University of Waterloo, Department of Electrical and Computer Engineering,
Undergraduate Program.

Cubic spline

In mathematics, a spline is a sufficiently smooth polynomial function that is piecewise-defined, and possesses a high degree of smoothness at the places where the polynomial pieces connect (which are known as knots).

In interpolating problems, spline interpolation is often referred to as polynomial interpolation because it yields similar results, even when using low-degree splines, to interpolating with higher degree polynomials while avoiding instability due to Runge's phenomenon. In computer graphics splines are popular curves 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.

The most commonly used splines are cubic spline, i.e., of order 3—in particular, cubic B-spline and cubic Bézier spline. They are common, in particular, in spline interpolation simulating the function of flat splines.

The term spline is adopted from the name of a flexible strip of metal commonly used by draftsmen to assist in drawing curved lines.

Splines are curves, which are usually required to be continuous and smooth. Splines are usually defined as piecewise polynomials of degree n with function values and first n-1 derivatives that agree at the points where they join. The abscissa values of the join points are called knots. The term "spline" is also used for polynomials (splines with no knots) and piecewise polynomials with more than one discontinuous derivative. As such, splines with no knots are generally smoother than splines with knots, which are generally smoother than splines with multiple discontinuous derivatives. Splines with few knots are generally smoother than splines with many knots; however, increasing the number of knots usually increases the fit of the spline function to the data. Knots give the curve freedom to bend to more closely follow the data.

This is an excerpt from the article Cubic spline from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.

In interpolating problems, spline interpolation is often referred to as polynomial interpolation because it yields similar results, even when using low-degree splines, to interpolating with higher degree polynomials while avoiding instability due to Runge's phenomenon. In computer graphics splines are popular curves 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.

The most commonly used splines are cubic spline, i.e., of order 3—in particular, cubic B-spline and cubic Bézier spline. They are common, in particular, in spline interpolation simulating the function of flat splines.

The term spline is adopted from the name of a flexible strip of metal commonly used by draftsmen to assist in drawing curved lines.

Splines are curves, which are usually required to be continuous and smooth. Splines are usually defined as piecewise polynomials of degree n with function values and first n-1 derivatives that agree at the points where they join. The abscissa values of the join points are called knots. The term "spline" is also used for polynomials (splines with no knots) and piecewise polynomials with more than one discontinuous derivative. As such, splines with no knots are generally smoother than splines with knots, which are generally smoother than splines with multiple discontinuous derivatives. Splines with few knots are generally smoother than splines with many knots; however, increasing the number of knots usually increases the fit of the spline function to the data. Knots give the curve freedom to bend to more closely follow the data.

This is an excerpt from the article Cubic spline from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.

The article Cubic spline at en.wikipedia.org was accessed 863 times in the last 30 days. (as of: 11/21/2013)

Search results from Google and Bing

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Cubic Spline -- from Wolfram MathWorld

A Cubic spline is a spline constructed of piecewise third-order polynomials which pass through a set of m control points. The second derivative of each polynomial is ...

mathworld.wolfram.com/CubicSpline.html

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Cubic Spline Interpolation

The Cubic spline interpolation is a piecewise continuous curve, passing through
each of the values in the table. There is a separate cubic polynomial for each ...

www.physics.utah.edu/~detar/phys6720/handouts/cubic_spline/cubic_spline/node1.html

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Spline (mathematics) - Wikipedia, the free encyclopedia

[edit]. Main article: Spline interpolation. Spline interpolation is one of the most
common ...

en.wikipedia.org/wiki/Spline_(mathematics)

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Spline interpolation - Wikipedia, the free encyclopedia

In the mathematical field of numerical
analysis, spline interpolation is a form of
...

en.wikipedia.org/wiki/Spline_interpolation

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The Math Behind Bezier Cubic Splines

Bezier Cubic splines are an excellent and preferred method to draw the smooth ... out exactly where the funny numbers relating Cubic spline power coefficients.

www.tinaja.com/glib/cubemath.pdf

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Cubic spline curves - UCLA Department of Mathematics

In contrast, Figure 2 shows an example of a "Cubic spline" curve through the
same data ... The spline curve was constructed by using a different cubic
polynomial.

www.math.ucla.edu/~baker/149.1.02w/handouts/dd_splines.pdf

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Cubic Spline Interpolation - MATLAB & Simulink - MathWorks

You can use the Cubic spline interpolant obtained by cs = csapi(x,y);. and plot the
spline, along with the data, with the following code: fnplt(cs); hold on plot(x,y ...

www.mathworks.com/help/curvefit/cubic-spline-interpolation.html

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Cubic Spline Interpolation Introduction Theory Process

Cubic spline Interpolation. Sky McKinley and Megan Levine. Math 45: Linear
Algebra. Abstract. An introduction into the theory and application of Cubic splines
...

online.redwoods.edu/instruct/darnold/laproj/Fall98/SkyMeg/Proj.PDF

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perform cubic spline interpolation on a set of data - Maple Help

The CubicSpline command interpolates the given data points xy using the Cubic spline method and stores all computed information in a POLYINTERP structure.

www.maplesoft.com/support/help/Maple/view.aspx?path=Student%2FNumericalAnalysis%2FCubicSpline

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Splines Cubic Spline Interpolation

S(x) is not a quadratic spline because limx→0− S (x) = limx→0+ S (x). Cubic spline Interpolation. Given f, x0,...,xn as above, find a Cubic spline S such that S(
xi) ...

www-personal.umich.edu/~yryamada/splines.pdf

Search results for "Cubic spline"

Google: approx. 1.760.000

Cubic spline in science

5.8 Cubic Spline Interpolation - Electrical and Computer Engineering

Solution of Transcendental Equation Using Clamped Cubic Spline ...

Solution of Transcendental Equation Using Clamped Cubic spline. ...
Department of Mathematics, Jagannath University, Dhaka-1100, Bangladesh.

[PDF]3.3 Cubic Spline Interpolation

Copyright (C) 1988-1992 by Cambridge University Press.Programs ... The goal of Cubic spline interpolation is to get an interpolation formula that is smooth in the ...

[PDF]ECG INTERPOLATION USING TAUT CUBIC SPLINES ... - Springer

ECG INTERPOLATION USING TAUT Cubic splineS. INTRODUCTION. E.
Tkacz. Technical University of Silesia. Department of Medical Electronics. Gliwice
...

Spline (mathematics) - Wikipedia, the free encyclopedia

A Cubic spline composed of seven polynomial segments. This shape is ... The
second derivative of the Cubic spline above. .... Cambridge University Press. p. 82
.

[PDF]Convergence of O(h**4) Cubic Spline Collocation ... - Purdue e-Pubs

Convergence of O(h**4) Cubic spline Collocation. Methods for Elliptic Partial
Differential Equations. Elias N. Houstis. Purdue University, enh@cs.purdue.edu.

Cubic Spline -- from Wolfram MathWorld

Cubic spline ... A Cubic spline is a spline constructed of piecewise third-order
polynomials which pass ... Cambridge, England: Cambridge University Press, pp.

[PDF]Interpolation & Polynomial Approximation Cubic Spline Interpolation I

Dublin City University cс 2011 Brooks/Cole, ... Conditions for a Cubic spline
Interpolant. 3 ... The construction of the Cubic spline does not, however, assume
that.

Books on the term Cubic spline

Interpolating Cubic Splines

This book presents a detailed examination of Cubic splines which includes a significant amount of original material not found elsewhere in the literature.

Interpolating Cubic Splines

Spline modeling affects a number of fields, including statistics, computer graphics, CAD programming and other areas of applied mathematics. This book presents a detailed examination of Cubic splines which includes a significant amount of original material not found elsewhere in the literature. Several C programs with interesting computational appr...

Longitudinal Data Analysis

11.2 Background: Cubic splines and spline models A Cubic spline g(t) for tmin ≤ t
≤ tmax with r distinct knots τ = (τ1 ,...,τ r), such that tmin < τ1 < ··· < τr < tmax,
satisfies the following conditions (Dierckx, 1993): (1) g(t) is a piecewise cubic ...

How to Build Cubic Spline Curve

The Japanese government bond analytic is a bit unique. It is different than any other countries in the world, so it is important to give a special introduction for it. I will use JGB as a short for Japanese government bond.For US government bond markets, they are very liquid and trading volumes are very high, so their price information are reliable...

Spline Regression Models (Quantitative Applications in the Social Sciences) (v. 137)

Spline Regression Models shows the nuts-and-bolts of using dummy variables to formulate and estimate various spline regression models. For some researchers this will involve situations where the number and location of the spline knots are known in advance, while others will need to determine the number and location of spline knots as part of the es...

Numerical Methods in Engineering with Python 3

If there are more than a few data points, a Cubic spline is hard to beat as a global
interpolant. It is considerably “stiffer” than a polynomial in the sense that it has
less tendency to oscillate between data points. Figure 3.6. Mechanical model of a
...

Spline Models for Observational Data (CBMS-NSF Regional Conference Series in Applied Mathematics)

This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. Convergence properties, data ba...

Development of Google searches

Blog posts on the term

Cubic spline

Cubic spline

Draw a cubic spline curve through Google Earth Placemarks | netkingcol

If you want to draw a spline curve through a set of Placemarks in Google Earth, then this post might help you. I've written a script to achieve this (with limitations) and you are welcome to the code which is written in Javascript. This YouTube video demonstrates the script in action: http://youtu.be/zFE6H_UW0SA You might want…

netkingcol.wordpress.com/2014/01/02/draw-a-cubic-spline-curve-through-google-earth-placemarks/
Nikola Vitas: Cubic spline interpolation: Periodic splines

If the unknown function is periodic, then the periodicity may be used to specify the boundary conditions. Before (in the case of the natural splines) we had $n+1$ value of x and y and as a result we obtained values of the cubic polynomial at $n$ intervals.

nikolavitas.blogspot.com/2013/09/cubic-spline-interpolation-periodic.html
Small Blender Things: Drawing cubic splines in OSL

Some time ago I wrote about a routine to calculate the closest distance to a quadratic bezier spline and recently I reused this routine again in a slightly optimized form to create wiggles.
Being able to calculate the closest distance to a quadratic spline is useful but I really wanted to use Cubic splines because they offer more control, allowing for easier ways to create nice shapes.

blenderthings.blogspot.com/2013/12/drawing-cubic-splines-in-osl.html
CenterSpace Blog » Blog Archive » Smoothed Cubic Splines

Smooth Cubic splines embody a curve fitting technique which blends the ideas of Cubic splines and curvature minimization to create an effective data modeling tool for noisy data. Traditional Cubic splines represent the tabulated data as a piece-wise continuous curve which passes through each value in the data table.

www.centerspace.net/blog/nmath/smoothed-cubic-splines/
11 Jun 11, 22:00h · Hadra Festival Party @ Shanti! :: Cubic Spline+Moonquake+Les · Rome (Italy) · goabase

[DJs] MOONQUAKE [ Hadra Records ], UK, Moonquake got into electronic music as a teenager and started djing in 2001. Moving to....
[Live] Cubic spline (Live) [ Hadra Records ], FRANCE, Cubic spline is French duo Olivier and Clément (Psychic Redundancies a...

www.goabase.net/party/details/57566
glomelurus.com: A Geek's Story: Cubic Spline Interpolation in Matlab

This was a homework in my geometric modeling class. Later I modified it to receive input with mouse click and a button to clear and redraw, and also a drop down to choose parametrization method.

www.glomelurus.com/2013/12/cubic-spline-interpolation-in-matlab.html
The Analytical Economist: Cubic Spline Interpolation and Econometrics

This paper was written for my Numerical Analysis class. It was a small project in which I had to write a code and also answer a real world problem.

analyticaleconomist.blogspot.com/2013/11/cubic-spline-interpolation-and.html
Applying Cubic B-Spline Quasi-Interpolation to Solve 1D Wave Equations in Polar Coordinates

ISRN Computational Mathematics is a peer-reviewed, open access journal that publishes original research articles as well as review articles in all areas of computational mathematics.

www.hindawi.com/isrn/computational.mathematics/2013/710529/
Hermit Cubic Spline & Order of Continuity - iTute - Connecting Tutors and Students

Explain about Hermit Cubic spline & order of continuity between the joining curves.

www.itute.net/374/hermit-cubic-spline-%26-order-of-continuity
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