and Limit Properties; Applications: Approximations of Fourier Transforms and the Smoothing of Histograms.
	www.ec-securehost.com /SIAM/CB12.html (234 words)

	Cardinal B-spline dictionaries on a compact interval
		It is proved there that such spaces can be spanned by dictionaries which are built by translating a prototype B-spline function of fixed support into the knots of the required cardinal spline space.
		This implies that cardinal spline spaces on a compact interval can be spanned by dictionaries of cardinal B-spline functions of broader support that the corresponding basis function.
		In other words, cardinal B-spline dictionaries provide an alternative way of increasing the dimension of the space.
	www.ncrg.aston.ac.uk /Projects/BiOrthog/latex/sigrep/node15.html (199 words)

	Interpolating Cardinal and Catmull-Rom splines (Site not responding. Last check: 2007-10-08)
		Interpolating piecewise Cardinal spline is composed of cubic Bezier splines joined with C
		Remember, that a cubic Bezier spline is determined by 4 vectors (e.g.
		Unfortunately the Cardinal curve cannot be subdivided in two sub-curves which coincide with the initial one.
	www.ibiblio.org /e-notes/Splines/Cardinal.htm (186 words)

	Cubic Hermite spline - Wikipedia, the free encyclopedia
		In the mathematical subfield of numerical analysis a cubic Hermite spline, named in honor of Charles Hermite (Hermite is pronounced air MIT), is a third-degree spline with each polynomial of the spline in Hermite form.
		The Hermite form consists of two control points and two control tangents on each for each polynomial.
		Since each subinterval must share tangents with neighboring subintervals, many techniques exist to determine values for shared tangents.
	en.wikipedia.org /wiki/Cubic_Hermite_curve (131 words)

	CS411 Assignment 4 - Patrick Wagstrom
		The hermite and cardinal splines use matrix math via SVL while the bezier curve uses expanded equations.
		Thus for the cardinal cubic spline, the first and last points are not connected to the curve.
		As opposed to the Cardinal where the first and last points are not included, in the Bezier the only points included are the first and the last points.
	patrick.wagstrom.net /projects/academic/cs411/prog4 (636 words)

	The eighties: an image processing view
		44] point out that the parameter a of the cardinal cubic splines has a physical meaning since it is the slope of the filter at x=1.
		The B-spline and cardinal splines are even more expensive with four contributing sample points.
		The cubic B-spline provides the most smoothing whereas the cardinal cubic spline with a=-1 provides the best high-frequency response along with some high frequency enhancement and the cardinal cubic spline with a=-0.5 has both a flat low-frequency response and good stop-band performance.
	www.cg.tuwien.ac.at /~theussl/DA/node11.html (1304 words)

	Introduction to curves (Site not responding. Last check: 2007-10-08)
		A Cardinal curve is made up of smooth arc segments.
		Cardinal curves have a parameter called tension, which can be edited in the Curve Info dialogue box (choose Info
		Linear, Bezier, Cardinal, and B-Splines curves have only a subset of the capabilities of NURBS.
	imagearts.ryerson.ca /abal/lectures/3D/curves.htm (397 words)

	NUI: nuiSpline class Reference
		Set the spline in Bezier mode: the tangents won't be recalculated automatically and they are in fact the second and third control points in a cubic bezier spline.
		Calculate the Tangents with the Cardinal algorithm (cardinal with a tightness of 0.5).
		Set the spline in Cardinal mode with the given tightness.
	www.nongnu.org /ngl/doc/nui/classnui_spline.html (490 words)

	Polynomial Splines
		The least-squares polynomial spline approximation of a signal g(t) in L
		It is shown that this process can be linked to the classical problem of cardinal spline interpolation by first convolving g(t) with a B-spline of order n.
		It is shown that this approximation can be obtained from a succession of three basic operations: prefiltering, sampling, and postfiltering, which confirms the parallel with the classical sampling/reconstruction procedure for bandlimited signals.
	bigwww.epfl.ch /publications/unser9202.html (317 words)

	Drawing Cardinal splines
		GDI+ supports two different forms of a complex curve that can't be represented as an arc of a circle or an ellipse: a cardinal spline and a Bézier spline.
		A cardinal spline is the curve that you would create by taking a piece of flexible material-such as a thin stripe of iron or wood-and making it pass through a given set of fixed points on the X-Y plane.
		Unless the material you're using is infinitely flexible (as it would be a string of rope or rubber), the path drawn by the material would be a curve that doesn't create any sharp angles at the connecting points.
	www.devx.com /vb2themax/Tip/18730 (313 words)

	[No title]
		In this module, Shannon's classical sampling theory is compared to digital to analog signal reconstruction using spline interpolation.
		Bandlimited continuous signals can be reconstructed from their samples using a linear combination of cardinal splines, where the spline functions are weighted by the sample values.
		, it may appear that the spline interpolation is smoother than the sinc interpolation.
	cnx.rice.edu /content/m11126/2.3/source (274 words)

	Tensor product spline surfaces
		All spline curves studied before work well in space of any dimension.
		But spline surfaces are used mainly in 3D space (and IMHO Internet is too "plain" yet :) therefore I made several 3D spline models.
		Cardinal spline curve can be generalized easy for 2D regular net of quadrilateral patches.
	www.ibiblio.org /e-notes/Splines/Inter.htm (554 words)

	Pointwise Error Bounds for Orthogonal Cardinal Spline Approximation (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Abstract: For orthogonal cardinal spline approximation, closed form expressions of the reproducing kernel and the Peano kernels in terms of exponential splines are proved.
		Concrete and sharp pointwise error bounds are deduced for low degree splines.
		1991 Mathematics Subject Classification: 41A15,42C15,65D07 Keywords and Phrases: pointwise error bounds, cardinal splines, orthogonal approximation, spline wavelet expansion, Peano kernels 1 Introduction Cardinal approximation operators are basic for...
	citeseer.ist.psu.edu /427805.html (421 words)

	Spline Curve Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-08)
		Looking For spline curve - Find spline curve and more at Lycos Search.
		Find spline curve - Your relevant result is a click away!
		Look for spline curve - Find spline curve at one of the best sites the Internet has to offer!
	www.karr.net /encyclopedia/Spline_curve (2457 words)

	Spline Wavelets of Small Support
		Spline Wavelets of Small Support:SIAM Journal on Mathematical Analysis Vol.
		Every $m$th order cardinal spline wavelet is a linear combination of the functions $\{N_{m+l}^{(l)}(2x-j), j\in \bold Z\}$.
		Each wavelet is constructed by spline multiresolution analysis.
	epubs.siam.org /sam-bin/dbq/article/24526 (115 words)

	What is a cardinal spline? (Site not responding. Last check: 2007-10-08)
		A Cardinal Spline takes the positions of the current point and,along with the previous and next points, averages out the positions using a tension value.
		This smoothes the line and makes a path that is gently curved through the points rather than zigzagging through them.
		Figure 1 shows a cardinal spline drawn through several points.
	www.bobpowell.net /cardinalspline.htm (125 words)

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