Yet the race to develop autonomous cars, which cannot run without guidance from machine-readable maps known as "splines" or "digital rails", could be a far bigger opportunity.
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This required a trip to the hardware store where, under the tutelage of a young man who I believe mostly felt sorry for me, I learned to cut screens and attach them to the window frame channels using SPLINES.
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M-splines can be integrated to produce a family of monotone splines called I-splines. M-splines can also be used directly as basis splines for regression analysis involving positive response data (constraining the regression coefficients to be non-negative).
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In the mathematical fields of numerical analysis and approximation theory, box splines are piecewise polynomial functions of several variables. Box splines are considered as a multivariate generalization of basis splines (B-splines) and are generally used for multivariate approximation/interpolation. Geometrically, a box spline is the shadow (X-ray) of a hypercube projected down to a lower-dimensional space. Box splines and simplex splines are well studied special cases of polyhedral splines which are defined as shadows of general polytopes.
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Bicubic surface patches, defined by three bicubic splines, are an essential tool in computer graphics. Cubic splines are often called csplines, especially in computer graphics. Hermite splines are named after Charles Hermite.
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For applications, linear combinations of shifts of one or more box splines on a lattice are used. Such splines are efficient, more so than linear combinations of simplex splines, because they are refinable and, by definition, shift invariant. They therefore form the starting point for many subdivision surface constructions. Box splines have been useful in characterization of hyperplane arrangements.
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Ming-Jun Lai is an American mathematician, currently a Professor of Mathematics at the University of Georgia. His area of research is splines and their numerical analysis. He has published a text on splines called Splines Functions on Triangulations. He was born in Hangzhou, China.
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Once a definition of knot vector is provided, several types of basis functions can be introduced in this context, such as B-splines, NURBS and T-splines.
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Also, box splines can be used to compute the volume of polytopes. In the context of multidimensional signal processing, box splines can provide multivariate interpolation kernels (reconstruction filters) tailored to non- Cartesian sampling lattices,Entezari, Alireza. Optimal sampling lattices and trivariate box splines. [Vancouver, BC.]: Simon Fraser University, 2007. .
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Moreover, box splines are used for designing efficient space-variant (i.e., non-convolutional) filters. Box splines are useful basis functions for image representation in the context of tomographic reconstruction problems as the spline spaces generated by box splines spaces are closed under X-ray and Radon transforms. In this application while the signal is represented in shift- invariant spaces, the projections are obtained, in closed-form, by non-uniform translates of box splines.
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Hex-splines are the generalization of B-splines for 2-D hexagonal lattices. Similarly, in 3-D and higher dimensions, Voronoi splines provide a generalization of B-splines that can be used to design non- separable FIR filters which are geometrically tailored for any lattice, including optimal lattices. Explicit construction of ideal low-pass filters (i.e., sinc functions) generalized to optimal lattices is possible by studying the geometric properties of Brillouin zones (i.e.
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NURBS curve - polynomial curve defined in homogeneous coordinates (blue) and its projection on plane - rational curve (red) In computer aided design, computer aided manufacturing, and computer graphics, a powerful extension of B-splines is non-uniform rational B-splines (NURBS). NURBS are essentially B-splines in homogeneous coordinates. Like B-splines, they are defined by their order, and a knot vector, and a set of control points, but unlike simple B-splines, the control points each have a weight. When the weight is equal to 1, a NURBS is simply a B-spline and as such NURBS generalizes both B-splines and Bézier curves and surfaces, the primary difference being the weighting of the control points which makes NURBS curves "rational".
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The cardinal B-splines are defined recursively starting from the B-spline of order 1, namely N_1(x), which takes the value 1 in the interval [0, 1) and 0 elsewhere. Computer algebra systems may have to be employed to obtain concrete expressions for higher order cardinal B-splines. The concrete expressions for cardinal B-splines of all orders up to 6 are given below. The graphs of cardinal B-splines of orders up to 4 are also exhibited.
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There are two complementary types of splines, internal and external. External splines may be broached, shaped (for example on a gear shaping machine), milled, hobbed, rolled, ground or extruded. There are fewer methods available for manufacturing internal splines due to accessibility restrictions. Methods include those listed above with the exception of hobbing (no access).
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For features better represented by smooth curves, the polygon representation requires much more data storage than, for example, splines, which can capture smoothly varying shapes efficiently. None of the shapefile format types supports splines.
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Often, with internal splines, the splined portion of the part may not have a through-hole, which precludes use of a pull / push broach or extrusion-type method. Also, if the part is small it may be difficult to fit a milling or grinding tool into the area where the splines are machined. To prevent stress concentrations the ends of the splines are chamfered (as opposed to an abrupt vertical end). Such stress concentrations are a primary cause of failure in poorly designed splines.
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Box splines provide a flexible framework for designing such non-separable reconstruction FIR filters that can be geometrically tailored for each lattice.A. Entezari. Optimal sampling lattices and trivariate box splines. [Vancouver, BC.]: Simon Fraser University, 2007. .
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Splines are ridges or teeth on a drive shaft that mesh with grooves in a mating piece and transfer torque to it, maintaining the angular correspondence between them. For instance, a gear mounted on a shaft might use a male spline on the shaft that matches the female spline on the gear. The splines on the pictured drive shaft match with the female splines in the center of the clutch plate, while the smooth tip of the axle is supported in the pilot bearing in the flywheel. An alternative to splines is a keyway and key, though splines provide a longer fatigue life, and can carry significantly greater torques for the size.
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Drive shafts on vehicles and power take-offs use splines to transmit torque and rotation and allow for changes in length. Splines are used in several places in bicycles. The crank arm to BB shaft interfaces that are splined include ISIS Drive, Truvativ GXP and Howitzer, Shimano's Octalink and many others, most of which are proprietary. Some cranksets feature modular spiders, where torque is transmitted through splines.
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I-splines can be used as basis splines for regression analysis and data transformation when monotonicity is desired (constraining the regression coefficients to be non-negative for a non-decreasing fit, and non-positive for a non-increasing fit).
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Generally these functions are provided in a tabularized format and interpolated by cubic splines.
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How polynomials can approximate sines and cosines. Includes information about cubic splines in design engineering.
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Sederberg co-founded T-Splines, inc. in 2004, which was acquired by Autodesk in 2011.
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There have been at least three solutions offered thus far, piecewise geodesic, principal geodesic and splines.
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In the mathematical subfields function theory and numerical analysis, a univariate polynomial spline of order m is called a perfect spline if its m-th derivative is equal to +1 or -1 between knots and changes its sign at every knot. The term was coined by Isaac Jacob Schoenberg. Perfect splines often give solutions to various extremal problems in mathematics. For example, norms of periodic perfect splines (they are sometimes called Euler perfect splines) are equal to Favard's constants.
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In most of these methods digital filters and approximation by splines can be used to decrease sensitivity to noise.
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Horizontal hobbing machines are usually used for cutting longer workpieces; i.e. cutting splines on the end of a shaft..
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In these applications, each coordinate of the plane or space is separately interpolated by a cubic spline function of a separate parameter t. Cubic polynomial splines are also used extensively in structural analysis applications, such as Euler–Bernoulli beam theory. Cubic splines can be extended to functions of two or more parameters, in several ways. Bicubic splines (Bicubic interpolation) are often used to interpolate data on a regular rectangular grid, such as pixel values in a digital image or altitude data on a terrain.
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B-spline with control points/control polygon, and marked component curves In the mathematical subfield of numerical analysis, a B-spline or basis spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. Any spline function of given degree can be expressed as a linear combination of B-splines of that degree. Cardinal B-splines have knots that are equidistant from each other. B-splines can be used for curve-fitting and numerical differentiation of experimental data.
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The seven-direction box spline has been used for modelling surfaces and can be used for interpolation of data on the Cartesian lattice as well as the body centered cubic lattice. Generalization of the four- and six-direction box splines to higher dimensionsKim, Minho. Symmetric Box-Splines on Root Lattices. [Gainesville, Fla.
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Direct collocation methods work by approximating the state and control trajectories using polynomial splines. These methods are sometimes referred to as direct transcription. Trapezoidal collocation is a commonly used low-order direct collocation method. The dynamics, path objective, and control are all represented using linear splines, and the dynamics are satisfied using trapezoidal quadrature.
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The resulting spline will be continuous and will have continuous first derivative. Cubic polynomial splines can be specified in other ways, the Bezier cubic being the most common. However, these two methods provide the same set of splines, and data can be easily converted between the Bézier and Hermite forms; so the names are often used as if they were synonymous. Cubic polynomial splines are extensively used in computer graphics and geometric modeling to obtain curves or motion trajectories that pass through specified points of the plane or three-dimensional space.
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Vasicek, Oldrich A., and H. Gifford Fong. "Term structure modeling using exponential splines." The Journal of Finance 37.2 (1982): 339-348.
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The research built on Riesenfeld and Cohen's prior work on B-splines, NURBs and the Oslo-algorithm for geometric and shaded rendering computations.
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In computer-aided design and computer graphics, spline functions are constructed as linear combinations of B-splines with a set of control points.
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In the mathematical field of numerical analysis, discrete spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a discrete spline. A discrete spline is a piecewise polynomial such that its central differences are continuous at the knots whereas a spline is a piecewise polynomial such that its derivatives are continuous at the knots. Discrete cubic splines are discrete splines where the central differences of orders 0, 1, and 2 are required to be continuous. Discrete splines were introduced by Mangasarin and Schumaker in 1971 as solutions of certain minimization problems involving differences.
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It enabled the staff to understand non-uniform splines and to appreciate the geometrical nature of the definition so as to use B-splines in solving engineering problems. The first use of the geometrical nature of B-splines was in the curve/curve intersection. The Bezier subdivision process was utilized, and a second use was our curve offset algorithm, which was based on a polygon offset process that was eventually communicated to and used by SDRC and explained by Tiller and Hanson in their offset paper of 1984. The staff also developed an internal NURBS class taught to about 75 Boeing engineers.
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A Shimano Octalink v1 Bottom Bracket before fitting The Octalink system uses a spindle with eight splines. The splines provide a contact area between crank and spindle for an interface. Octalink exists in the marketplace in two variants, Octalink v1, and Octalink v2. The difference between the two can be seen by the depth of mounting grooves on the bottom bracket spindle.
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I. J. Schoenberg in 1971 Isaac Jacob Schoenberg (April 21, 1903 - February 21, 1990) was a Romanian-American mathematician, known for his discovery of splines.
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Consider: the design of a wing demands free-form, C2 continuous, cubic splines to satisfy the needs of aerodynamic analysis, yet the circle and cylinders of manufacturing require at least rational Bézier curves. The properties of Bézier curves and uniform B-splines were well known, but the staff had to gain an understanding of non-uniform B-splines and rational Bézier curves and try to integrate the two. It was necessary to convert circles and other conics to rational Bézier curves for the curve/curve intersection. At that time, none of the staff realized the importance of the work and was considered “too trivial” and “nothing new”.
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In computer graphics, Catmull–Rom splines are frequently used to get smooth interpolated motion between key frames. For example, most camera path animations generated from discrete key- frames are handled using Catmull–Rom splines. They are popular mainly for being relatively easy to compute, guaranteeing that each key frame position will be hit exactly, and also guaranteeing that the tangents of the generated curve are continuous over multiple segments.
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In the mathematical subfield of numerical analysis de Boor's algorithmC. de Boor [1971], "Subroutine package for calculating with B-splines", Techn.Rep. LA-4728-MS, Los Alamos Sci.Lab, Los Alamos NM; p.
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This means the output shaft rotates at the same speed as the selected gear, thus determining the gear ratio of the transmission. The dog clutch is a sliding selector mechanism that sits around the output shaft. It has teeth to fit into the splines on the shaft, forcing that shaft to rotate at the same speed as the gear hub. However, the clutch can move back and forth on the shaft, to either engage or disengage the splines.
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The places where the pieces meet are known as knots. The key property of spline functions is that they and their derivatives may be continuous, depending on the multiplicities of the knots. B-splines of order n are basis functions for spline functions of the same order defined over the same knots, meaning that all possible spline functions can be built from a linear combination of B-splines, and there is only one unique combination for each spline function.
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In case the kernel should also be inferred nonparametrically from the data, the critical filter can be used. Smoothing splines have an interpretation as the posterior mode of a Gaussian process regression.
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However, the global nature of the basis functions leads to ill-conditioning. This is completely mitigated by using splines of compact support, such as are implemented in Boost.Math and discussed in Kress.
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If a single control point moves, the whole spline needs to be re- evaluated. B-splines have both C2 continuity and local control, but they lose the interpolation property of a piecewise Bézier.
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Elaine Cohen is an American researcher in geometric modeling and computer graphics, known for her pioneering research on B-splines. She is a professor in the school of computing at the University of Utah.
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The Volkswagen variator is referred to as a 'fluted variator', owing to the shape of the hydraulic components. Unlike the Alfa Romeo system with its helical splines and indirect actuation,Hydraulic action in the Alfa Romeo is axial, using helical splines to then cause a rotation of the variator. the Volkswagen system has a direct rotational action. The internal components of the variator resemble a paddle wheel inside a loose casing, so that it is free to move a few degrees from side to side.
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Since the rectangular shape of CMAC receptive field functions produce discontinuous staircase function approximation, by integrating CMAC with B-splines functions, continuous CMAC offers the capability of obtaining any order of derivatives of the approximate functions.
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J. Duchon, 1976, Splines minimizing rotation invariant semi- norms in Sobolev spaces. pp 85–100, In: Constructive Theory of Functions of Several Variables, Oberwolfach 1976, W. Schempp and K. Zeller, eds., Lecture Notes in Math., Vol.
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Players interact with the rhythm of a song using their hands, which are tracked using motion controllers. There are currently three ways in which rhythm events are converted into gameplay: Catching orbs, following splines and spinning spinners.
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Such large drawings were done with the help of flexible strips of wood, called splines. The splines were held in place at a number of predetermined points, called "ducks"; between the ducks, the elasticity of the spline material caused the strip to take the shape that minimized the energy of bending, thus creating the smoothest possible shape that fit the constraints. The shape could be adjusted by moving the ducks. In 1946, mathematicians started studying the spline shape, and derived the piecewise polynomial formula known as the spline curve or spline function.
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The term "spline" is used to refer to a wide class of functions that are used in applications requiring data interpolation and/or smoothing. The data may be either one-dimensional or multi-dimensional. 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.
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Other materials include tin, zinc, and lead alloys and iron and steel are also cast in graphite molds.. Typical products are components such as gears, splines, wheels, gear housings, pipe fittings, fuel injection housings, and automotive engine pistons.
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In mathematics, moduli of smoothness are used to quantitatively measure smoothness of functions. Moduli of smoothness generalise modulus of continuity and are used in approximation theory and numerical analysis to estimate errors of approximation by polynomials and splines.
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Source code for spline smoothing can be found in the examples from Carl de Boor's book A Practical Guide to Splines. The examples are in the Fortran programming language. The updated sources are available also on Carl de Boor's official site .
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In 2005, the YWCA of Salt Lake City gave Cohen their Outstanding Achievement Award. In 2009, Cohen and Riesenfeld won the Pierre Bézier Award of the Solid Modeling Association for their work on B-splines in computer aided geometric design.
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The kernel density estimates are sums of Gaussians and may therefore be represented as Gaussian mixture models (GMM). Jian and Vemuri use the GMM version of the KC registration algorithm to perform non-rigid registration parametrized by thin plate splines.
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It is commonly accepted that the first mathematical reference to splines is the 1946 paper by Schoenberg, which is probably the first place that the word "spline" is used in connection with smooth, piecewise polynomial approximation. However, the ideas have their roots in the aircraft and shipbuilding industries. In the foreword to (Bartels et al., 1987), Robin Forrest describes "lofting", a technique used in the British aircraft industry during World War II to construct templates for airplanes by passing thin wooden strips (called "splines") through points laid out on the floor of a large design loft, a technique borrowed from ship-hull design.
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The use of splines for modeling automobile bodies seems to have several independent beginnings. Credit is claimed on behalf of de Casteljau at Citroën, Pierre Bézier at Renault, and Birkhoff, Garabedian, and de Boor at General Motors (see Birkhoff and de Boor, 1965), all for work occurring in the very early 1960s or late 1950s. At least one of de Casteljau's papers was published, but not widely, in 1959. De Boor's work at General Motors resulted in a number of papers being published in the early 1960s, including some of the fundamental work on B-splines.
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If one chooses axis-aligned bounding boxes, one gets AABBTrees. Oriented bounding box trees are called OBBTrees. Some trees are easier to update if the underlying object changes. Some trees can accommodate higher order primitives such as splines instead of simple triangles.
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Lai received a B.Sc. from Hangzhou University and a Ph.D. in mathematics from the Texas A&M; University in 1989. His dissertation was entitled "On Construction of Bivariate and Trivariate Vertex Splines on Arbitrary Mixed Grid Partitions" and supervised by Charles K. Chui.
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Computer Aided Geometric Design, 26(3):279{286, 2009 solve this problem, but use a slightly different calculation. P. J. Barry and R. N. Goldman. A recursive evaluation algorithm for a class of Catmull-Rom splines. SIGGRAPH Computer Graphics, 22(4):199{204, 1988.
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Many algorithms explicitly fit 0-degree splines to the noisy signal in order to detect steps (including stepwise jump placement methods), but there are other popular algorithms that can also be seen to be spline fitting methods after some transformation, for example total variation denoising.
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Thomas W. Sederberg is the associate dean of the college of physcial and mathematical sciences and professor of Computer Science at Brigham Young University in Provo, Utah. His research involves computer graphics and computer aided design. He helped invent free-form deformation and T-splines.
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A spline A spline, or the more modern term flexible curve, consists of a long strip fixed in position at a number of points whose tension creates a smooth curve passing through those points, for the purpose of transferring that curve to another material. Before computers were used for creating engineering designs, drafting tools were employed by designers drawing by hand. To draw curves, especially for shipbuilding, draftsmen often used long, thin, flexible strips of wood, plastic, or metal called splines (or laths, not to be confused with lathes). The splines were held in place with lead weights (called ducks because of their duck-like shape).
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Splines are piecewise-smooth, hence in PDIFF, but not globally smooth or piecewise-linear, hence not in DIFF or PL. In geometric topology, PDIFF, for piecewise differentiable, is the category of piecewise-smooth manifolds and piecewise-smooth maps between them. It properly contains DIFF (the category of smooth manifolds and smooth functions between them) and PL (the category of piecewise linear manifolds and piecewise linear maps between them), and the reason it is defined is to allow one to relate these two categories. Further, piecewise functions such as splines and polygonal chains are common in mathematics, and PDIFF provides a category for discussing them.
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In 1982, Arthur M. Lesk and co-workers first enabled automatic generation of ribbon diagrams through a computational implementation that uses Protein Data Bank files as input.. This conceptually simple algorithm fit cubic polynomial B-spline curves to the peptide planes. Most modern graphics systems provide either B-splines or Hermite splines as a basic drawing primitive. One type of spline implementation passes through each Cα guide point, producing an exact but choppy curve. Both hand-drawn and most computer ribbons (such as those shown here) are smoothed over about four successive guide points (usually the peptide midpoint) to produce a more visually pleasing and understandable representation.
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A hob — the cutter used for hobbing. Hobbing is a machining process for gear cutting, cutting splines, and cutting sprockets on a hobbing machine, which is a special type of milling machine. The teeth or splines of the gear are progressively cut into the material (a flat, cylindrical piece of metal) by a series of cuts made by a cutting tool called a hob. Compared to other gear forming processes it is relatively inexpensive but still quite accurate, thus it is used for a broad range of parts and quantities.. It is the most widely used gear cutting process for creating spur and helical gears.
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Tensor implemented a grade-8 buttonhead kingpin with machined splines on it to prevent it from spinning in the baseplate. The buttonhead is lighter than the hex kingpin, which was the then-industry standard. Independent, Thunder, Venture, Krux, Fury, and Destructo have since implemented buttonhead kingpins.
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A smooth parallel coordinate plot is achieved with splines. In the smooth plot, every observation is mapped into a parametric line (or curve), which is smooth, continuous on the axes, and orthogonal to each parallel axis. This design emphasizes the quantization level for each data attribute.
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The term "B-spline" was coined by Isaac Jacob Schoenbergde Boor, p. 114 and is short for basis spline.Gary D. Knott (2000), Interpolating cubic splines. Springer. p. 151 A spline function of order n is a piecewise polynomial function of degree n-1 in a variable x .
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Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing. They were introduced to geometric design by Duchon. They are an important special case of a polyharmonic spline. Robust Point Matching (RPM) is a common extension and shortly known as the TPS-RPM algorithm.
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Ball splines (Ball Spline bearings) are a special type of linear motion bearing that are used to provide nearly frictionless linear motion while allowing the member to transmit torque simultaneously. There are grooves ground along the length of the shaft (thus forming splines) for the ball bearings to run inside. The outer shell that houses the balls is called a nut rather than a bushing, but is not a nut in the traditional sense—it is not free to rotate about the shaft, but is free to travel up and down the shaft. For a shaft travel of any significant length the nut will have channels that recirculate the balls, operating in the same way as a ball screw.
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These projectiles were pre-rifled with angled splines along their midsection which were aligned with the guns rifling before firing. The rocket assisted projectile was known as the 28cm R. GR.4351. This carried of explosive and was boosted by around of double-base powder rocket propellant. The total weight was .
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In 1994 Billera won the Fulkerson Prize for his paper, Homology of smooth splines. This prize is given every three years to the best paper in discrete mathematics. In 2012 he became a fellow of the American Mathematical Society.List of Fellows of the American Mathematical Society, retrieved 2013-07-07.
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Broaching is often impossible without the specific broaching or keyway machines unless you have a system that can be used in conjunction with a modern machining centre or driven tooling lathe; these extra bits of equipment open up the possibility of producing keyways, splines and torx through one-hit machining.
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With Richard F. Riesenfeld and Gershon Elber, Cohen is the author of the book Geometric Modeling with Splines: An Introduction (AK Peters, 2001). She has also contributed to the development of the Utah teapot, improving it from a two-dimensional surface with no thickness to a bona-fide three-dimensional object.
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This is analogous to spline surfaces and curves, where Bézier curves are required to interpolate certain control points, while B-Splines are not. There is another division in subdivision surface schemes as well: the type of polygon that they operate on. Some function for quadrilaterals (quads), while others operate on triangles.
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One is Truvativ's Power Spline interface. It is a 12 spline spindle proprietary to Truvativ offered as a lower cost alternative to other spline designs. It is essentially a beefed-up square taper spindle with splines instead of tapers. Phil Wood uses a similar splined design to the Shimano bottom bracket.
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The NURBS module allows segmented 3D image data to be fitted with non-uniform rational B-splines (NURBS) using automated patch fitting techniques for export as IGES (`.iges` and `.igs` files). Autosurface algorithms provide a straightforward route from image data to CAD-ready NURBS models, with options available for contour and curvature detection.
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Additionally, numeric control over size, position, and other aspects of objects is available in the Geometry panel. Path drawing tools. The program has dedicated tools for drawing quadratic (2nd order) and cubic (3rd order) splines, as well as an Arc tool to draw consecutive arcs in a single Bézier curve. Reusable items.
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See "Circle and B-Splines clipping algorithms" under the subject Clipping (computer graphics) for an example of use. A convex hull is the smallest convex volume containing the object. If the object is the union of a finite set of points, its convex hull is a polytope. A ' ('DOP) generalizes the bounding box.
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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. The term spline comes from the flexible spline devices used by shipbuilders and draftsmen to draw smooth shapes.
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Agricultural PTOs are standardized in dimensions and speed. The ISO standard for PTOs is ISO 500, which as of the 2004 edition was split into three parts: #ISO 500-1 General specifications, safety requirements, dimensions for master shield and clearance zone #ISO 500-2 Narrow-track tractors, dimensions for master shield and clearance zone #ISO 500-3 Main PTO dimensions and spline dimensions, location of PTO. The original type (designated as Type 1) calls for operation at 540 revolutions per minute (rpm). A shaft that rotates at 540 rpm has 6 splines on it, and a diameter of . Two newer types, supporting higher power applications, operate at 1000 rpm and differ in shaft size. The larger shaft has 20 splines (diameter ) (designated as Type 3), while the smaller has 21 splines (diameter ) (designated as Type 2). Farmers typically differentiate these two types by calling them "large 1000" or "small 1000" as compared to the Type 1 which is commonly referred to as the "540". Due to ever-increasing horsepower requirements from farm implements, and higher horsepower engines being installed in farm tractors, a still larger type (designated as Type 4) has been added to ISO 500.
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ZModeler is capable of complex modeling and Importing. On later versions it supports important modeling functions such as extruding, or beveling. Version 1 does not support polygons other than triangles, or NURBs, or other forms of modeling other than polygonal and splines. It comes with filters to import and export meshes of other formats.
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Obj files support higher-order surfaces using several different kinds of interpolation, such as Taylor and B-splines, although support for those features in third party file readers is far from universal. Obj files also do not support mesh hierarchies or any kind of animation or deformation, such as vertex skinning or mesh morphing.
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The key idea is include energy minimization as an integral part of the algorithm and the underlying mathematics. This concept is now industry standard. Hans Hagen has a strong background in differential geometry and topology. His geometric modeling publication record started with a work on geometric splines, where he introduced a torsion continuous spline curve.
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The tooth flanks and outer diameter of the external gear are crowned to allow for angular displacement between the two gears. Mechanically, the gears are equivalent to rotating splines with modified profiles. They are called gears because of the relatively large size of the teeth. Gear couplings and universal joints are used in similar applications.
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Multivariate adaptive regression splines (MARS) is a non-parametric technique that builds flexible models by fitting piecewise linear regressions. Multivariate and adaptive regression spline approach deliberately overfits the model and then prunes to get to the optimal model. The algorithm is computationally very intensive, and in practice an upper limit on the number of basis functions is specified.
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Many authors include also Neural networks into this list. The general idea behind Volterra LMS and Kernel LMS is to replace data samples by different nonlinear algebraic expressions. For Volterra LMS this expression is Volterra series. In Spline Adaptive Filter the model is a cascade of linear dynamic block and static non-linearity, which is approximated by splines.
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Grace can be used from a point-and-click interface or scripted (using either the built-in programming language or a number of language bindings). It performs both linear and nonlinear least-squares fitting to arbitrarily complex user-defined functions, with or without constraints. Other analysis tools include FFT, integration and differentiation, splines, interpolation, and smoothing.
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As the dimension increases there are some restrictions on the smallest order of differential that can be used, but actually Duchon's original paper,J. Duchon, 1976, Splines minimizing rotation invariant semi-norms in Sobolev spaces. pp 85–100, In: Constructive Theory of Functions of Several Variables, Oberwolfach 1976, W. Schempp and K. Zeller, eds., Lecture Notes in Math.
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It was during this time that he initiated the work for which he is most famous, the theory of splines. In 1966 he moved to the University of Wisconsin–Madison where he became a member of the Mathematics Research Center. He remained there until he retired in 1973. In 1974 he won a Lester R. Ford Award.
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In both processes the cut is performed in one pass of the broach, which makes it very efficient. Broaching is used when precision machining is required, especially for odd shapes. Commonly machined surfaces include circular and non-circular holes, splines, keyways, and flat surfaces. Typical workpieces include small to medium-sized castings, forgings, screw machine parts, and stampings.
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In computer graphics, Doo–Sabin subdivision surface is a type of subdivision surface based on a generalization of bi-quadratic uniform B-splines. It was developed in 1978 by Daniel Doo and Malcolm Sabin.D. Doo: A subdivision algorithm for smoothing down irregularly shaped polyhedrons, Proceedings on Interactive Techniques in Computer Aided Design, pp. 157 - 165, 1978 (pdf)D.
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The mechanism of a mechanical system is assembled from components called machine elements. These elements provide structure for the system and control its movement. The structural components are, generally, the frame members, bearings, splines, springs, seals, fasteners and covers. The shape, texture and color of covers provide a styling and operational interface between the mechanical system and its users.
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Work was also being done at Pratt & Whitney Aircraft, where two of the authors of (Ahlberg et al., 1967) — the first book-length treatment of splines — were employed, and the David Taylor Model Basin, by Feodor Theilheimer. The work at General Motors is detailed nicely in (Birkhoff, 1990) and (Young, 1997). Davis (1997) summarizes some of this material.
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For a number of meaningful definitions of the roughness measure, the spline functions are found to be finite dimensional in nature, which is the primary reason for their utility in computations and representation. For the rest of this section, we focus entirely on one-dimensional, polynomial splines and use the term "spline" in this restricted sense.
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H. Owhadi, L. Zhang, L. Berlyand, Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization, ESAIM: Mathematical Modelling and Numerical Analysis. Special issue, 48 (2), pp. 517–552 (2014) Together with H. Owhadi, he introduced a "transfer-of-approximation" modeling concept, based on the similarity of the asymptotic behavior of the errors of Galerkin solutions for two elliptic PDEs.
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He wrote about 175 papers on many disparate subjects. Around 50 of these were on Splines. He also wrote on Approximation theory, the Kakeya problem, Polya frequency functions, and a problem of Edmund Landau. His coauthors included John von Neumann, Hans Rademacher, Theodore Motzkin, George Polya, A. S. Besicovitch, Gábor Szegő, Donald J. Newman, Richard Askey, Bernard Epstein and Carl de Boor.
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The sketch consists of geometry such as points, lines, arcs, conics (except the hyperbola), and splines. Dimensions are added to the sketch to define the size and location of the geometry. Relations are used to define attributes such as tangency, parallelism, perpendicularity, and concentricity. The parametric nature of SolidWorks means that the dimensions and relations drive the geometry, not the other way around.
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This has replaced hobbing for some involute gears and cutting external splines and slots. Straddle broaches use two slab broaches to cut parallel surfaces on opposite sides of a workpiece in one pass. This type of broaching holds closer tolerances than if the two cuts were done independently. It is named after the fact that the broaches "straddle" the workpiece on multiple sides..
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As in Myst, the topography of the islands was originally created as grayscale images, where brightness corresponded to elevation. In Softimage, these maps were turned into the terrain models seen in the game. The large island objects were broken apart to facilitate efficient rendering, which required them to be created using polygonal geometry. All other objects were modeled using B-splines and NURBS.
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Once the concept is understood, the principle of operation can lead to all manner of designs where internal grooves, keyways, splines, etc. may be measured in a simple yet effective manner. These will often be made to order by the toolmakers, or a related skilled tradesman. Go/no-go gauges play an integral part in setting the correct headspace during gunsmithing.
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The term P-spline stands for "penalized B-spline". It refers to using the B-spline representation where the coefficients are determined partly by the data to be fitted, and partly by an additional penalty function that aims to impose smoothness to avoid overfitting.Eilers, P.H.C. and Marx, B.D. (1996). Flexible smoothing with B-splines and penalties (with comments and rejoinder).
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All letters were in capital. Each character was individually drawn as a series of splines using technology developed for displays in military cockpits. Later Uniscopes supported a 24 X 80 screen using raster technology, and upper and lower case characters. There were versions that had the various national code sets for different European countries to enable pound signs, and various accented characters, etc.
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Springer, 1999. are useful for sampling multivariate functions in 2-D, 3-D and higher dimensions. In the 2-D setting the three- direction box spline is used for interpolation of hexagonally sampled images. In the 3-D setting, four-direction and six-direction box splines are used for interpolation of data sampled on the (optimal) body-centered cubic and face- centered cubic lattices respectively.
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In finance, the shape is widely called a "hockey stick", due to the shape being similar to an ice hockey stick. hinge functions with a knot at x=3.1 In statistics, hinge functions of multivariate adaptive regression splines (MARS) are ramps, and are used to build regression models. In machine learning, it is commonly known as the rectifier used in rectified linear units (ReLUs).
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The old method of gear cutting is mounting a gear blank in a shaper and using a tool shaped in the profile of the tooth to be cut. This method also works for cutting internal splines. Another is a pinion-shaped cutter that is used in a gear shaper machine. It is basically when a cutter that looks similar to a gear cuts a gear blank.
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Version 1 was demonstrated at the January 2005 Motion Graphics LA (MGLA) meeting. Versions 1 and 2 were broken into separate rotoscoping and paint products. Version 3 (released May 2008) and beyond combined all core features (roto and paint) into a single product. With the release of Version 3 in May 2008, SilhouetteFX gained a stereoscopic workflow, planar tracking, x-splines plus keying and compositing capabilities.
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Though these wavelets are orthogonal, they do not have compact supports. There is a certain class of wavelets, unique in some sense, constructed using B-splines and having compact supports. Even though these wavelets are not orthogonal they have some special properties that have made them quite popular. The terminology spline wavelet is sometimes used to refer to the wavelets in this class of spline wavelets.
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AF coatings are applied where fretting and galling is a problem (such as splines, universal joints and keyed bearings), where operating pressures exceed the load-bearing capacities of ordinary oils and greases, where smooth running in is desired (piston, camshaft), where clean operation is desired (AF coatings will not collect dirt and debris like greases and oils), and where parts may be stored for long periods.
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The figure shows how the splines of the Med 14 subunit connect a large portion of the complex together while still allowing flexibility. Mediator complexes that lack a subunit have been found or produced. These smaller mediators can still function normally in some activity, but lack other capability. This indicates somewhat independent function of some of the subunits while part of the larger complex.
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Hosmer et al have a better one d.f. omnibus test of fit, implemented in the R rms package residuals.lrm function." "But I recommend specifying the model to make it more likely to fit up front (especially with regard to relaxing linearity assumptions using regression splines) and using the bootstrap to estimate overfitting and to get an overfitting-corrected high-resolution smooth calibration curve to check absolute accuracy.
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Les Piegl and Wayne Tiller (a partner of Solid Modeling Solutions) wrote the definitive "The NURBS Book" on non-uniform rational B-splines (NURBS) with aids to designing geometry for computer-aided environment applications.Piegl, Les & Tiller, Wayne. The NURBS Book, Springer 1997 The fundamental mathematics is well defined in this book, and the most faithful manifestation in software is implemented in the SMS product line.
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Composite Bezier curves can be smoothed to any desired degree of smoothness using Stärk's construction. C2 continuous composite cubic Bezier curves are actually cubic B-splines, and vice versa. Individual curves are by definition C1 and C2 continuous. The geometric condition for C1 continuity when transiting across an endpoint joining two curves is that the associated control points are mutually opposed and collinear with the endpoint.
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The main graphical primitive in SWF is the path, which is a chain of segments of primitive types, ranging from lines to splines or bezier curves. Additional primitives like rectangles, ellipses, and even text can be built from these. The graphical elements in SWF are thus fairly similar to SVG and MPEG-4 BIFS. SWF also uses display lists and allows naming and reusing previously defined components.
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Before computers were used, numerical calculations were done by hand. Although piecewise-defined functions like the sign function or step function were used, polynomials were generally preferred because they were easier to work with. Through the advent of computers splines have gained importance. They were first used as a replacement for polynomials in interpolation, then as a tool to construct smooth and flexible shapes in computer graphics.
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PyMol ribbon of the structure of the tubby protein () One popular program used for drawing ribbon diagrams is Molscript. Molscript utilizes Hermite splines to create coordinates for coils, turns, strands and helices. The curve passes through all its control points (Cα atoms) guided by direction vectors. The program was built on the basis of traditional molecular graphics by Arthur M. Lesk, Karl Hardman, and John Priestle.
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Most applications, however, do not need true zero backlash and can use a spline type connection. Some of these connections between the armature and the hub are standard splines others are hex or square hub designs. The spline will have the best initial backlash tolerance. Typically around 2° but the spline and the other connection types can wear over time and the tolerances will increase.
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In statistics, multivariate adaptive regression splines (MARS) is a form of regression analysis introduced by Jerome H. Friedman in 1991. It is a non- parametric regression technique and can be seen as an extension of linear models that automatically models nonlinearities and interactions between variables. The term "MARS" is trademarked and licensed to Salford Systems. In order to avoid trademark infringements, many open-source implementations of MARS are called "Earth".
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Bee married George Douglas and had two children, Rex Douglas and Arwen Douglas, in that marriage. She married Carl R. de Boor, an emeritus professor at the University of Wisconsin–Madison, in 1991.Y.K. Leong, Carl de Boor: On wings of splines , Imprints (newsletter of the Institute for Mathematical Sciences, National University of Singapore), Issue 5, 2004. retrieved 18 March 2008 She lives on Orcas Island, in Washington state.
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It operates at a higher rotational speed of 1300 rpm in order to allow for power transfer at reduced levels of torque. The shaft has 22 splines with a major diameter of 57.5 millimeters (mm). It is meant to handle PTO powers up to 450 kilowatts (kW), or roughly 600 horsepower (hp). All four types rotate counterclockwise when viewed from the tractor (When standing behind the tractor, the shaft turns clockwise).
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WAMIT is a computer program for computing wave loads and motions of offshore structures in waves. It is based on the linear and second-order potential theory. The velocity potential is solved by means of boundary integral equation method, also known as panel method. WAMIT has the capability of representing the geometry of the structure by a higher-order method, whereby the potential is represented by continuous B-splines.
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It was fitted with a Zoller supercharger and produced at 7200 rpm. The gearbox was a four-speed preselector type unit. At the rear the differential in its aluminium casing was fastened to the chassis and drove the wheels through short shafts with sliding splines and universal joints. The revolutionary Y-shaped steel chassis had a backbone that divided around the engine and gearbox, and was very light.
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The Producer Edition includes all of the features of the Fruity Edition, as well as full recording for internal and external audio and post-production tools. It allows for hand-drawing point and curve based splines (referred to as "Automation Clips"). Plugins include Edison, Slicex (loop slicer and re- arranger), Sytrus, Maximus, Vocodex and Synthmaker. It also allows for waveform viewing of audio clips and the ability to add cue points.
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The use of keys and keyways instead of, or in combination with, set screws is common for applications requiring high torque resistance or transmission. Splines offer yet more strength. For longer life, set screws are usually made of alloy steel and case hardened. Hardened set screws often leave a plastic deformation, in the form of a circular or semicircular mark, in the shaft that the screw sets against.
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The third component in SIPs is the spline or connector piece between SIP panels. Dimensional lumber is commonly used but creates thermal bridging and lowers insulation values. To maintain higher insulation values through the spline, manufacturers use Insulated Lumber, Composite Splines, Mechanical Locks, Overlapping OSB Panels, or other creative methods. Depending on the method selected, other advantages such as full nailing surfaces or increased structural strength may become available.
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This left the sheets embedded in about of the blue clay. Sheet-driving was subcontracted to the Great Lakes Dredge & Dock Co. Each steel sheet dovetailed with the one next to it, and soft pine splines inserted into the dovetails. The wood swelled when it came into contact with water, helping to ensure a tight seal. Sheet-driving began in the middle of the west side, and worked counter-clockwise.
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Although the bilinear Coons patch exactly meets its four boundary curves, it does not necessarily have the same tangent plane at those curves as the surfaces to be joined, leading to creases in the joined surface along those curves. To fix this problem, the linear interpolation can be replaced with cubic Hermite splines with the weights chosen to match the partial derivatives at the corners. This forms a bicubically blended Coons patch.
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In mathematics, bicubic interpolation is an extension of cubic interpolation for interpolating data points on a two-dimensional regular grid. The interpolated surface is smoother than corresponding surfaces obtained by bilinear interpolation or nearest-neighbor interpolation. Bicubic interpolation can be accomplished using either Lagrange polynomials, cubic splines, or cubic convolution algorithm. In image processing, bicubic interpolation is often chosen over bilinear or nearest-neighbor interpolation in image resampling, when speed is not an issue.
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Ronald Neil Goldman is a Professor of Computer Science at Rice University in Houston, Texas. Professor Goldman received his B.S. in Mathematics from the Massachusetts Institute of Technology in 1968 and his M.A. and Ph.D. in Mathematics from Johns Hopkins University in 1973. Dr. Goldman's current research interests lie in the mathematical representation, manipulation, and analysis of shape using computers. His work includes research in computer- aided geometric design, solid modeling, computer graphics, and splines.
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Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra. Hermite polynomials, Hermite interpolation, Hermite normal form, Hermitian operators, and cubic Hermite splines are named in his honor. One of his students was Henri Poincaré. He was the first to prove that e, the base of natural logarithms, is a transcendental number.
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Extending the results of Young, the Birkhoff–Varga collaboration led to many publications on positive operators and iterative methods for p-cyclic matrices. Birkhoff's research and consulting work (notably for General Motors) developed computational methods besides numerical linear algebra, notably the representation of smooth curves via cubic splines. Birkhoff published more than 200 papers and supervised more than 50 Ph.D.s. He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences.
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This plastic pilot shaft guide tool is used to align the clutch disk as the spring-loaded pressure plate is installed. The transmission's drive splines and pilot shaft have a complementary shape. A number of such devices fit various makes and models of drivetrains. In a modern truck or car with a manual transmission the clutch is operated by the left-most pedal using a hydraulic or cable connection from the pedal to the clutch mechanism.
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By 1946, mathematicians had begun to devise mathematical formulae to serve a similar purpose, and ultimately created efficient algorithms to find piecewise polynomial curves, also known as splines, that go smoothly through designated points. This has led to the widespread use of such functions in computer-aided design, especially in the surface designs of vehicles, replacing the draftsman's spline. I. J. Schoenberg gave the spline function its name after its resemblance to the mechanical spline used by draftsmen.
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Topera developed a 3D mapping tool to assists physicians in identifying the electrical source of complex cardiac arrhythmias. The FIRMap catheter, used with the RhythmView workstation, received CE clearance and FDA clearance in 2013. The tip of the catheter has a spherical wire basket that has 64 evenly placed electrodes over the 8 splines that make up the basket. The basket expands, capturing the contours of the heart chambers and creating a panoramic map of the electrical heart activity.
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After studies at the Universities of Freiburg and Hamburg Frank Natterer in 1968 earned his PhD with a thesis "Einschließungen für die großen Eigenwerte gewöhnlicher Differentialgleichungen zweiter und vierter Ordnung" under the supervision of Prof. Lothar Collatz. In 1971, he made the habilitation "Verallgemeinerte Splines und singuläre Rand-Eigenwertaufgaben gewöhnlicher Differentialgleichungen". Following a visiting assistant professorship at Indiana University Bloomington, Indiana (USA) he was full professor at the Universität des Saarlandes, Saarbrücken (Germany), from 1973-1981.
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Gerlind Plonka-Hoch is a German applied mathematician specializing in signal processing and image processing, and known for her work on refinable functions and curvelets. She is a professor at the University of Göttingen, in the Institute for Numerical and Applied Mathematics. Plonka earned her Ph.D. from the University of Rostock in 1993. Her dissertation, Periodische Lagrange- und Hermite-Spline-Interpolation, concerned polynomial interpolation using Lagrange polynomials and Hermite splines, and was supervised by Manfred Tasche.
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Lastly, on the TSi and TSi AWD models, the aluminum wheels were increased to and incorporated more angles replacing the curved 5-spoke wheel. Another important, non-cosmetic change concerned the driveline. There was a slight change in gear ratios and the number of splines on the shaft feeding power to the transfer case was altered. The TSi and TSi AWD models again featured an intercooled turbocharged engine, now replacing the 14B Mitsubishi turbo with a Garrett T25 model.
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The first begins with construction curves (splines) from which the 3D surface is then swept (section along guide rail) or meshed (lofted) through. A surface being created from curves. The second method is direct creation of the surface with manipulation of the surface poles/control points. Surface edit by poles From these initially created surfaces, other surfaces are constructed using either derived methods such as offset or angled extensions from surfaces; or via bridging and blending between groups of surfaces.
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It sheared, causing the driveshaft to rip open the lubricating oil system, and the engine seized up soon afterward. Air Force mechanics had first noticed excessive wear on the driveshafts of a Corsair in November 1984, and subsequently two others. This prompted a safety directive to check driveshaft splines during compressor work on all in-service Corsairs. The charred building stood for more than two years; the hotel owners never rebuilt because they were unable to decide on an appropriate design.
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Pugh eventually lost the dispute following appeal to the House of Lords. The design of the centerlock hub has three main elements - a splined hub to locate the wheel and two mating cones, one at the inner end which centres the wheel and the other at the nut end. These cones transmit the majority of the torque to the wheel freeing the splines of much of the load. One of the key features of the Pugh design is that it is self tightening.
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Orthogonal collocation is technically a subset of direct collocation, but the implementation details are so different that it can reasonably be considered its own set of methods. Orthogonal collocation differs from direct collocation in that it typically uses high-order splines, and each segment of the trajectory might be represented by a spline of a different order. The name comes from the use of orthogonal polynomials in the state and control splines.Camila C. Francolin, David A. Benson, William W. Hager, Anil V. Rao.
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Newcomb-Macklin picture frames were distinguished by their unique, perpendicular corner splines, a construction feature that prevented the corners of a frame from separating over time.Article in PDF format presents a visual description of a Newcomb-Macklin frame's distinctive corner construction. Basswood was the company's preferred wood for hand-carving, eventually giving way to poplar as the domestic supply of basswood dwindled in the 1960s. Newcomb-Macklin frames were gilded with a wide variety of gold leaf, silver leaf and metal leaf finishes.
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The final Bugatti race car of the 1930s was the Type 59 of 1934. It used an enlarged 3.3 L (3257 cc/198 in³) version of the straight-eight Type 57's engine sitting in a modified Type 54 chassis. The engine was lowered for a better center of gravity, and the frame was lightened with a number of holes drilled in the chassis. The signature piano wire wheels used splines between the brake drum and rim, and relied on the radial spokes to handle cornering loads.
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Fretting examples include wear of drive splines on driveshafts, wheels at the lug bolt interface, and cylinder head gaskets subject to differentials in thermal expansion coefficients. There is currently a focus on fretting research in the aerospace industry. The dovetail blade- root connection and the spline coupling of gas turbine aero engines experience fretting. Another example in which fretting corrosion may occur are the pitch bearings of modern wind turbines, which operate under oscillation motion to control the power and loads of the turbine.
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Smoothing splines are function estimates, \hat f(x), obtained from a set of noisy observations y_i of the target f(x_i), in order to balance a measure of goodness of fit of \hat f(x_i) to y_i with a derivative based measure of the smoothness of \hat f(x). They provide a means for smoothing noisy x_i, y_i data. The most familiar example is the cubic smoothing spline, but there are many other possibilities, including for the case where x is a vector quantity.
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From 1938 until his death Sard published almost forty research articles in refereed mathematical journals. Also he wrote two monographs: in 1963 the book Linear Approximation and in 1971, in collaboration with Sol Weintraub, A Book of Splines. According to the book review from the Deutsche Mathematiker-Vereinigung the content-rich („inhaltsreiche“) Linear Approximation is an important contribution to the theory of approximation of integrals, derivatives, function values, and sums („ein wesentlicher Beitrag zur Theorie der Approximation von Integralen, Ableitungen, Funktionswerten und Summen“).Manfred v.
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The first was that IGES was in great need of a way to represent objects. Up to that point there were, for example, only two surface definitions in IGES and the B-spline form was restricted to cubic splines. The other, surprisingly important, reason for the rapid acceptance was that Boeing, not being a CAD system supplier, was not a threat to any of the major turnkey system vendors. Evidently, IGES easily bogs down when different vendors support their own slightly different representations for the same objects.
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The simple structure of polynomial functions makes them quite useful in analyzing general functions using polynomial approximations. An important example in calculus is Taylor's theorem, which roughly states that every differentiable function locally looks like a polynomial function, and the Stone–Weierstrass theorem, which states that every continuous function defined on a compact interval of the real axis can be approximated on the whole interval as closely as desired by a polynomial function. Practical methods of approximation include polynomial interpolation and the use of splines.
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Sometimes the exact form of a dot gain curve is difficult to model on the basis of geometry, and empirical modeling is used instead. To a certain extent, the models described above are empirical, as their parameters cannot be accurately determined from physical aspects of image microstructure and first principles. However, polynomials, cubic splines, and interpolation are completely empirical, and do not involve any image-related parameters. Such models were used by Pearson and Pobboravsky, for example, in their program to compute dot area fractions needed to produce a particular color in lithography.
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For example, if smoothing with respect to distance and time an isotropic smoother will give different results if distance is measure in metres and time in seconds, to what will occur if we change the units to centimetres and hours. The second class of generalizations to multi-dimensional smoothing deals directly with this scale invariance issue using tensor product spline constructions. Such splines have smoothing penalties with multiple smoothing parameters, which is the price that must be paid for not assuming that the same degree of smoothness is appropriate in all directions.
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However, with good drawbar force, it is very solidly immobile. NMTB/CAT, BT and HSK are examples of the self-releasing variety. For light loads (such as encountered by a lathe tailstock or a drill press), tools with self-holding tapers are simply slipped onto or into the spindle; the pressure of the spindle against the workpiece drives the tapered shank tightly into the tapered hole. The friction across the entire surface area of the interface provides a large amount of torque transmission, so that splines or keys are not required.
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For example, the architect templates can be used to draw different sized doors with their "opening arcs", building and equipment symbols and furniture. The templates also provide the symbols for thermal insulation. Two methods of drawing smooth curves in manual drafting are the use of French curves and flat splines (flexible curves). A French curve is a drawing aid with many different smoothly-varying radiused curves on it; the manual drafter can fit the French curve to some known reference points and draw a smooth curved line between them.
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Jorge Stolfi (born 1950 in São Paulo) is a full professor of computer science at the State University of Campinas, working in computer vision, image processing, splines and other function approximation methods, graph theory, computational geometry and several other fields. According to the ISI Web Of Science, he was the most highly cited computer scientist in Brazil. Jorge Stolfi was born in Vila Carrão, a suburb of São Paulo. His parents had immigrated to Brazil from the Veneto region of Italy only two years earlier, and so he spoke Venetian as his first language.
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Because the aim of step detection is to find a series of instantaneous jumps in the mean of a signal, the wanted, underlying, mean signal is piecewise constant. For this reason, step detection can be profitably viewed as the problem of recovering a piecewise constant signal corrupted by noise. There are two complementary models for piecewise constant signals: as 0-degree splines with a few knots, or as level sets with a few unique levels. Many algorithms for step detection are therefore best understood as either 0-degree spline fitting, or level set recovery, methods.
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The relatively pliable willow is less likely to split while being woven than many other woods, and can be bent around sharp corners in basketry. Willow wood is also used in the manufacture of boxes, brooms, cricket bats, cradle boards, chairmans and other furniture, dolls, flutes, poles, sweat lodges, toys, turnery, tool handles, veneer, wands and whistles. In addition, tannin, fibre, paper, rope and string can be produced from the wood. Willow is also used in the manufacture of double basses for backs, sides and linings, and in making splines and blocks for bass repair.
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The flat base painted by spraying it with an acidic mixture to give it the bluish-green patina. The brain and base were fastened together, and a polished brass circle engraved with the awardee's name is mounted on the trophy. The wooden box for the trophy is made by a furniture maker, Lawrence Gandsey of Oakland. The box is of eastern maple grown (Acer saccharum) in the Appalachians and is held together with splines of mahogany (Swietenia macrophylla) from Honduras, and is finished with a mixture of linseed oil and turpentine.
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In mathematics, nonlinear modelling is empirical or semi-empirical modelling which takes at least some nonlinearities into account. Nonlinear modelling in practice therefore means modelling of phenomena in which independent variables affecting the system can show complex and synergetic nonlinear effects. Contrary to traditional modelling methods, such as linear regression and basic statistical methods, nonlinear modelling can be utilized efficiently in a vast number of situations where traditional modelling is impractical or impossible. The newer nonlinear modelling approaches include non-parametric methods, such as feedforward neural networks, kernel regression, multivariate splines, etc.
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In computer graphics, free-form deformation (FFD) is a geometric technique used to model simple deformations of rigid objects. It is based on the idea of enclosing an object within a cube or another hull object, and transforming the object within the hull as the hull is deformed. Deformation of the hull is based on the concept of so-called hyper-patches, which are three-dimensional analogs of parametric curves such as Bézier curves, B-splines, or NURBs. The technique was first described by Thomas W. Sederberg and Scott R. Parry in 1986, and is based on an earlier technique by Alan Barr.
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Curves in Metafont are defined as cubic splines rather than quadratic, for greater versatility at the cost of more complex arithmetic. Unlike more common outline font formats (such as TrueType or PostScript Type 1), a Metafont font is primarily made up of strokes with finite-width "pens", along with filled regions. Thus, rather than describing the outline of the glyph directly, a Metafont file describes the pen paths. Some simpler Metafont fonts, such as the calligraphic mathematics fonts in the Computer Modern family, use a single pen stroke with a relatively large pen to define each visual "stroke" of the glyphs.
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Broken off splines from the Standard Companion estate car (station wagon) half axles of a Lotus Seven series II The front was by "A" arms and coil springs with an anti-roll bar serving as the front half of the top A-arm. The rear had trailing arms, a triangular centre locating member, and a solid rear axle. The geometry and high (relative to total) unsprung weight gave it some bump steer, which owners sometimes treated by moving the supports forward and lengthening the trailing arms. A model that was sold in the US had independent rear suspension and a Coventry Climax engine.
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The extensive use of kernel smoothing and smoothing splines to ensure smoothness assumptions signify why functional data analysis is at its core a nonparametric statistical technique. Nevertheless, models for functional data and methods for their analysis may resemble those for conventional multivariate data, including linear and nonlinear regression models, principal components analysis among others; that is because functional data can be thought of as multivariate data with order on its dimensions. But the possibility of using derivative information greatly extends the power of these methods, and also leads to purely functional models such as those defined by differential equations, often called dynamical systems.
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A high-dimensional model representation (HDMR) (the term is due to H. Rabitz) is essentially an emulator approach, which involves decomposing the function output into a linear combination of input terms and interactions of increasing dimensionality. The HDMR approach exploits the fact that the model can usually be well-approximated by neglecting higher-order interactions (second or third-order and above). The terms in the truncated series can then each be approximated by e.g. polynomials or splines (REFS) and the response expressed as the sum of the main effects and interactions up to the truncation order.
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Shimano cassette and freehub Cassettes are distinguished from freewheels in that a cassette has a series of straight splines that form the mechanical connection between the sprockets and the cassette compatible hub, called a freehub, which contains the ratcheting mechanism. The entire cassette is held on the hub by means of a threaded lockring. Some cassette systems from the late 1980s and early 1990s use a threaded small sprocket to hold on the larger splined sprockets. Cassettes resemble freewheels when installed, but are clearly different when removed as they do not contain a freewheel's internal ratcheting mechanism.
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I. J. Schoenberg gave the spline function its name after its resemblance to the mechanical spline used by draftsmen. As computers were introduced into the design process, the physical properties of such splines were investigated so that they could be modelled with mathematical precision and reproduced where needed. Pioneering work was done in France by Renault engineer Pierre Bézier, and Citroën's physicist and mathematician Paul de Casteljau. They worked nearly parallel to each other, but because Bézier published the results of his work, Bézier curves were named after him, while de Casteljau’s name is only associated with related algorithms.
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According to Forrest, one possible impetus for a mathematical model for this process was the potential loss of the critical design components for an entire aircraft should the loft be hit by an enemy bomb. This gave rise to "conic lofting", which used conic sections to model the position of the curve between the ducks. Conic lofting was replaced by what we would call splines in the early 1960s based on work by J. C. Ferguson at Boeing and (somewhat later) by M.A. Sabin at British Aircraft Corporation. The word "spline" was originally an East Anglian dialect word.
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To give the right radius for helical spirals while preserving smooth β-strands, the splines can be modified by offsets proportional to local curvature, as first developed by Mike Carson for his Ribbons program. and later adapted by other molecular graphics software, such as the open-source Mage program for kinemage graphics that produced the ribbon image at top right (other examples: 1XK8 trimer and DNA polymerase). Since their inception, and continuing in the present, ribbon diagrams have been the single most common representation of protein structure and a common choice of cover image for a journal or textbook.
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This creates a moving band of heat which when quenched creates the hardened surface layer. The quench ring can be either integral a following arrangement or a combination of both subject to the requirements of the application. By varying speed and power it is possible to create a shaft which is hardened along its whole length or just in specific areas and also to harden shafts with steps in diameter or splines. It is normal when hardening round shafts to rotate the part during the process to ensure any variations due to concentricity of the coil and the component are removed.
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This parameter is often used in biomechanics, when describing the motion of joints of the body. For any period of time, joint motion can be seen as the movement of a single point on one articulating surface with respect to the adjacent surface (usually distal with respect to proximal). The total translation and rotations along the path of motion can be defined as the time integrals of the instantaneous translation and rotation velocities at the IHA for a given reference time.Woltring HJ, de Lange A, Kauer JMG, Huiskes R. 1987 Instantaneous helical axes estimation via natural, cross-validated splines.
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One THM350 weak point was excessive end-play between the pump and center support and resulting wobble of the direct clutch drum due to both the end play and use of a relatively narrow bushing in the drum. This weak point can be addressed by using an extra thrust washer between the planetary gear and direct clutch to remove the end play and using a wider aftermarket bushing in the direct clutch drum. Another weak point is the relatively thin center support and the lightweight matching splines in the case. This weakness can be addressed by using an inexpensive aftermarket case saver kit.
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Tortuosity of blood vessels (for example, retinal and cerebral blood vessels) is known to be used as a medical sign. In mathematics, cubic splines minimize the functional, equivalent to integral of square of curvature (approximating the curvature as the second derivative). In many engineering domains dealing with mass transfer in porous materials, such as hydrogeology or heterogeneous catalysis, the tortuosity refers to the ratio of the diffusivity in the free space to the diffusivity in the porous medium (analogous to arc-chord ratio of path). Strictly speaking, however, the effective diffusivity is proportional to the reciprocal of the square of the geometrical tortuosityGommes, C.J., Bons, A.-J.
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Here, since the observed average overnight rate is swapped for the -IBOR rate over the same period (the most liquid tenor in that market), and the -IBOR IRSs are in turn discounted on the OIS curve, the problem entails a nonlinear system, where all curve points are solved at once, and specialized iterative methods are usually employed — very often a modification of Newton's method. Other tenor's curves can be solved in a "second stage", bootstrap-style. Under both frameworks, the following apply. (i) Maturities for which rates are solved directly are referred to as "pillar points", these correspond to the input instrument maturities; other rates are interpolated, often using Hermitic splines.
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NURBS surfaces can represent, in a compact form, simple geometrical shapes. T-splines and subdivision surfaces are more suitable for complex organic shapes because they reduce the number of control points twofold in comparison with the NURBS surfaces. In general, editing NURBS curves and surfaces is highly intuitive and predictable. Control points are always either connected directly to the curve/surface, or act as if they were connected by a rubber band. Depending on the type of user interface, editing can be realized via an element’s control points, which are most obvious and common for Bézier curves, or via higher level tools such as spline modeling or hierarchical editing.
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The TeraScale tessellator units allow the developers to take a simple polygon mesh and subdivide it using a curved surface evaluation function. There are different tessellation forms, such as Bézier surfaces with N-patches, B-splines and NURBS, and also some subdivision techniques of the surface, which usually includes displacement map some kind of a texture.ExtremeTech review Essentially, this allows a simple, low-polygon model to be increased dramatically in polygon density in real-time with very small impact on the performance. Scott Wasson of Tech Report noted during an AMD demo that the resulting model was so dense with millions of polygons that it appeared to be solid.
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This problem was partly due to the design of the shafts themselves. Due to the fully floating design of the rear wheel hubs, the half shafts can be removed very quickly without even having to jack the vehicle off the ground. The tendency for commercial operators to overload their vehicles exacerbated this flaw which blighted the series Land Rovers in many of their export markets and established a reputation that continues in many markets to the present day. This is despite the 1982 re-design (mainly the increase of driving-splines from 10 to 24 to reduce stress) that all but solved the problem.
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The Central Utah Project was active in the area for 20 years and provided good jobs from 1967 to 1987. A recent expansion to the water treatment plant northwest of town will start supplying culinary water to the community of Roosevelt some away. Duchesne is home to a number of heavy machine and steel manufacturers. A wide variety of products and parts are manufactured, including underground cranes, shield haulers, rifle barrels, steam locomotive parts, drill collars, turbine parts, gears, sprockets, and splines for the oil fields, steel mills, coal mines, trona mines, power plants, other machine shops, manufacturers and other industries in many capacities.
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The development began in 2009 and was inspired by the edition project Keilschrifttexte aus Assur literarischen Inhalts (KAL, cuneiform texts with literary content) of the Heidelberg Academy of Sciences and Humanities. In parallel it was applied within the Austrian Corpus Vasorum Antiquorum of the Austrian Academy of Sciences for documentation of red-figure pottery. Current projects are funded by the DFG and the BMBF for contextualization and analysis of seals and sealings of the Corpus der minoischen und mykenischen Siegel, where Thin Plate Splines are used for comparing sealings. Analog to the developments for processing cuneiform tablets there are further approaches for adaption of the combined Computer Vision and Machine Learning methods for other Scripts in 3D.
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Recreational fishing of lobsters ("crayfishing") in New Zealand does not require a permit provided catch limits, size restrictions, and seasonal and local restrictions set by the Ministry for Primary Industries (MPI) are followed. The legal recreational daily limit is six lobsters per person, with a maximum of three lobster pots permitted per person. Lobsters cannot be taken if they are in berry (carrying eggs) or in the soft shell stage. For J. edwardsii, the minimum legal size is 54 mm for males (no pincers on the rear legs and single pleopods) and 60 mm for females (pincers on the rear legs and paired pleopods), measuring the width of the tail over the primary splines on the second segment.
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Ernst Bettler, Pfäfferli+Huber and its drugs do not exist, and neither do the Swiss towns "Sumisdorf" and "Burgwald" that feature in the article – their names are presumably based on the real Swiss towns of Sumiswald and Burgdorf. Nonetheless, the story was well received in graphic design circles. Among others, the September/October 2001 "Graphic Anarchy" issue of Adbusters magazine hailed Bettler's work as "one of the greatest design interventions on record", and the 2002 graphic design textbook Problem Solved by Michael Johnson covers Bettler as one of the "founding fathers of the 'culture- jamming' form of protest". Wilson's article was first revealed to be false in a 2002 entry in the blog Lines and Splines by Andy Crewdson.
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With the exception of the L98A2, the SA80 system is a selective fire gas-operated design that uses ignited powder gases bled through a port in the barrel to provide the weapon's automation. The rifle uses a short-stroke gas piston system located above the barrel, which is fed gas through a three-position adjustable gas regulator. The first gas setting is used for normal operation, the second ('Excess') is for use in difficult environmental conditions, while the third setting ('Off') prevents any gas from reaching the piston and is used to launch rifle grenades. The weapon uses a rotating cylindrical bolt that contains seven radially mounted locking splines, an extractor and casing ejector.
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In September 2019, Boris FX merged with SilhouetteFX, Academy Award-winning developer of Silhouette, a high-end digital paint, advanced rotoscoping, motion tracking, and node-based compositing application for visual effects in film post-production. In November 2019, Boris FX released Silhouette 2020 which includes free built-in Mocha planar tracking, new rotoscoping tools such as magnetic splines and a visual overlay preview, three new paint brushes, and a paint detail separation workflow. In April 2020, Boris FX released the new Silhouette Paint plug-in product for Adobe, Autodesk, Nuke, and other OFX hosts. Silhouette has been used on major films including Avatar, Avengers: Infinity War, Blade Runner 2049, Ex Machina, and Interstellar.
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PostScript became commercially successful due to the introduction of the graphical user interface (GUI), allowing designers to directly lay out pages for eventual output on laser printers. However, the GUI's own graphics systems were generally much less sophisticated than PostScript; Apple's QuickDraw, for instance, supported only basic lines and arcs, not the complex B-splines and advanced region filling options of PostScript. In order to take full advantage of PostScript printing, applications on the computers had to re-implement those features using the host platform's own graphics system. This led to numerous issues where the on-screen layout would not exactly match the printed output, due to differences in the implementation of these features.
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The definition imitates Gromov's definition of the Gromov–Hausdorff distance in that it involves taking an infimum over all distance-preserving maps of the given spaces into all possible ambient spaces Z. Once in a common space Z, the flat distance between the images is taken by viewing the images of the spaces as integral currents in the sense of Ambrosio–Kirchheim. The rough idea in both intrinsic and extrinsic settings is to view the spaces as the boundary of a third space or region and to find the smallest weighted volume of this third space. In this way, spheres with many splines that contain increasingly small amounts of volume converge "SWIF-ly" to spheres.
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As well as exploring patterns of variation, Multivariate statistical methods can be used to test statistical hypotheses about factors that affect shape and to visualize their effects, although PCA is not needed for this purpose unless the method requires inverting the variance-covariance matrix. Landmark data allow the difference between population means, or the deviation an individual from its population mean, to be visualized in at least two ways. One depicts vectors at landmarks that show the magnitude and direction in which that landmark is displaced relative to the others. The second depicts the difference via the thin plate splines, an interpolation function that models change between landmarks from the data of changes in coordinates of landmarks.
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The string method and uses splines connecting the points, , to measure and enforce distance constraints between the points and to calculate the tangent at each point. In each step of an optimization procedure, the points might be moved according to the force acting on them perpendicular to the path, and then, if the equidistance constraint between the points is no-longer satisfied, the points can be redistributed, using the spline representation of the path to generate new vectors with the required spacing. Variations on the string method include the growing string method, in which the guess of the pathway is grown in from the end points (that is the reactant and products) as the optimization progresses.
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From 1967 the LH-type overdrive was introduced, and this featured in a variety of models, including 1968–1980 MGBs, the MGC, the Ford Zephyr, early Reliant Scimitars, TVRs, and Gilberns. The J-type overdrive was introduced in the late 1960s, and was adapted to fit Volvo, Triumph, Vauxhall/Opel, American Motors and Chrysler motorcars, and Ford Transit vans. The P-type overdrive marked the last updates and included both a Gear Vendors U.S. version and a Volvo version. The Volvo version kept the same package size as the J-type but with the updated 18 element freewheel and stronger splines through the planet carrier. The Gear Vendors U.S. version uses a larger 1.375 outer diameter output shaft for higher capacity and a longer rear case.
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Data-driven prognostics usually use pattern recognition and machine learning techniques to detect changes in system states. The classical data-driven methods for nonlinear system prediction include the use of stochastic models such as the autoregressive (AR) model, the threshold AR model, the bilinear model, the projection pursuit, the multivariate adaptive regression splines, and the Volterra series expansion. Since the last decade, more interests in data- driven system state forecasting have been focused on the use of flexible models such as various types of neural networks (NNs) and neural fuzzy (NF) systems. Data-driven approaches are appropriate when the understanding of first principles of system operation is not comprehensive or when the system is sufficiently complex such that developing an accurate model is prohibitively expensive.
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Thus Krupp decided to use only eight grooves in the barrel and to machine matching ribs or splines on the shells to eliminate the need for a massive copper driving band to start the shell spinning without shearing off, which had been one of the prime causes of the excessive barrel wear in the earlier weapon. Gas sealing would be handled by a copper band, mounted in the place normally occupied by the driving band, with an asbestos and graphite packing to form the initial seal. Several test barrels, known as the 10.5 cm K 12 M, and shells were made in 1935 and were compared to a conventionally rifled barrel (the 10.5 cm K 12 MKu). The tests proved that Krupp's concept was correct.
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The elementary mechanical components of a machine are termed machine elements. These elements consist of three basic types (i) structural components such as frame members, bearings, axles, splines, fasteners, seals, and lubricants, (ii) mechanisms that control movement in various ways such as gear trains, belt or chain drives, linkages, cam and follower systems, including brakes and clutches, and (iii) control components such as buttons, switches, indicators, sensors, actuators and computer controllers.Robert L. Norton, Machine Design, (4th Edition), Prentice-Hall, 2010 While generally not considered to be a machine element, the shape, texture and color of covers are an important part of a machine that provide a styling and operational interface between the mechanical components of a machine and its users.
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Machine element refers to an elementary component of a machine. These elements consist of three basic types: # structural components such as frame members, bearings, axles, splines, fasteners, seals, and lubricants, # mechanisms that control movement in various ways such as gear trains, belt or chain drives, linkages, cam and follower systems, including brakes and clutches, and # control components such as buttons, switches, indicators, sensors, actuators and computer controllers.Robert L. Norton, Machine Design, (4th Edition), Prentice-Hall, 2010 While generally not considered to be a machine element, the shape, texture and color of covers are an important part of a machine that provide a styling and operational interface between the mechanical components of a machine and its users. Machine elements are basic mechanical parts and features used as the building blocks of most machines.
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"Meet Geri: The New Face of Animation" , Computer Graphics World, 1998. To achieve the goal of producing a believable 3D human character, two people were brought on to do research for the project: Michael Kass, who did the calculations behind the physics for a dynamic cloth system, and Tony DeRose, who made use of subdivision surfaces, a technique invented by Catmull in conjunction with Silicon Graphics founder Jim Clark, which allowed for more lifelike skin surfaces. Previously, most 3D character surfaces were crafted using several non-uniform rational B-splines (NURBS) that had to be "stitched" together, which made for less expressive movement and caused models to frequently tear. The use of subdivision surfacing, which renders a character's skin as one large surface, allowed for smoother object movement, as well as more intricate detail.
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The Jacobs type chuck, with three converging splines or jaws, is perhaps the most usual design. This one is tightened with a key, but some types may be sufficiently tightened by hand Tooling similar to today's chucks seems likely to have evolved from faceplate work, as workers using faceplates for repetitive work began to envision types of clamps or dogs for the faceplate that could be opened and closed in more convenient ways than repeated total disassembly and reassembly. A chock was originally just a lump of wood. However, by 1703 it could be "… Chocks, belonging to the Screw-Mandrel". By 1807 the word had changed to the more familiar 'chuck: "On the end of the spindle … is screwed … a unversal Chuck for holding any kind of work".
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In contrast, a torque tube arrangement uses only a single universal at the end of the transmission tailshaft, typically a constant velocity joint, and the axle housing is held fast by the torque tube, which anchors the differential housing to the transmission. In the Hotchkiss drive, slip-splines or a plunge-type (ball and trunnion u-joint) eliminate thrust transmitted back up the driveshaft from the axle, allowing simple rear-axle positioning using parallel leaf springs. In the torque-tube type, this thrust is taken by the torque tube to the transmission and thence to the transmission and motor mounts to the frame. While the torque-tube type, when combined with rear coil springs (1938-62 Buick), requires additional locating elements, such as a Panhard rod, this is not needed with a torque tube/leaf spring combination (1906-1937 Buick, early Ford, etc).
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If the emergency brakes had been functional, they would have caught Sinai when the cable snapped tight, but without the emergency brakes, the force of the jerk caused by the daily test was directed through the spline (the part that failed) and to the service brake. In addition, it was found that the original design called for the spline to be made of AISI 1018 steel on one drawing and of AISI 8822 steel on a different drawing, but it is unlikely that this ambiguity in the design contributed to the accident. However, regular analysis of gear box oil-samples was discontinued in May 1998, despite the fact that the company performing the tests recommending that the rising particulate level in the oil samples warranted the test occurring more frequently. The continued rising particulate level may have been in part caused by unusual wear of the splines.
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Timely, meticulous, rigorous, and often the final word on a given topic, they have been of immense value to the development and definition of these two projects. In addition to the mathematical principles they frequently include working algorithms (often with source code when relevant). Amongst them are, for Hipparcos, the three-step astrometric reduction, optimization of the scanning law, notes on the imaging properties used for the multiple star analysis, assessment of chromatic effects, attitude developments, and many others. For Gaia, his technical notes cover the mathematical and statistical aspects of the Gaia instrument and processing (including the attitude determination and its mathematical representation with quaternions and splines), the modelling of the point/line spread functions, the CCD geometric calibrations, broad band photometry design, maximum likelihood determination of the CCD image centroiding, differential equations and optimal properties of the scanning law, along with the subtle systematic effects in astrometry caused by instrumental misalignments.
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The PSP's eDRAM memory chip is the earliest known use of a three- dimensional integrated circuit (3D IC) chip in a commercial product. The eDRAM (embedded DRAM) memory was manufactured by Toshiba in a 3D system-in-package chip with two integrated circuit (IC) dies stacked vertically. Toshiba called it "semi-embedded DRAM" at the time, before later calling it a stacked "chip- on-chip" (CoC) solution. The 166 MHz graphics chip has 2 MiB embedded memory and through its 512 bit interface provides hardware polygon and NURBS rendering, 16bit Depth Buffer, Bézier Surfaces, Bézier Curves, B-Splines, hardware directional per-vertex lighting, Bloom, Motion Blur, Gouraud Shading, Cel Shading, culling, mipmapping, LOD, clipping, Lightmapping, environment mapping, Render to Texture, shadow mapping, shadow volumes, environment projection and perspective-correct texture mapping, texture compression, tessellation, Hardware Transform and Lighting (T&L;), fogging, alpha blending, alpha, depth and stencil tests, transparency effects, post-processing effects, vertex blending for morphing effects, and dithering, all in 16 or 24 bit color.
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In general, form·Z allows design in 3D or in 2D, using numeric or interactive graphic input through either line or smooth shaded drawings (OpenGL) among drafting, modeling, rendering, and animation platforms. Key modeling features include Boolean solids to generate complex composite objects; the ability to create curved surfaces from a variety of splines, including NURBS and Bézier/Coons patches; mechanical and organic forms using the previous as well as metaforms, patches, subdivisions, displacements, or skinning, plus specialty tools such as Terrain models, Platonic solids, geodesic spheres, double line/wall objects, staircases, helixes, screws, and bolts. In addition, form·Z supports transforming and morphing of 3D shapes, and their animated capture therein. Technical output oriented modeling allows users to refine the design with double precision CAD accuracy to full structural detail for 3D visualization for the production of 2D construction drawings, 3D printing, rapid prototyping, and CNC milling and offers information management of bills of materials and spreadsheet support for construction documents.
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Interlocked panels can be "slid" across and out of the grid An older, less common type of dropped ceiling is the concealed grid system, which uses a method of interlocking panels into one another and the grid with the use of small strips of metal called 'splines', thus making it difficult to remove panels to gain access above the ceiling without damaging the installation or the panels. Normally, they have a "key panel" (usually in the corner) that can be removed, allowing for the other panels to be slid out of the grid (a series of metal channels called 'z bars') one by one, until eventually removing the desired panel. This type of ceiling is more commonly found in older installations or installations where access to above the ceiling is generally considered unnecessary. This system has some major disadvantages, compared to the more common "drop panel" system, most notably the difficulty in removing and reattaching panels from the grid, which, in some cases, can cause irreparable damage to the panels removed.
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SIGGRAPH Computer Graphics, 17(3):377-388 One algorithm proposed for computing the temporal intensity function is: For each image frame: For each object in the frame: Calculate the temporal transformation function for each dynamic attribute Determine the areas the object covers during the filtered interval For each pixel: Determine which objects are covering this pixel at some time in the sampled interval Determine the subintervals of time during which each object projects onto this pixel Perform hidden surface removal by removing subintervals of occluded objects Determine pixel intensity function based on the remaining subintervals and the object's temporal transformation function Filter resulting pixel intensity function Note: The "temporal transformation function" in the above algorithm is simply the function mapping the change of a dynamic attribute (for example, the position of an object moving over the time of a frame). In the cases where either object attributes (shape, color, position, etc.) are either not explicitly defined or are too complex for efficient analysis, interpolation between the sampled values may be used. To obtain results closest to the source data, B-splines can be used to interpolate the attributes. In cases where speed is a major concern, linear interpolation may be a better choice.
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