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Topic: B-spline

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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 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)

B-spline - Wikipedia, the free encyclopedia In the mathematical subfield of numerical analysis a B-spline is a special spline curve. The term B-spline was coined by Isaac Jacob Schoenberg and is short for basis spline. The De Boor algorithm is a numerically stable way to evaluate B-splines. www.wikipedia.org /wiki/B-spline

Spline Roadbed Spline roadbed has been around for a while and many materials including wood, masonite, and homasote have been used all of which can give good results (while tearing down the Virginian & Ohio the work crew discovered that spline roadbed made from homosote strips nearly 40 years ago was still in good shape!). Spline roadbed is made by taking several strips of fairly skinny material, standing them on edge, and laminating (gluing) them together to form a solid roadbed. The splines are just a bit wider than the ties and if I kept a constant distance from the edge of the spline to the edge of the ties the track was centered. www.bcsj.org /rr/splines/index.shtml

Spline Spline is available in 6' length, 50', 100', and 1000' bundles. The wedge-shaped reed spline is used to secure the woven cane to chair frames having a groove. It is very important to select the proper size spline. www.cbsc.us /spline.htm

Spline curve Splines of degree 3 are by far the most commonly used in practice. If the control point polygon is concave the spline passes through the midpoint, if the polygon is concave the spline is tangential at the edge midpoint. Following are three functions which implement spline curves, at the end there is a small demonstration program which calls these routines to create the image shown earlier. astronomy.swin.edu.au /~pbourke/curves/spline

Cubic Spline Quadrature Construct the cubic spline for 41 nodes and use it for quadrature. Construct the cubic spline for 21 nodes and use it for quadrature. Construct the cubic spline for 11 nodes and use it for quadrature. mathews.ecs.fullerton.edu /n2003/splinequad/SplineQuadMod/Links/SplineQuadMod_lnk_2.html

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. 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. Handles on a Bezier Vertex, dragged to control curvature of the spline segment as it enters, and leaves the vertex. www.phong.com /tutorials/3dmax/spline

Spline Tutorial I tried modelling a complex spline character by extruding it and it made it fine, but the end and start caps were tessalated, so I could have never done modelling that way because Anim8or doesnt have a connected extrude. This can be fixed by deleting that face, then mirroring the extruded the spline and joining the solids, and merging the points. I never messed around with Anim8or splines before, I always modelled using basically box modelling. www.geocities.com /elimar48/tutorials/Spline_Tut/tutorial.html

Omkrets arkitektur: spline A spline is the shape taken by bending material objects, like beams, that minimizes the elastic energy (or internal strain energy) stored in the beam. In 3D modeling it is a curve defined by control points, often supplemented by interactive methods to modify tangents to the curve at these points and to adjust a local weighting factor. Mathematically, it is the smoothest curve that passes through a set of fixed points. omkrets.se /spline

Spline Toolbox 3.1.1 Release Notes (Spline Toolbox Release Notes) This M-file also provides you with a written record of the Spline Toolbox commands used to generate the current graph(s), and can be edited, or executed in a loop over different data sets. The Spline Toolbox 3.1.1 that is part of Release 13 has no substantive changes from the Spline Toolbox 3.1. If you are upgrading from the Spline Toolbox 2.0, then you should also see New Features in the Spline Toolbox 3.0 Release Notes. www-rohan.sdsu.edu /doc/matlab/base/relnotes/splines/splines13.html

Cardinal Spline 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. A Cardinal Spline is a series of individual curves between points joined to form a larger curve. www.geomet-cmm-software.com /KB10083.htm

Systat Software Inc. - TableCurve 2D - HTML Help A cubic spline is smooth in the first derivative and continuous in the second derivative. A quartic spline is smooth in both first and second derivatives and continuous in the third derivative. option fits a cubic spline interpolant where the breakpoints or knots of the spline are the X values of the data. www.systat.com /products/TableCurve2D/help?sec=1055

splines.htm Splines are used for lathing to make circular objects, for loft paths and shapes, and for paths for objects to follow. Being able to easily and quickly draw splines (lines) in MAX is a very handy skill. This tutorial is designed to give you practice in working with splines so you can create them more efficiently. www.maxhelp.com /content/tutorials/splines/splines.htm

Visual Numerics - Developers of IMSL and PV-WAVE CSCON (DCSCON) Compute a cubic spline interpolant that is consistent with the concavity of the... DCSCON (CSCON) Compute a cubic spline interpolant that is consistent with the concavity of the... BS1GD (DBS1GD) Evaluate the derivative of a spline on a grid, given its B-spline representation... www.vni.com /products/imsl/alphabetized_functions.html

BMW Airhead Spline Lubrication - Spline Lube - webBikeWorld I carried out a spline lube because I found the gears were often hard to shift without experiencing a considerable clunk and grate of gears, particularly shifting down from 3rd to 2nd and from 2nd to 1st. The '84 must have had a spline lube done by the previous owner, because I could still see the lube on the splines. Lubing the splines on the '86 has made a big difference in the way it shifts -- it really shifts beautifully and the transmission seems like it "snicks" right into gear. www.webbikeworld.com /t2/spline

Functional Data analysis - The Characteristics of Spline Functions - Page2 A cubic spline is smooth in itself, but its first derivative will appear to change with noticeable abruptness at the breakpoints, and its second derivative will be a polygonal line. This discussion only gives a vague idea of how to construct spline functions, and does not address the issue of how a basis function system can be set up, linear combinations of which define any spline of a specified order and number of breakpoints. However, if you simply need to work with spline functions and are content to leave the properties of the spline basis functions to the experts, you probably already know enough. www.psych.mcgill.ca /misc/fda/ex-basis-b2.html

Cubic Spline Interpolation The cubic spline interpolation is a piecewise continuous curve, passing through each of the values in the table. Cubic splines are popular because they are easy to implement and produce a curve that appears to be seamless. Cubic splines avoid this problem, but they are only piecewise continuous, meaning that a sufficiently high derivative (third) is discontinous. www.physics.utah.edu /~detar/phycs6720/handouts/cubic_spline/cubic_spline/node1.html

Spline Macro File Tutorial 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. 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. If you've used the lathe or prism object in POV-Ray you should have a pretty good understanding of how splines work. www.geocities.com /ccolefax/spline

FRENCO Verzahnungstechnik/Messtechnik Products Gear Inspection The very accurate measurement of gear and spline profiles is not possible with standard 3 coordinate measuring systems. Since May 2000 the FRENCO Measuring Room is accredited by the PTB as Calibration Lab for Gear and Spline sizes. Periodical supervision of spline gages, master gears, indicating gages and toothed clamping systems to wear of size and form. www.frenco.de /products/p-en.shtm

Spline Interpolation Demo 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. The term "relaxed" is used because the endpoints of the cubic spline have their second derivative equal to zero. We use a relaxed cubic spline to interpolate the six points. www.math.ucla.edu /~baker/java/hoefer/Spline.htm

Spline Tools The Spline tool uses Bézier curve segments and automatically calculates the control handle positions. 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

Service Over those 22 years we have rebuilt splines for many of the BMW dealers on the West Coast. New wheel coupler on "R" models, or new driveshaft on "K" must be installed at time of spline repair and must appear on the repair order. Although each owner and motorcycle are different and wear may vary, we have several of these splines with 50 to 80,000 miles on them with minimal wear. www.hansensmc.com /spline.html

World of Trainz - Spline File and Folder Tutorial For a normal spline object there are no subfolders required however there is an optional folder called the tutorial_spline_object 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. www.worldoftrainz.com /Pages/TutorialsTRS/SplinesFolderTutTRS.htm

Another R bike spline lube approach I found an EASY way to reassemble the rear spline and rear drive, I did it on the bench, but it could be done on the bike if you understand the concept.. Lube sparingly, the contact points where the spring rides in the flywheel (the entire outer circumference), the points where the springs contacts the front of the pressure plate, the clutch plate spline, center bushing in the flywheel, as well as the center bushing in the spring. At Paul's suggestion I removed the clutch disk and cleaned everything thouroughly, especially the spline which was quite dry, even though it was lubed the previous year. www.ibmwr.org /r-tech/airheads/r100gspline2.shtml

Addix Software Consultancy - Spline library overview 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. 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. 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. www.addix.com /products/spline/overview.html

Larry Schumaker's Home Page Lagrange interpolation by $C^1$ cubic splines on triangulated quadrangulations, (with G. Nurnberger and F. Zeilfelder), Adv. Local Lagrange interpolation with $C^2$ splines of degree seven on triangulations, with G. N\"urnberger, V. Rayevskaya, and F. Zeilfelder, in {\sl Advances in Constructive Approximation: Vanderbilt 2003}, Mike Neamtu and Ed Saff (eds.), Nashboro Press, Brentwood, 2004, 345--370. Local Lagrange interpolation by $C^1$ cubic splines on triangulations of separable quadrangulations, (with G. Nurnberger and F. Zeilfelder, in Approximation Theory X: Splines, Wavelets, and Applications, Charles K. Chui and Larry L. Schumaker (eds.), Vanderbilt University Press, Nashville, 2002, 405--424. www.math.vanderbilt.edu /~schumake

B-Spline Curve Visualization 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". The curve is drawn in two colors, cyan and orange: these two colors alternate between adjacent spline segments. graphics.stanford.edu /courses/cs348c-95-fall/software/scurvy

spline The following figure shows the I-splines that were derived from the M-splines above. }, where n is the number of free parameters that specify the spline function, is derived from the These spline formula's were taken from Ramsay (1988) and the errors in his I-spline formulas were corrected. fonsg3.let.uva.nl /praat/manual/spline.html

Riverside Spline & Gear, Inc. on powertransmission.com Riverside Spline & Gear, Inc. was established in Marine City, Michigan in 1963. Riverside Spline & Gear, Inc. recognizes the demand for quiet, cooler running gears and exceeds this demand with the development of its gear grinding facility. For the last 40 years this company has supplied new and replacement gears to diversified customers at their 30,000 sq. www.powertransmission.com /copage/riverside.htm

Optimal Quadratic Spline Collocation Methods for the (ResearchIndex) In the standard formulation, the quadratic spline is computed by making the residual of the differential equations zero at a set of collocation points; the resulting error is second order, while the... A quadratic spline collocation method approximates the solution of a differential problem by a quadratic spline. 1 A spline collocation scheme for the spherical shallow water.. citeseer.ist.psu.edu /624800.html

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