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	spline :: Functions (MATLAB Function Reference)
		are used as the endslopes for the cubic spline.
		This illustrates the use of clamped or complete spline interpolation where end slopes are prescribed.
		uses the cubic spline to extrapolate and predict the population in the year 2000.
	www.mathworks.com /access/helpdesk/help/techdoc/ref/spline.shtml (0 words)

	Bezier spline curves
		Linear Bezier spline is obtained by linear interpolation between two control points P
		Quadratic Bezier spline is obtained by deCasteljau algorithm as a linear interpolation between linear interpolation between control points P
		By construction Bezier spline goes through its terminal control points, i.e.
	www.ibiblio.org /e-notes/Splines/Bezier.htm (402 words)

	Plot \| Doc / SplineFitInspector browse
		Spline fit automatically determines a function that is flexible enough to represent the underlying trend, yet smooth enough not to fit the noise.
		Spline fit assumes that the error in each Y value is independent of the error in the next Y value.
		The reason that this is possible is that spline fit uses special statistical tests, which are insensitive to user misjudgements of the errors in the data and even immune to a misjudgement in the form of a common scaling factor.
	plot.micw.eu /Doc/SplineFitInspector (1263 words)

	i/spline
		With two arguments, Y and X, spline returns the derivatives DYDX at the points, an array of the same length as X and Y. The DYDX values are chosen so that the piecewise cubic function returned by the four argument call will have a continuous second derivative.
		In a cubic spline, the second derivative of the spline function varies linearly between the points X. In the tensioned spline, the curvature is concentrated near the points X, falling off at a rate proportional to the tension.
		With three arguments, Y and X, spline returns the derivatives D2YDX2 at the points, an array of the same length as X and Y. The D2YDX2 values are chosen so that the tensioned spline function returned by the five argument call will have a continuous first derivative.
	www.maumae.net /yorick/doc/html_i/spline_i.php (933 words)

	eScience Lectures Notes : Spline
		Slide 14 : The Gradient of a Cubic Spline
		Slide 14 : 14 / 42 : The Gradient of a Cubic Spline
		The mathematical equivalent is the cubic polynomial spline.
	cs.anu.edu.au /escience/lecture/cg/Spline/printNotes.en.html (4330 words)

	phongTUTORIALS- [ 3D Studio MAX, Photoshop, and POV-Ray Tutorials ]
		Splines are lines going anywhere in 3D space, used to create paths for modifiers and other renderable, or animatable objects.
		Handles on a Bezier Vertex, dragged to control curvature of the spline segment as it enters, and leaves the vertex.
		To edit an existing spline (add, subtract, smooth, sharpen or edit locations of vertices), in the modify tab click 'Sub-Object' to use the array of functions available for editing your shape.
	www.phong.com /tutorials/3dmax/spline (280 words)

	Introduction to Catmull-Rom Splines
		Splines are a mathematical means of representing a curve, by specifying a series of points at intervals along the curve and defining a function that allows additional points within an interval to be calculated.
		One of the features of the Catmull-Rom spline is that the specified curve will pass through all of the control points - this is not true of all types of splines.
		While a spline segment is defined using four control points, a spline may have any number of additional control points.
	www.mvps.org /directx/articles/catmull (511 words)

	The Plotutils Package - The spline Program
		If the tension is zero (the default, or cubic spline case), then the computation of the spline will be unaffected by linear scaling of the data.
		This is not the same as splining, at least as the term is conventionally defined.
		The reason is that `splining' refers to construction of a function, rather than the construction of a curve that may or may not be the graph of a function.
	www.gnu.org /software/plotutils/manual/html_chapter/plotutils_7.html (2769 words)

	Online Portfolio of Erik Asorson
		Splines would be perfectly suited for the job becuase the contour of the object exists independant of the amount of polygons in the model.
		Splines connecting smooth points will automatically form the smoothest curve based on the position of the points before and after it on the spline path.
		The the only purpose of points on a spline is to define the shape of the spline, either by the position, or the bezier handles attributed to that point.
	www.erikasorson.com /tutorials/tutorial_splines.html (2634 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 4 of cubic spline interpolation, born on 2003-06-11, modified 2006-10-19.
	planetmath.org /encyclopedia/CubicSplinInterpolation.html (489 words)

	Spline (mathematics) - Wikipedia, the free encyclopedia
		Splines are popular 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.
	en.wikipedia.org /wiki/Spline_(mathematics) (2330 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 (622 words)

	Riten Industries: Spline Rolling Live Centers
		Spline rolling is the fastest and most economical method of producing an involute tooth form.
		Spline shafts are used in automobiles, washing machines, tractors, industrial equipment, and many other applications where there is a need to transmit torque from one part to another.
		Riten Spline rolling live centers are designed and manufactured specifically for this demanding process.
	www.riten.com /industries_served/spline_rolling/default.asp (539 words)

	spline (MATLAB Function Reference)
		are used as the endslopes for the cubic spline.
		This illustrates the use of clamped or complete spline interpolation where end slopes are prescribed.
		uses the cubic spline to extrapolate and predict the population in the year 2000.
	www.cs.berkeley.edu /titan/sww/software/matlab/techdoc/ref/spline.html (313 words)

	Spline Macro File Tutorial
		Notice also that the colour of the previewed spline changes from red at the first point to white at the last: this lets us know which direction the spline is travelling in.
		The next option we can try is the spline bias value: like the spline tension this is normally zero, which means that the spline is curved equally on either side of each point in the spline.
		Bezier splines have the advantage over TCB splines of allowing you to set the curvature of the spline directly for each section, so you can create some sharp corners and some smooth, and generally have more control over the spline's shape.
	www.geocities.com /ccolefax/spline/index.html (1676 words)

	SPLINE - Interpolation and Approximation of Data
		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 (695 words)

	Spline Tools
		A 'smooth curve' is not an easily defined entity; however, for the purposes of this tool, an important requirement is that a spline connecting points along a circle should match the curve of a circle.
		To draw a spline, you draw with the same method that you use to draw a polygon.
		The Spline tool also allows you to convert an existing polygon to a spline or to convert one type of spline to another.
	www.seqair.com /WildTools/Splines/Splines.html (588 words)

	splinetool (Spline Toolbox)
		The Spline Tool is shown below comparing cubic spline interpolation with a smoothing spline on sample data created by adding noise to the cosine function.
		Therefore, the error shown in the graph is the error in the spline as an approximation to the cosine rather than as an approximation to the given values.
		This example uses cubic spline interpolation and least-squares approximation to determine an estimate of the initial acceleration for a drag car.
	www.phys.ufl.edu /docs/matlab/toolbox/splines/splinetool.html (1520 words)

	Spline method of interpolation: ebook
		The first derivatives of two quadratic splines are continuous at the interior points.
		Using the quadratic splines as velocity functions, find the distance covered by the rocket from t=11s to t=16s.
		Using the quadratic splines as velocity functions, find the acceleration of the rocket at t=16s.
	numericalmethods.eng.usf.edu /ebooks/spline_05inp_ebook.htm (1123 words)

	Tutorial (Spline Toolbox)
		This is, more precisely, the cubic spline interpolant with the not-a-knot end conditions, meaning that it is the unique piecewise cubic polynomial with two continuous derivatives with breaks at all interior data sites except for the leftmost and the rightmost one.
		changes from 0 to 1, the smoothing spline changes, correspondingly, from one extreme, the least-squares straight-line approximation to the data, to the other extreme, the "natural" cubic spline interpolant to the data.
		Vector-valued splines are also used in the approximation to gridded data, in any number of variables, using tensor-product splines.
	www.phys.ufl.edu /docs/matlab/toolbox/splines/tutor.html (1196 words)

	Spline Macro File Tutorial - Animation
		We've seen how splines can be used as the basis for objects in POV-Ray scenes, but what we haven't looked at yet is one of the most common uses of splines: animation.
		The first type include the number of points in the spline, whether or not the spline loops back on itself, the length of the spline, and the direct length between the spline points, all of which remain the same throughout an animation.
		In the previous animation the spline clock was the same as the POV-Ray scene clock, and so the motion along the spline path matched the length of the rendered animation.
	www.geocities.com /ccolefax/spline/tutorial3.html (1360 words)

	Spline (JMSL Numerical Library)
		Spline represents and evaluates univariate piecewise polynomial splines.
		Returns the value of the derivative of the spline at each point of an array.
		, the integral of the spline from a to b
	www.vni.com /products/imsl/jmsl/v30/api/com/imsl/math/Spline.html (517 words)

	B-Spline Curve Visualization
		The curve is drawn in two colors, cyan and orange: these two colors alternate between adjacent spline segments.
		Each spline segment is drawn by approximating the shape of the ideal curve by as many line segments as specified by the "Pieces" slider.
		The spacing between the spline knots can be interactively modified using the sliders labeled "Knot i to i+1".
	graphics.stanford.edu /courses/cs348c-95-fall/software/scurvy (1162 words)

	spmak (Spline Toolbox)
		-vectors (e.g., 2-vectors or 3-vectors), in which case the resulting spline is a curve or surface (in 2-space or 3-space).
		is taken to be a B-spline coefficient of the spline.
		This follows the general agreement in this package that, in case of a vector-valued spline, any vector in its target, be it a coefficient, or the value of the spline at a point, is written as a 1
	www.tau.ac.il /cc/pages/docs/matlab/help/toolbox/splines/spmak.html (313 words)

	Spline Doctors
		Yes, its summer, and that means things are a bit slow.
		Story Spline Cast with Mark Andrews and Ted Mathot...
		This is a paragraph of text that could go in the sidebar.
	splinedoctors.blogspot.com (0 words)

	Addix Software Consultancy - Spline library overview
		This product provides the ability to generate a wide variety of spline curves by adding a number of additional functions to the list of built-in functions available to users of Excel, Visual Basic and Visual Basic for Applications.
		Once the product is loaded via the appropriate Add-In/Reference Manager, all of the spline interpolation functions that it provides appear as native functions and can be invoked either from spreadsheet cell formulae or from Visual Basic code.
		Access to all the other supported spline types is unrestricted during the evaluation period but is restricted to registered users once the evaluation period has expired.
	www.addix.com /products/spline/overview.html (172 words)

	Edit spline stuff (Site not responding. Last check: )
		The answer is, you attach two splines together: the pentagon is the outer border of the shape and the circle is the inner border.
		If the two splines intersect or if they are separated, they will each extrude individually.
		The direction of the spline affects any measurement of the "percent" along the spline.
	www.bergen.org /AAST/Projects/3DSMaxTutorial/edit_spline.html (581 words)

	spapi (Spline Toolbox)
		, unless the spline is to be scalar-valued, in which case, in contrast to the univariate case,
		by a cubic spline, and its slope is also to be matched at a subsequence
		Gridded data are fitted, in tensor-product fashion, one variable at a time, taking advantage of the fact that a univariate spline fit depends linearly on the values being fitted.
	www.eecs.umich.edu /dco/faq/matlab-6.5/help/toolbox/splines/spapi.html (403 words)

	Adobe Illustrator 2D Spline Shape Import Converter
		Import of one form of 2D spline curve data (such as Cardinal curves from the OpenFlight file format) and conversion to another 2D spline format for subsequent output as 2D spline curves again (such as Bezier curves output to 3DS MAX).
		If multiple spline paths are surrounded by the U and u commands, then the source program wishes for these multiple spline paths to be stored as a single, complex spline shape object.
		For example, the letter O might be defined as 2 closed spline curves within a U/u command pair; this pair of curves should ideally be imported as a single object so that the hole in the letter O appears when rendered.
	www.okino.com /conv/imp_ai.htm (963 words)

	World of Trainz - Spline File and Folder Tutorial
		If the splines directory is not present then you will need to create it.
		Create a folder for the project and use an appropriate name add _spline to the end of the folder and avoid using spaces in the name.
		For a normal spline object there are no subfolders required however there is an optional folder called the tutorial_spline_object
	www.worldoftrainz.com /Pages/TutorialsTRS/SplinesFolderTutTRS.htm (607 words)

	Interactive Spline Editor
		ISE (Interactive Spline Editor) is a simple program for user to interactively input, edit, and sample cubic splines.
		If the point happens to be a control point, you will move that control point to the place where you release the mouse button (you would not be able to see the effect unless you release the button).
		To delete a spline curve, you need to press left button inside the bounding box and hold the shift key while you release the button.
	graphics.stanford.edu /courses/cs368/spline.html (765 words)

	Autodesk Inventor Spline Commands
		Bowties are used to define the shape of the spline near spline points, and they can take three forms: a Handle, a Handle and Curvature, and a Handle and Flat.
		You can also define the radius of the spline near the spline point by changing the bowtie to a handlebar and curve.
		While splines are more difficult to define the exact size and shape than lines and arcs, knowing these commands give you more control over them.
	trainingtutorial.com /TAT9.htm (590 words)

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