While coasters can still be assembled piece by piece in painstaking precision, there's now a spline-based mode that allows for quicker building of those big-money attractions.
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The circular spline is a rigid circular ring with teeth on the inside. The flex spline and wave generator are placed inside the circular spline, meshing the teeth of the flex spline and the circular spline. Because the flex spline is deformed into an elliptical shape, its teeth only actually mesh with the teeth of the circular spline in two regions on opposite sides of the flex spline (located on the major axis of the ellipse). Assume that the wave generator is the input rotation.
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Animation showing the compactly supported cardinal B-spline wavelets of orders 1, 2, 3, 4 and 5. In the mathematical theory of wavelets, a spline wavelet is a wavelet constructed using a spline function. There are different types of spline wavelets. The interpolatory spline wavelets introduced by C.K. Chui and J.Z. Wang are based on a certain spline interpolation formula.
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In the mathematical subfield of numerical analysis, a Hermite spline is a spline curve where each polynomial of the spline is in Hermite form.
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These special wavelets are also called B-spline wavelets and cardinal B-spline wavelets. The Battle-Lemarie wavelets are also wavelets constructed using spline functions.
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In the mathematical subfield of numerical analysis, an I-spline is a monotone spline function. An I-spline family of order three with four interior knots.
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In the mathematical subfield of numerical analysis, an M-spline is a non- negative spline function. An M-spline family of order three with four interior knots.
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It is also called a linear spline. A closed linear spline (i.e, the first knot and the last are the same) in the plane is just a polygon. A common spline is the natural cubic spline of degree 3 with continuity C2.
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The spline is often manufactured with parallel ridges running along the length of the spline to provide a better grip and compression when it is pressed into the spline channel. A spline roller -- a special tool that consists of a metal (or plastic) wheel on a handle -- is used to press the spline into the frame. The wheel edge is concave, to help it hold the spline and not slip off to the side. Some spline rollers are double-ended and have both convex and concave rollers; the convex roller can be used to seat the spline deeper into the channel without risk of cutting the screen.
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This demonstrates that the degree of a spline is the maximum degree of its polynomial parts.) The extended knot vector for this type of spline would be (0, 1, 2, 2, 3). The simplest spline has degree 0. It is also called a step function. The next most simple spline has degree 1.
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Transmissions used in later AMC vehicles came with either a 21-spline or a 23-spline output shaft. Transmissions coupled to four-cylinder engines typically used 21-spline output shafts. The 23-spline manual transmission was universal in the Eagle lines and was generally used with six-cylinder applications. All transfer cases were available with inputs matching either 21- or 23-spline shafts, making transmission swaps possible among various models and years.
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In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. Spline interpolation is often preferred over polynomial interpolation because the interpolation error can be made small even when using low degree polynomials for the spline. Spline interpolation avoids the problem of Runge's phenomenon, in which oscillation can occur between points when interpolating using high degree polynomials.
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All Dana 70 rear axles are full floating and typically have a gross axle rating of . The Dana 70 rear axle was first used in the Dodge W300 in 1958. The Dana 70 started out using 10 spline pinions and 23 spline axle shafts. The later, more current, Dana 70 axles use 29 spline pinions and 32 or 35 spline axle shafts.
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Plot of the data with spline interpolation applied Remember that linear interpolation uses a linear function for each of intervals [xk,xk+1]. Spline interpolation uses low-degree polynomials in each of the intervals, and chooses the polynomial pieces such that they fit smoothly together. The resulting function is called a spline. For instance, the natural cubic spline is piecewise cubic and twice continuously differentiable.
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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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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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Moreover, the penalized spline method for partially linear models and intensive simulation experiments were introduced to discover the numerical feature of the penalized spline method, profile and backfitting methods.
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As the wave generator plug rotates, the flex spline teeth which are meshed with those of the circular spline slowly change position. The major axis of the flex spline's ellipse rotates with wave generator, so the points where the teeth mesh revolve around the center point at the same rate as the wave generator's shaft. The key to the design of the strain wave gear is that there are fewer teeth (often for example two fewer) on the flex spline than there are on the circular spline. This means that for every full rotation of the wave generator, the flex spline would be required to rotate a slight amount (two teeth in this example) backward relative to the circular spline.
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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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This unique discrete cubic spline is the discrete spline interpolant to f(x) in the interval [x0 \- h, xn \+ h]. This interpolant agrees with the values of f(x) at x0, x1, . . ., xn.
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In this figure, there is a self-intersection/loop on the uniform Catmull-Rom spline (green), whereas for chordal Catmull-Rom spline (red), the curve does not follow tightly through the control points.
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Bending contours defined as spline- or polynomial- functions can be manufactured.
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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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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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In computer vision, centripetal Catmull-Rom spline has been used to formulate an active model for segmentation. The method is termed active spline model. The model is devised on the basis of active shape model, but uses centripetal Catmull-Rom spline to join two successive points (active shape model uses simple straight line), so that the total number of points necessary to depict a shape is less. The use of centripetal Catmull-Rom spline makes the training of a shape model much simpler, and it enables a better way to edit a contour after segmentation.
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109, 121. is a polynomial- time and numerically stable algorithm for evaluating spline curves in B-spline form. It is a generalization of de Casteljau's algorithm for Bézier curves. The algorithm was devised by Carl R. de Boor.
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Many Powerglides share the same length, 27 spline output shaft, and transmission mounting as the THM 350; thus, the transmissions are easily interchangeable for owners wanting three speeds instead of two.Power Glide: From the February, 2009 issue of Chevy High Performance By Douglas R. Glad; Retrieved April 27, 2011. Other Powerglides came with an incompatible 16 spline output shaft.Denny's Driveshafts - Output Spline Shafts for Chevy transmissions.
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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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There are five main types of keys: sunk, saddle, tangent, round, and spline.
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Cassettes engage the freehub via a spline that has one groove wider than the others to enforce a fixed orientation. Disc brake mounting interfaces that are splined include Centerlock, by Shimano. Aircraft engines may have a spline upon which mounts the propeller. There may be a master spline which is wider than the others, so that the propeller may go on at only one orientation, to maintain dynamic balance.
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This results in significant flexibility of the walls at the open end due to the thin wall, and in the closed side being quite rigid and able to be tightly secured (to a shaft, for example). Teeth are positioned radially around the outside of the flex spline. The flex spline fits tightly over the wave generator, so that when the wave generator plug is rotated, the flex spline deforms to the shape of a rotating ellipse and does not slip over the outer elliptical ring of the ball bearing. The ball bearing lets the flex spline rotate independently to the wave generator's shaft.
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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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Single knots at 1/3 and 2/3 establish a spline of three cubic polynomials meeting with C2 continuity. Triple knots at both ends of the interval ensure that the curve interpolates the end points In mathematics, a spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees. In the computer science subfields of computer-aided design and computer graphics, the term spline more frequently refers to a piecewise polynomial (parametric) curve.
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Several algorithms have been developed to identify TADs from Hi-C data. Hi-C and its subsequent analyses are evolving. Fit-Hi-C is a method based on a discrete binning approach with modifications of adding distance of interaction (initial spline fitting, aka spline-1) and refining the null model (spline-2). The result of Fit-Hi-C is a list of pairwise intra-chromosomal interactions with their p-values and q-values.
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B-spline windows can be obtained as k-fold convolutions of the rectangular window. They include the rectangular window itself (k = 1), the (k = 2) and the (k = 4). Alternative definitions sample the appropriate normalized B-spline basis functions instead of convolving discrete-time windows. A kth order B-spline basis function is a piece-wise polynomial function of degree k−1 that is obtained by k-fold self-convolution of the rectangular function.
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A spline joint can be viewed as an extended biscuit. Two boards have extended, matching grooves lined up and facing each other. The void between is filled with a thin piece of wood, forming a spline joint. This is very similar to tongue and groove.
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Like the rear Dana 70 axles, the Dana 70 front axle started out with 23 spline axle shafts and then went to 35 spline axle shafts. While these axles were being manufactured, Dana offered a "Power-Lok" limited slip differential for some of these axles.
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The problem can be avoided by using spline curves which are piecewise polynomials. When trying to decrease the interpolation error one can increase the number of polynomial pieces which are used to construct the spline instead of increasing the degree of the polynomials used.
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The elasticity of the spline material combined with the constraint of the control points, or knots, would cause the strip to take the shape that minimized the energy required for bending it between the fixed points, this being the smoothest possible shape. One can recreate an original draftsman's spline device with weights and a length of thin plastic or wood, flexible to bend enough without breaking. Crosses are marked on the paper to designate the knots or control points. The spline is placed on the drafting paper, and weights are attached to the shaft near each knot so that the spline passes through each one.
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In some regions such as the northern United States and Canada, screens were required to be replaced by glass storm windows in the winter, but now combination storm and screen windows are available, which allow glass and screen panels to slide up and down. For screens installed on aluminium frames, the material is cut slightly larger than the frame, then laid over it, and a flexible vinyl cord, called a spline, is pressed over the screen into a groove (spline channel) in the frame. The excess screen is then trimmed close to the spline with a sharp utility knife. Common spline sizes range from to , in increments of .
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A spline is a flexible ruler, usually rubber or plastic coated with a metal "backbone", which can be smoothly shaped to follow a desired curve and allows drawing a smooth line between initial reference points. Sometimes a spline is temporarily held in position with small weights.
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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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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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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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The word "natural" means that the second derivatives of the spline polynomials are set equal to zero at the endpoints of the interval of interpolation :S(a) \, = S(b) = 0. This forces the spline to be a straight line outside of the interval, while not disrupting its smoothness.
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In the context of image processing, box spline frames have been shown to be effective in edge detection.
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Cross section of a harmonic gear. Blue (outer circle): circular spline (fixed) Red (middle flexible circle): flex spline (attached to output shaft, which is not shown) Green (inner oval): wave generator (attached to input shaft; inner ball bearing and shaft are not shown) The strain wave gearing theory is based on elastic dynamics and utilizes the flexibility of metal. The mechanism has three basic components: a wave generator (2 / green), a flex spline (3 / red), and a circular spline (4 / blue). More complex versions have a fourth component normally used to shorten the overall length or to increase the gear reduction within a smaller diameter, but still follow the same basic principles.
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Example showing non-monotone cubic interpolation (in red) and monotone cubic interpolation (in blue) of a monotone data set. Monotone interpolation can be accomplished using cubic Hermite spline with the tangents m_i modified to ensure the monotonicity of the resulting Hermite spline. An algorithm is also available for monotone quintic Hermite interpolation.
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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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The Oxford English Dictionary finds the first recorded usage in the 18th century in East Anglia, England, and suggests the term spline may be related to splinter. Spline devices have been used to designs shapes for pianos, violins, and other wooden instruments. The Wright brothers used one to shape the wings of their aircraft.
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7.1M, which was withdrawn in 2011, making the spline drive obsolescent. Spline drives were specified for 5, 6.3, 8, 10, 12, 14, 16, and 20 mm size screws. Its primary advantage is its ability to resist cam out, so it is used in high-torque applications, such as tamper-proof lug nuts, cylinder head bolts, and other engine bolts.
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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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The difference is that the spline essentially forms a tongue, a 'loose tongue', for both grooves. It is often joined with glue.
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Several different competing standards for splined interfaces exist. The tool for installing and removing these bottom brackets is often also a spline.
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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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Contrary to the integral method, the resulting stress values are approximated by a polynomial or a spline. The power series method is very stable but it cannot capture rapidly changing stress values. The spline method is more stable and less susceptible to errors than the integral method. It can capture the actual stress values better than the power series method.
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Runge's phenomenon shows that for high values of , the interpolation polynomial may oscillate wildly between the data points. This problem is commonly resolved by the use of spline interpolation. Here, the interpolant is not a polynomial but a spline: a chain of several polynomials of a lower degree. Interpolation of periodic functions by harmonic functions is accomplished by Fourier transform.
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A Hirth joint is similar to a spline joint but with the teeth on the end of the shaft instead of on the surface.
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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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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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Statistical Science 11(2): 89-121. Two- and multidimensional P-spline approximations of data can use the Face-splitting product of matrices to the minimization of calculation operations.
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Both operations have a number of applications in mathematics and in geometric modeling, especially whenever some function or shape needs to be approximated piecewise, e.g. by a spline.
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Hermite-Simpson Collocation is a common medium-order direct collocation method. The state is represented by a cubic-Hermite spline, and the dynamics are satisfied using Simpson quadrature.
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In computer-aided geometric design a control point is a member of a set of points used to determine the shape of a spline curve or, more generally, a surface or higher-dimensional object.. For Bézier curves, it has become customary to refer to the d-vectors p_i in a parametric representation \sum_i p_i \phi_i of a curve or surface in d-space as control points, while the scalar-valued functions \phi_i, defined over the relevant parameter domain, are the corresponding weight or blending functions. Some would reasonably insist, in order to give intuitive geometric meaning to the word "control", that the blending functions form a partition of unity, i.e., that the \phi_i are nonnegative and sum to one. This property implies that the curve lies within the convex hull of its control points.. This is the case for Bézier's representation of a polynomial curve as well as for the B-spline representation of a spline curve or tensor-product spline surface.
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Miter joint (pieces ready to be joined) Miter joint of two pipes A mitre joint (often miter in American English) is a joint made by cutting each of two parts to be joined, across the main surface, usually at a 45° angle, to form a corner, usually a 90° angle. It is called beveling when the angled cut is done on the side, although the resulting joint is still a mitre joint. For woodworking, a disadvantage of a mitre joint is its weakness, but it can be strengthened with a spline (a thin wafer of wood inserted into a slot, usually arranged with the long grain of the spline across the short grain of the frame timber). There are two common variations of a splined mitre joint, one where the spline is long and runs the length of the mating surfaces and another where the spline is perpendicular to the joined edges.
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GM also sourced a Jatco electronic four-speed automatic. Those that opted for a manual received 5-speed Nissan gearboxes. The turbo and non-turbo variants designated MX7 and MF5 respectively. Irrespective of transmission, Power was sent to the rear wheels through a Borgwarner 28-Spline (Turbo variants) /25-spline open center (non- turbo variant) with a 3.45 or 3.23 Final Drive ratio with a Limited-Slip version available as an option.
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The wave generator is made up of two separate parts: an elliptical disk called a wave generator plug and an outer ball bearing. The elliptical plug is inserted into the bearing, forcing the bearing to conform to the elliptical shape but still allowing rotation of the plug within the outer bearing. The flex spline is shaped like a shallow cup. The sides of the spline are very thin, but the bottom is relatively rigid.
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Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation. SIAM J. Numer. Anal., 7:112–124, 1970. and in domain decomposition methods and multigrid methods.
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Like Barco Creator, Strike was set up as a modular system. The base was the "LW-Brix" linework software library (unlimited zoom, unlimited undo/redo, spline data, editable text, transparency etc.).
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Driving the spline into the channel tends to tension the screen on the frame, so the installer must avoid pre-tensioning the screen excessively to prevent the frame from becoming warped.
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The left side spline interface looks similar, but is different so as to prevent installation of older ISIS Drive crankarms—which are no longer compatible because Q-factor and chain line cannot be maintained using these older cranks with an external bearing BB. They refer to this design as 'Giga-X-Pipe' or 'GXP.' They also make a heavier duty external bearing bottom bracket called 'Howitzer.' The Howitzer BB is more like a traditional BB in that the spindle is not permanently pressed into the right crank. Again, the Howitzer spline looks similar to the ISIS Drive standard spline but is actually different, so as to prevent the usage of ISIS Drive cranks on the external bearing BB, which would affect chainline and Q-factor.
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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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Splined canvases differ from traditional side- stapled canvas in that canvas is attached with a spline at the rear of the frame. This allows the artist to incorporate painted edges into the artwork itself without staples at the sides, and the artwork can be displayed without a frame. Splined canvas can be restretched by adjusting the spline. Stapled canvases stay stretched tighter over a longer period of time, but are more difficult to re-stretch when the need arises.
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In order to ensure alignment of each sprocket with its neighbour, the freehub has a narrow spline at one position, and each sprocket has a corresponding wide tooth on its inside face.
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If the eigenmodes of variation of the point set are known, the nonlinear transformation may be parametrized by the eigenvalues. A nonlinear transformation may also be parametrized as a thin plate spline.
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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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The Dana 50 was made as a solid axle and as a Twin Traction Beam (TTB) which pivots in the center allowing the wheels to move independently of each other. A unique quality of the Dana 50 axle is the lack of variation in both TTB and Solid axle versions, which simplifies repairs and upgrades. There were no carrier breaks and only one spline count (30 spline). Gross axle weight ratings were lowered by Ford for safety and tire reasons.
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In the images, the graphs of the terms contributing to the corresponding two-scale relations are also shown. The two dots in each image indicate the extremities of the interval supporting the B-spline.
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Tatyana Krivobokova is a Kazakh statistician known for her work on spline estimators, with applications in biophysics and econometrics. She is University Professor for Statistics with Applications in Economics at the University of Vienna.
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Alternatively polynomial interpolation or spline interpolation is used where piecewise polynomial functions are fit into time intervals such that they fit smoothly together. A different problem which is closely related to interpolation is the approximation of a complicated function by a simple function (also called regression).The main difference between regression and interpolation is that polynomial regression gives a single polynomial that models the entire data set. Spline interpolation, however, yield a piecewise continuous function composed of many polynomials to model the data set.
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The goal of nonlinear filters is to overcome limitation of linear models. There are some commonly used approaches: Volterra LMS, Kernel adaptive filter, Spline Adaptive Filter and Urysohn Adaptive Filter.M.Poluektov and A.Polar. Urysohn Adaptive Filter. 2019.
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The parameter is a tension parameter that must be in the interval . In some sense, this can be interpreted as the "length" of the tangent. Choosing yields all zero tangents, and choosing yields a Catmull–Rom spline.
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The kriging estimation may also be seen as a spline in a reproducing kernel Hilbert space, with the reproducing kernel given by the covariance function. The difference with the classical kriging approach is provided by the interpretation: while the spline is motivated by a minimum norm interpolation based on a Hilbert space structure, kriging is motivated by an expected squared prediction error based on a stochastic model. Kriging with polynomial trend surfaces is mathematically identical to generalized least squares polynomial curve fitting. Kriging can also be understood as a form of Bayesian inference.
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The spline is curved so that when the user strikes the outer sleeve with a hammer, its downward force works on the spline to produce turning force on the core and any socket or work bit attached to it. The tool translates the heavy rotational inertia of the sleeve to the lighter core to generate large amounts of torque. At the same time, the striking blow from the hammer forces the impact driver forward into the screw reducing or eliminating cam out. This attribute is beneficial for Phillips screws which are prone to cam out.
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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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Once the note has started and is sustained, the player now has to keep following an orb that keeps moving along the spline path which is synchronized with the duration of the given note. That path starts when the note starts, and it ends when the note ends. The full spline path is visualized from the beginning, so the player knows where to move and by an orb following that path with the correct speed, the player also knows at what pace to move. This way, any hand movement could be choreographed.
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In the UK the 70HD Dana axles were license built by Salisbury Engineering in an early 10/23 spline version with a rating for the Ford A-series truck with a European 6 × DIN standard hub bolt pattern.
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If a cubic Hermite spline of any of the above listed types is used for interpolation of a monotonic data set, the interpolated function will not necessarily be monotonic, but monotonicity can be preserved by adjusting the tangents.
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The lemma was proved by Bramble and Hilbert J. H. Bramble and S. R. Hilbert. Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation. SIAM J. Numer. Anal., 7:112–124, 1970.
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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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HIWIN () is a major Taiwanese company which manufactures machinery components. It was founded in 1989 and is based in Taichung, Taiwan. HIWIN is a combination of HI-tech WINner. The company is known for linear motion guides, ball spline, ball screws.
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It also supports several font formats, including PostScript, TrueType, and OpenType. For this reason the fonts are derived from original work made in FontForge, and stored in .sfd (Spline Font Database) files. The most recent release is from May 2012.
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An example of a broached workpiece. Here the broaching profile is a spline. Broaching was originally developed for machining internal keyways. However, it was soon discovered that broaching is very useful for machining other surfaces and shapes for high volume workpieces.
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If a C0 function is insufficient, for example if the process that has produced the data points is known to be smoother than C0, it is common to replace linear interpolation with spline interpolation or, in some cases, polynomial interpolation.
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Not all welded materials are equally amenable to ultrasonic inspection; some materials have a large grain size that produces a high level of background noise in measurements. spline cracking Ultrasonic thickness measurement is one technique used to monitor quality of welds.
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A 10-spline type was used with some early equipment such as the 1948 Land Rover. A six- spline adapter was usually supplied. It is customary for agricultural machines manufacturers to provide the nominal PTO power specification, an indication of the available instantaneous power at the shaft. Newer tractors may come equipped with 540/540E and/or 1000/1000E options that allow the tractor to power certain low-power-demand implements like hay rakes or tedders using lower engine speeds to maintain the revolutions per minute needed, using less fuel and placing less stress on the engine thereby improving efficiency and reducing costs.
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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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In addition, a powerful Spline class can be used to easily store and visualize data. Many features of the CMBEASY package are also accessible via a graphical user interface. This may be helpful for gaining intuition, as well as for instruction purposes.
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An interpolation of a finite set of points on an epitrochoid. The points in red are connected by blue interpolated spline curves deduced only from the red points. The interpolated curves have polynomial formulas much simpler than that of the original epitrochoid curve.
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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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There has been a great deal of research in applying the principles of computer-aided geometric design (CAGD) to the problem of computer-aided motion design. In recent years, it has been well established that rational Bézier and rational B-spline based curve representation schemes can be combined with dual quaternion representation of spatial displacements to obtain rational Bézier and B-spline motions. Ge and Ravani, developed a new framework for geometric constructions of spatial motions by combining the concepts from kinematics and CAGD. Their work was built upon the seminal paper of Shoemake, in which he used the concept of a quaternion for rotation interpolation.
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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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Searching for a single form, the group worked together, learning about knots, multiple knots and how nicely Bézier segments, especially the conics, could be imbedded into a B-spline curve with multiple knots. Looking back, it seemed so simple: It is easy to verify that the equation for P(t) is valid for the B-spline basis functions as well as for Bernstein basis functions. By the end of 1980 the staff knew we had a way to present all the required curve forms using a single representation, now known as the NURBS form. But this new representation could easily have died at this point.
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A beziergon (also called bezigon) is a closed path composed of Bézier curves. It is similar to a polygon in that it connects a set of vertices by lines, but whereas in polygons the vertices are connected by straight lines, in a beziergon the vertices are connected by Bézier curves.Microsoft polybezier API Papyrus beziergon API reference "A better box of crayons". InfoWorld. 1991. Some authors even call a C0 composite Bézier curve a "Bézier spline"; the latter term is however used by other authors as a synonym for the (non-composite) Bézier curve, and they add "composite" in front of "Bézier spline" to denote the composite case.
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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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In the 1980s the Dana 70U or Dana 70B was offered. GM, Ford and Dodge all used this axle. This axle had a smaller pinion bearing and mostly have 32 spline axle shafts. The Dana 70U and Dana 70B both have gross axle weight ratings of .
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Eclipse was a professional 2D image editing program available on Silicon Graphics and Windows workstations. Designed to manipulate high-resolution images like digitized movie frames and photographs for print, it offered color correction tools, image processing effects, rudimentary paint features, and spline-based drawing and masking.
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A Bézier curve is also a polynomial curve definable using a recursion from lower degree curves of the same class and encoded in terms of control points, but a key difference is that all terms in the recursion for a Bézier curve segment have the same domain of definition (usually [0,1]) whereas the supports of the two terms in the B-spline recursion are different (the outermost subintervals are not common). This means a Bézier curve of degree n given by m \gg n control points consists of about m/n mostly independent segments, whereas the B-spline with the same parameters smoothly transitions from subinterval to subinterval. To get something comparable from a Bézier curve, one would need to impose a smoothness condition on transitions between segments, resulting in some manner of Bézier spline (for which many control points would be determined by the smoothness requirement). A piecewise/composite Bézier curve is a series of Bézier curves joined with at least C0 continuity (the last point of one curve coincides with the starting point of the next curve).
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For a temporal signal of length M, the complexity of cubic spline sifting through its local extrema is about the order of M, and so is that of the EEMD as it only repeats the spline fitting operation with a number that is not dependent on M. However, as the sifting number (often selected as 10) and the ensemble number (often a few hundred) multiply to the spline sifting operations, hence the EEMD is time consuming compared with many other time series analysis methods such as Fourier transforms and wavelet transforms.The MEEMD employs EEMD decomposition of the time serie s at each division grids of the initial temporal signal, the EEMD operation is repeated by the number of total grid points of the domain. The idea of the fast MEEMD is very simple. As PCA/EOF- based compression expressed the original data in terms of pairs of PCs and EOFs, through decomposing PCs, instead of time series of each grid, and using the corresponding spatial structure depicted by the corresponding EOFs, the computational burden can be significantly reduced.
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The 9 and 1/2 inch rear end, while durable in its own right, is generally regarded as less desirable in high torque applications. The 9-1/2 c clip rear was in both the Suburban and pickups in both 6 or 8 lug varieties. 33 spline axles.
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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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The Dana 45 was introduced during the 1950s as an upgraded Dana 44 with larger 20 spline axle shafts. Since the Dana 45 is no longer being made you can use the Dana 44 gears in the Dana 45 housing if you use model 53 pinion bearings and plenty of shims.
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By the early 1980s, numerous other devices were supported. In 1989, the first GNU versions of `graph', `plot', `tek2plot', `spline' and their respective documentation were written. Richard Stallman further directed development of the programs and documentation. The distribution, as it stood in 1991, was distributed under the name `GNU graphics'.
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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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V1 spline grooves are 5 mm long, while V2 grooves are 9mm long. Shimano 105, Ultegra 6500 and Dura Ace 7700 cranksets mate to version one bottom brackets, while later mountain bike designs use the deeper-grooved version two. The system is proprietary and protected by Shimano patents and license fees.
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Centripetal Catmull–Rom spline has several desirable mathematical properties compared to the original and the other types of Catmull-Rom formulation. First, it will not form loop or self-intersection within a curve segment. Second, cusp will never occur within a curve segment. Third, it follows the control points more tightly.
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According to Liang’s paper in 2010 (Liang, 2010), The smoothing spline technique was introduced in partially linear model by Engle, Heckman and Rice in 1986. After that, Robinson found an available LS estimator for nonparametric factors in partially linear model in 1988. At the same year, profile LS method was recommended by Speckman.
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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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The sifting process is as follows: # Identify all the local extrema in the test data. # Connect all the local maxima by a cubic spline line as the upper envelope. # Repeat the procedure for the local minima to produce the lower envelope. The upper and lower envelopes should cover all the data between them.
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This branch is also known as geometric modelling and computer- aided geometric design (CAGD). Core problems are curve and surface modelling and representation. The most important instruments here are parametric curves and parametric surfaces, such as Bézier curves, spline curves and surfaces. An important non-parametric approach is the level-set method.
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Those were the days of the oversupply of math PhD's. The task was to choose the representations for the 11 required curve forms, which included everything from lines and circles to Bézier and B-spline curves. By early 1980, the staff were busy choosing curve representations and developing the geometry algorithms for TIGER.
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The drive pinion was arranged on a swinging link so that it was thrown out-of-mesh automatically, once the main engine started to rotate at full speed. As the ratio was perhaps 1000:1 and the main engine ran at 60 rpm, this would otherwise have been a disastrous overspeed. Some engines instead used a final pinion on a helical spline, similar to that later used for the starters of internal combustion engines: once the main engine started, the pinion would be thrown out of engagement axially along this spline as the flywheel over- speeded the pinion relative to the shaft. As mill engines became more powerful, from around 1870 there was a shift from single belt drives to multiple rope drives.
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However, as the radial resolution (along the beam) is far better than the lateral resolution which also decreases with depth, both the angle independence and the tracking ability across the sector is lower. Also, instead of angle independency, the resulting strain values are dependent on the ROI (Region Of Interest) size and shape. Finally, in order to achieve tracking quality, the values are in most commercial applications smoothed by a spline smoothing function along the ROI, so the regional measurements are not pure regional, but rather to a degree, spline functions of the global average. In addition, the method has a lower sampling rate due to the limited frame rate of B-mode, which reduces tracking validity, especially at high heart rates.
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Podium is a Digital Audio Workstation software program that integrates audio recording, VST plugins and external MIDI and audio gear. An object based project structure allows for advanced media and device management. Feature highlights include hierarchic track layout, integrated sound editor, surround sound, spline curve automation, 64-bit mixing, multiprocessing and a customizable user interface.
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Kernel density estimation is a nonparametric technique for density estimation i.e., estimation of probability density functions, which is one of the fundamental questions in statistics. It can be viewed as a generalisation of histogram density estimation with improved statistical properties. Apart from histograms, other types of density estimators include parametric, spline, wavelet and Fourier series.
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Arthur Sard (28 July 1909, New York City - 31 August 1980, Basel) was an American mathematician, famous for his work in differential topology and in spline interpolation. His fame stems primarily from Sard's theorem, which says that the set of critical values of a differential function which has sufficiently many derivatives has measure zero.
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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 Skyactiv-MT is a family of manual transmissions. To achieve lighter shift effort with a short shift lever stroke, the lever ratio is increased. However, to overcome the shorter internal stroke, a small module spline is used. Shift throws are reduced by 15 percent, making it the shortest shifting of any passenger car.
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More generally, the shape of the resulting curve, especially for very high or low values of the independent variable, may be contrary to commonsense, i.e. to what is known about the experimental system which has generated the data points. These disadvantages can be reduced by using spline interpolation or restricting attention to Chebyshev polynomials.
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Note: All (1992 up, non-Prelude) "Big Spline" B series Transmissions are interchangeable. YS1 casing can take S80 Internals or a hydraulic conversion kit can be used to operate hydraulic transmissions in cable operated models, however A1/S1/J1/Y1 internals do not swap into the later model YS1 or hydraulic casings due to different shaft diameters.
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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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RM 030 with the characteristic Richard Mille case shape The characteristic Richard Mille case shape is now the principal element of the brand's visual identity, ensuring that the watches are clearly recognisable, as are the spline screws visible on both the case and the inside of the movement. The movement is always visible in a Richard Mille watch.
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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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In the 1970s the Dana 70HD was offered. The axle tubes were increased to diameter and carrier bearings were larger and thicker, the axle shafts were 35 spline only. These upgrades gave the Dana 70HD a gross axle rating of . The Dana 70 front drive axles used in the Chevrolet Kodiaks and GMC Topkicks also had these features.
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RollerCoaster Tycoon World was developed by Nvizzio Creations for Atari and released on 16 November 2016. The installment is different from previous games in that players build coasters with a spline- based system. It also introduced a new "Architect mode" and "safety-rating" options when building coasters. The game is also the first to incorporate the Steam Workshop.
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"Fast calculation of thermodynamic properties of water and steam in process modelling using spline interpolation." Proceedings of the 15h International Conference on the Properties of Water and Steam. 2008. Boundary conditions (normally temperature of the geothermal gradients) are input into the equations to calculate the temperature at boundaries. Results are compared with petrological experimental results for validation.
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They are suitable only if there are small changes in the stress profiles. Both the methods give numerically correct results for uniform stresses. The power series method and the spline method are other modifications of the integral method. They both take into account both the distance of the stress effect from the surface and the total hole depth.
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For very large gears or spline, a vertical broach is used. It consists of a vertical rail that carries a single tooth cutter formed to create the tooth shape. A rotary table and a Y axis are the customary axes available. Some machines will cut to a depth on the Y axis and index the rotary table automatically.
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Raphael "Raphi" Rom is an Israeli computer scientist working at Technion – Israel Institute of Technology.Faculty profile, Technion, retrieved 2014-05-01. Rom earned his Ph.D. in 1975 from the University of Utah, under the supervision of Thomas Stockham.. He is known for his contribution to the development of the Catmull–Rom spline,. and for his research on computer networks.
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The Qax goes on to speculate that the torus created a Kerr metric, and that it allowed egress from the current universe, that it was in effect an escape route for the Xeelee. Before Parz, the Spline warship, and the Qax exit the wormhole, the Qax asks, "What do Xeelee fear, do you suppose?". Regardless, Bolder escaped the Great Attractor and returned to the Qax home system, where he was supposed to be taken into custody by dozens of Spline warships wielding gravitational-wave based "starbreakers" and his priceless data on the god-like Xeelee's ultimate project secured. Bolder either did not, or somehow escaped; in the ensuing fight, the starbreakers were accidentally fired at the Qax system primary star, and true to their name, destabilised it, causing it to go nova.
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She received her bachelor's degree in 1956 and a master's degree from the University of Maryland, College Park in 1962. She worked in industry for several years before receiving her doctorate from Stanford University in 1966 and settling in Madison in 1967. She is the author of Spline Models for Observational Data. She retired in August 2018 from the University of Wisconsin-Madison.
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Area charts which use vertical and horizontal lines to connect the data points in a series forming a step-like progression are called step-area charts. Area charts in which data points are connected by smooth curves instead of straight lines are called spline-area charts. Stacked area charts in which the area is displaced around the central axis are called streamgraphs.
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Several utilities were inspired by Unix plotting utilities. A graph utility and various plot filters were present in the first releases of Unix from Bell Laboratories. By the time of Version 7 Unix, `graph', `plot', `spline', and several device-dependent versions of `libplot' were a standard Unix features. The first display device supported by the package was a Tektronix 611 storage scope.
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1991 (Wye, Kent, UK): H. Isil Bozma, Yale University, New Haven, CT, USA. H.I. Bozma, J.S. Duncan: Model-based recognition of multiple deformable objects using a game-theoretic framework. 1993 (Flagstaff, AZ, USA): Jeffrey A. Fessler, University of Michigan, Ann Arbor, MI, USA. J.A. Fessler: Tomographic reconstruction using information-weighted spline smoothing. 1995 (Brest, France): Maurits K. Konings, University Hospital, Utrecht, The Netherlands.
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At this first IGES meeting, it was discovered that the people with the best understanding of the presentation were the SDRC representatives. Evidently SDRC was also active in defining a single representation for the standard CAD curves and was working on a similar definition. So that's how NURBS started at Boeing. Boehm's B-spline refinement paper from CAD ’80 was of primary importance.
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Bézier curves can be combined to form a Bézier spline, or generalized to higher dimensions to form Bézier surfaces. The Bézier triangle is a special case of the latter. In vector graphics, Bézier curves are used to model smooth curves that can be scaled indefinitely. "Paths", as they are commonly referred to in image manipulation programs, are combinations of linked Bézier curves.
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While a spline roller (also referred to as a "spline tool") is said to look like a less-sharp version of a pizza cutter (which it does), its origins are in fact from something different. Somewhere around or before 1920 a man named Julius Alexander Muhlberg who was co-owner of Winchester and Muhlberg, a New Jersey- based company. An innovator at heart, Julius had taken some other tool's handle, drilled a hole through a silver dollar, and after putting them both together with a nut and bolt, found it to be much faster to squish screening into the sides of a frame rather than the regular method of the time, nailing the screen into the frames. The original tool remained in the possession of his son, Julius Muhlberg, but unfortunately it seems to be hopelessly lost to time.
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Xfig is a free and open-source vector graphics editor which runs under the X Window System on most UNIX-compatible platforms. In Xfig, figures may be drawn using objects such as circles, boxes, lines, spline curves, text, etc. It is also possible to import images in formats such as GIF, JPEG, EPS, PostScript, etc. Those objects can be created, deleted, moved or modified.
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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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Datig and Schlurmann [2004] conducted a comprehensive study on the performance and limitations of HHT with particular applications to irregular water waves. The authors did extensive investigation into the spline interpolation. The authors discussed using additional points, both forward and backward, to determine better envelopes. They also performed a parametric study on the proposed improvement and showed significant improvement in the overall EMD computations.
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Once there is a machine-readable bitmap, the image can be imported into a graphics editing program (such as Adobe Illustrator, CorelDRAW, or Inkscape). Then a person can manually trace the elements of the image using the program's editing features. Curves in the original image can be approximated with lines, arcs, and Bézier curves. An illustration program allows spline knots to be adjusted for a close fit.
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In statistics, originally in geostatistics, kriging or Gaussian process regression is a method of interpolation for which the interpolated values are modeled by a Gaussian process governed by prior covariances. Under suitable assumptions on the priors, kriging gives the best linear unbiased prediction of the intermediate values. Interpolating methods based on other criteria such as smoothness (e.g., smoothing spline) may not yield the most likely intermediate values.
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The differential uses the 31-spline axles and the ring gear. The standard final drive ratio of 2005 and 2006 Mustang GTs with a manual transmission was 3.55:1. Since the 2007 model year, a 3.31:1 ratio final drive was standard with the 3.55:1 gearing available as a factory installed option. Automatic transmission-equipped models of all years come with 3.31:1 ratio.
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Standard components of the Rubicon package include front and rear next generation Dana 44 axles with electric lockers, Rock-Trac four-wheel drive with 4:1 transfer case, rock rails, 32-spline rear axle with an 8.8-inch ring gear, 4.10 axle gearing, electric releasing sway bar, "Yes Essentials" seats (2007–08), 7-speaker infinity sound system, and any other available option can be added.
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Primary among these are the compasses, used for drawing simple arcs and circles, and the French curve, for drawing curves. A spline is a rubber coated articulated metal that can be manually bent to most curves. Drafting templates assist the drafter with creating recurring objects in a drawing without having to reproduce the object from scratch every time. This is especially useful when using common symbols; i.e.
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The most important instruments here are parametric curves and parametric surfaces, such as Bézier curves, spline curves and surfaces. An important non-parametric approach is the level-set method. Application areas include shipbuilding, aircraft, and automotive industries, as well as architectural design. The modern ubiquity and power of computers means that even perfume bottles and shampoo dispensers are designed using techniques unheard of by shipbuilders of 1960s.
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It was released in 1993. Version 2 was redesigned with a new source code base. It introduced ground breaking features - booleans, CSG primitives, b-spline curves, physically based animation simulation, morph based animation techniques and phenomenal rendered output. It took full advantage of the multi tasking abilities of the Amiga - allowing the user to continue editing a scene on another window while it rendered.
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A Hurst shifter came with a large metal "T" handle. The rear end was an AMC 3.54:1 "Twin-Grip" limited slip differential using Dana internals, with outer wheel hubs attached through a spline and keyway system. Factory cast iron manifolds exited to a true dual exhaust with Thrush (a Tenneco brand) two-chamber oval mufflers with Woodpecker logos. These were baffled mufflers, not glasspacks.
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A plastic welding rod, also known as a thermoplastic welding rod, is a rod with circular or triangular cross-section used to bind two pieces of plastic together. They are available in a wide range of colors to match the base material's color. Spooled plastic welding rod is known as "spline". An important aspect of plastic welding rod design and manufacture is the porosity of the material.
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Xu graduated from Smith College in 1996, with a bachelor's degree in computer science. She credits going to a women's college with the nurturing environment that allowed her to become interested in computer science. She completed her Ph.D. in 2002 in computer and information science at the University of Pennsylvania. Her dissertation, Incremental Algorithms for the Design of Triangular-Based Spline Surfaces, was supervised by Jean Gallier.
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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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A heavily upgraded version of the Hellcat was introduced as the Hellcat Redeye for 2021. Like the Challenger Redeye, it is equipped with a supercharged 6.2L V8 rated at and of torque, an increase of and over the standard Hellcat motor. Other upgrades include reinforced ZF 8 speed automatic transmission, track-tuned suspension, Torque Reserve and 41-Spline Heavy-Duty Half-Shafts, SRT Power Chiller and After-Run Chiller.
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According to the Universities Admissions Centre which administers ATAR-based tertiary entry for NSW and the ACT. Starting in 2017, all jurisdictions except Queensland use a one-parameter cubic spline model to convert their aggregate scores into percentiles. Since 2020, Queensland uses the same system. In most states, when a student achieves an ATAR between 0.00 and 30.00, their notification will only indicate an ATAR of "30 or less".
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Data is collected by a computer and recorded as data points within three- dimensional space, with processing this can be converted into a triangulated mesh and then a computer-aided design model, often as non-uniform rational B-spline surfaces. Hand-held laser scanners can combine this data with passive, visible-light sensors — which capture surface textures and colors — to build (or "reverse engineer") a full 3D model.
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For examples which go near key points see nonuniform rational B-spline, or Bézier curve. This is extended to the forming of three- dimensional curves, shapes and complex, dynamic artistic patterns such as used in laser light shows. The process can be extended to motions. The path of an object can be interpolated by providing some key locations, then calculating many in between locations for a smooth motion.
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Do-it- yourself screen and frame replacement kits are widely available at hardware and home improvement stores. One kind is composed of straight aluminum sides (which can be cut to size) and plastic corner inserts. Screen replacement kits usually consist of a roll of nylon screening fabric and a generous supply of rubber spline. In addition to insect screening, denser screen types that also reduce sunlight and heat gain are available.
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An FCurve (also written f-curve) is a function curve or the graph of a function. An example of a FCurve is a spline. In the field of computer animation and especially in animation editors, e.g. Maya, an FCurve is an animation curve with a set of keyframes, which are represented as points, curve segments between keys, and tangents that control how curve segments enter and exit a key.
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The term lofting originally came from the shipbuilding industry where loftsmen worked on "barn loft" type structures to create the keel and bulkhead forms out of wood. This was then passed on to the aircraft then automotive industries who also required streamline shapes. The term spline also has nautical origins coming from East Anglian dialect word for a thin long strip of wood (probably from old English and Germanic word splint).
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The Mark 11 nose was a pointed ogive shape. The MK-11 also known as the MK-91 had variable yields by changing the target rings. A major difference over the MK-8 was that the MK-91 had an electric operated actuator as a safety device that would rotate a spline ring to prevent the projectile from being fired into the target rings. The MK-8 had no safety devices.
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Hexagon is a subdivision-type 3D modeler owned by DAZ 3D. It was originally developed and published by Eovia and was acquired shortly before the release of version 2.0 by DAZ 3D in 2006. The software drew heavily on Eovia's other modeler, Amapi (it shared the same developers), though it omitted the NURBs and precision measuring tools. The focus is subdivision modeling, but it includes spline tools and surface tools.
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There are two input files. They are the coordinates and the details of the contents and appearance of the picture. #Picture generation – Geometric transformation of coordinates are generated by the program into picture elements. For example, a cylinder of appropriate size and orientation about the z-axis represents α-helix; each peptide plane is determined for Ribbon Diagrams and β-sheets; and spline fit is used for curved sheets.
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The partially linear model enables and simplifies the linear transformation of data (Engle, Granger, Rice and Weiss, 1986). They also applied the smoothing spline technique for their research. There was a case of application of partially linear model in biometrics by Zeger and Diggle in 1994. The research objective of their paper is the evolution period cycle of CD4 cell amounts in HIV (Human immune-deficiency virus) seroconverters (Zeger and Diggle, 1994).
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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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Wang studied economics at Tongji University, graduating in 2000, and earned a master's degree in mathematics from Tongji University in 2003. She completed a Ph.D. in statistics at Michigan State University in 2007. Her dissertation, Polynomial Spline Smoothing for Nonlinear Time Series, was supervised by Li-Jian Yang. She became a faculty member in the University of Georgia department of statistics in 2007, and moved to Iowa State University as an associate professor in 2014.
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Huichon Machine Tool Factory Huichon Machine Tool Factory in Huichon is North Korea's leading manufacturer of heavy-duty machine tools for domestic use and for export. The 50-year-old factory group is involved in machine tool production processes including steel-making, casting, processing, assembly, painting and packing. Product is produced on serial basis and small lot basis. Its output of precision machine tools includes an assortment of spline-grinding machines and industrial lathes.
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A number of "special shanks" have been developed by various manufacturers. Over the years a fair number of these proprietary systems evolved, but the remaining shanks in use today are: SDS+, SDS-MAX, and SPLINE SHANK. These shanks were developed in order to allow for the bit to "slide" back and forth while rotating, so that the drill bit can efficiently transfer the force of the electro-pneumatic hammering mechanism to the working surface.
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More complex methods that interpolate independently within each color plane include bicubic interpolation, spline interpolation, and Lanczos resampling. Although these methods can obtain good results in homogenous image regions, they are prone to severe demosaicing artifacts in regions with edges and details when used with pure-color CFAs. However, linear interpolation can obtain very good results when combined with a spatio-spectral (panchromatic) CFA. One could exploit simple formation models of images for demosaicing.
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The computed interpolation process is then used to insert many new values in between these key points to give a "smoother" result. In its simplest form, this is the drawing of two- dimensional curves. The key points, placed by the artist, are used by the computer algorithm to form a smooth curve either through, or near these points. For a typical example of 2-D interpolation through key points see cardinal spline.
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D65 is a tabulated SPD in increments of 5 nm from 300 nm to 830 nm, using linear interpolation on the original data binned at 10 nm.Relative SPD of D65 , 300–830nm in 1nm increments. Derived by linear interpolation of the 5nm table. The CIE recommends using linear interpolation of the component SPDs, S0, S1, and S2 if the application requires greater precision, but there is a proposal to use spline interpolation instead.
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Calculations are dependent on the type of object. At the conclusion of object calculation, the resulting material product(s) are connected to the out-point(s) of the object. Curve Interpolation: Particle Size Distributions (PSD) in NIAflow are generated using either linear or 3D+ (cubic spline) interpolation methods and can be viewed on Linear, Log, Log-Log and RRSB grids.[2] Interpolation methods and grids are stored together with the object properties.
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TPS has been widely used as the non-rigid transformation model in image alignment and shape matching. An additional application is the analysis and comparisons of archaeological findings in 3D and was implemented for triangular meshes in the GigaMesh Software Framework. The thin plate spline has a number of properties which have contributed to its popularity: #It produces smooth surfaces, which are infinitely differentiable. #There are no free parameters that need manual tuning.
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Thus, the change in slope between each successive point is small, reducing the apparent "jaggedness" of the approximation. ;Drawing with Bézier paths: Composite Bézier curves may also be used to draw an ellipse to sufficient accuracy, since any ellipse may be construed as an affine transformation of a circle. The spline methods used to draw a circle may be used to draw an ellipse, since the constituent Bézier curves behave appropriately under such transformations.
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Despite its seeming organicism, blob architecture is unthinkable without this and other similar computer-aided design programs. Architects derive the forms by manipulating the algorithms of the computer modeling platform. Some other computer aided design functions involved in developing this are the nonuniform rational B-spline or NURB, freeform surfaces, and the digitizing of sculpted forms by means akin to computed tomography.John K. Waters, Blobitecture: Waveform Architecture and Digital Design(Rockport, 2003).
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A spline Before computers, designs were drawn by hand on paper with various drafting tools. Rulers were used for straight lines, compasses for circles, and protractors for angles. But many shapes, such as the freeform curve of a ship's bow, could not be drawn with these tools. Although such curves could be drawn freehand at the drafting board, shipbuilders often needed a life-size version which could not be done by hand.
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The B-spline basis functions used in the construction of NURBS curves are usually denoted as N_{i,n}(u), in which i corresponds to the ith control point, and n corresponds with the degree of the basis function. The parameter dependence is frequently left out, so we can write N_{i,n}. The definition of these basis functions is recursive in n. The degree-0 functions N_{i,0} are piecewise constant functions.
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The boundaries of facial features and the attributes of facial textures are resulted from the information taken away from the facial color image. A volumetric facial model is produced by these two sources when integrated. The two methods of feature localization may be utilized by the concept of deformable template， and the technique of chromatic edge detection.Automatic identification of human faces by 3-D shape of surfaces – using vertices of B spline surface Syst.
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Key screenshot of Holodance V0.8, in the environment "Virtual Clubbing", with gameplay (anime girl catching orbs). This mechanic is introduced in Level 4 of the story mode of Holodance. It is used for sustained instruments. The way this mechanic works is similar to catching orbs in the initial phase until a note starts: The floating spline flies towards the player from a distance and arrives near the player when the note starts.
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Krivobokova earned a diploma in applied mathematics from Al-Farabi Kazakh National University in 1996, a master's degree in applied mathematics from the University of Kaiserslautern in 2002, and a doctorate (Dr. rer. pol.) in statistics from Bielefeld University in 2007. Her dissertation, Theoretical and Practical Aspects of Penalized Spline Smoothing, was jointly supervised by Göran Kauermann and . After postdoctoral research at KU Leuven in Belgium, she joined the Bielefeld University faculty in 2008.
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This is a different approach to data collection than using landmarks and semilandmarks. In this approach, deformation grids are used to capture the morphological shape differences and changes. The general idea is that shape variations can be recorded from one specimen to another based on the distortion of a grid. Bookstein proposed the use of a thin-plate spline (TPS) interpolation, which is a computed deformation grid that calculates a mapping function between two individuals that measures point differences.
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A surface may be composed of one or more patches, where each patch has its own U-V coordinate system. These surface patches are analogous to the multiple polynomial arcs used to build a spline. They allow more complex surfaces to be represented by a series of relatively simple equation sets rather than a single set of complex equations. Thus, the complexity of operations such as surface intersections can be reduced to a series of patch intersections.
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The equivalent of a ruler for drawing or reproducing a smooth curve, where it takes the form of a rigid template, is known as a French curve. A flexible device that can be bent to the desired shape is known as a flat spline, or (in its more modern incarnation) a flexible curve. Historically, a flexible lead rule used by masons that could be bent to the curves of a molding was known as a lesbian rule.
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Algorithms such as the Kochanek–Bartels spline provide additional adjustment parameters which allow customizing the in-between behavior to suit a wide variety of situations. Another important area of this subject is the computational burden of these algorithms. Algorithms with faster execution times are sought to produce more of these results in less time in order to complete these projects quicker. As the resolution increases to produce animated feature films, the amount of processing can increase greatly.
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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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At that point the workstation would immediately render the model, and any future changes made to the model would instantly be reflected in all applicable workstation views. PHIGS originally lacked the capability to render illuminated scenes, and was superseded by PHIGS+. PHIGS+ works in essentially the same manner, but added methods for lighting and filling surfaces within a 3D scene. PHIGS+ also introduced more advanced graphics primitives, such as Non-uniform rational B-spline (NURBS) surfaces.
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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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Perhaps the most common use of composite Béziers is to describe the outline of each letter in a PostScript or PDF file. Such outlines are composed of one beziergon for open letters, or multiple beziergons for closed letters. Modern vector graphics and computer font systems like PostScript, Asymptote, Metafont, OpenType, and SVG use composite Bézier curves composed of cubic Bézier curves (3rd order curves) for drawing curved shapes. Sinc function approximated using a smooth Bézier spline, i.e.
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The limit subdivision surface is the surface produced from this process being iteratively applied infinitely many times. In practical use however, this algorithm is only applied a limited, and usually fairly small, number of times. Mathematically, the neighborhood of an extraordinary point (non-4-valent node for quad refined meshes) of a subdivision surface is a spline with a parametrically singular point J. Peters and U. Reif: Subdivision Surfaces, Springer series Geometry and Computing monograph 3, 2008, doi .
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The barycentric subdivision is chiefly used to replace an arbitrarily complicated convex polytope or topological cell complex by an assemblage of pieces, all of them of bounded complexity (simplices, in fact). A typical application is modeling the shape of a car body by a spline -- a piecewise-defined polynomial function. The algebra of such functions becomes much simpler and easier to program if each "piece" is a "topological triangle", i.e. is attached to exactly three other pieces.
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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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In the past, Poole joins Berg on the Friend vessel shortly before the Qax emerges, having travelled aboard his ship, Hermit Crab, from the Oort Cloud. He is accompanied by a Virtual of his father, Harry. Together they elude the control of the Friends, whose project fails under the bombardment of the Spline's starbreaker beam. Miriam Berg commandeers the singularity cannon used to sculpt Jupiter and fires a pair of black holes into the Spline, which merge and disable it.
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Yokai (Professor Robert Callaghan) is a supervillain who was once a kind and respectable Professor and dean at SFIT. Coming from a military background, Professor Robert Callaghan is a pioneer in developing many cutting edge tech inventions including the Callaghan-Catmull Spline. He had a daughter that he loved dearly named Abigail who grew up to become a test pilot for Krei Tech. When a teleportation accident left her test pod lost in an abyss, Callaghan angrily blamed Krei and swore revenge.
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Solid Modeling Solutions is a company who has an implementation of a mathematical representation of NURBS (Non-uniform rational B-spline), 3D geometry, and Solid modeling technology which emerged in the 1980s and 1990s into a commercial implementation known as SMLib (for solid modeling library).Potts Steves, Michelle and Frechette, Simon. "Viewing Technologies for CAD Models", NIST, February 2003. This article will provide the background and history of this implementation into a commercial product line from Solid Modeling Solutions™ (SMS).
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This makes bounding spheres appropriate for objects that can move in any number of dimensions. A ' is the volume that projects to an extent on an axis, and can be thought of as the slab bounded between two planes. A bounding box is the intersection of orthogonally oriented bounding slabs. Bounding slabs have been used to speed up ray tracing POV-Ray Documentation A ' in 2-D is quite useful to speedup the clipping or visibility test of a B-Spline curve.
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There are three categories of parametrization: elastic, global and local transformation. The elastic transformations respect the partition of unity, there are no holes created or surfaces counted several times. This is commonly used in Image Registration by the use of B-Spline functionsJ. Réthoré, T. Elguedj, P. Simon, and M. Correct, "On the use of nurbs functions for displacement derivatives measurement by digital image correlation," Experimental mechanics, vol. 50, iss. 7, pp. 1099–1116, 2010. and in solid mechanics with finite element basis.
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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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The authors noted that HHT is capable of differentiating between time-variant components from any given data. Their study also showed that HHT was able to distinguish between riding and carrier waves. Huang and Wu [2008] reviewed applications of the Hilbert–Huang transformation emphasizing that the HHT theoretical basis is purely empirical, and noting that "one of the main drawbacks of EMD is mode mixing". They also outline outstanding open problems with HHT, which include: End effects of the EMD, Spline problems, Best IMF selection and uniqueness.
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Dupuis grew up in Memramcook, New Brunswick, and graduated from the Université de Moncton in 1989 with a bachelor's degree in mathematics and a minor in computer science. With the support of an NSERC graduate fellowship, she earned a master's degree in mathematics and statistics from Queen's University. She completed her Ph.D. in 1994 from the University of New Brunswick. Her dissertation, Knots in Spline Regression: Estimation and Inference Using Laplace Transform Techniques, was supervised by Roman Mureika, and won the Governor General's Gold Medal.
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The Face-splitting product and the Block Face-splitting product used in the tensor-matrix theory of digital antenna arrays. These operations used also in Artificial Intelligence and Machine learning systems to minimization of convolution and tensor sketch operations, in a popular Natural Language Processing models, and hypergraph models of similarityBryan Bischof. Higher order co-occurrence tensors for hypergraphs via face-splitting. Published 15 February, 2020, Mathematics, Computer Science, ArXiv, Generalized linear array model in statistics and two- and multidimensional P-spline approximation of data.
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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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On 8 September 1997 Flight 451, a Eurocopter AS 332L1 Super Puma, from the Norwegian helicopter operator Helikopter Service, crashed into the Norwegian Sea, northwest of Brønnøysund, Norway. The aircraft was en route from Brønnøysund Airport, Brønnøy to Norne, an offshore Floating production storage and offloading vessel (FPSO). The accident was caused by a fatigue crack in a spline of a power transmission shaft connector, which ultimately caused the power transmission shaft to fail. All twelve people on board were killed in the crash.
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The name thin plate spline refers to a physical analogy involving the bending of a thin sheet of metal. Just as the metal has rigidity, the TPS fit resists bending also, implying a penalty involving the smoothness of the fitted surface. In the physical setting, the deflection is in the z direction, orthogonal to the plane. In order to apply this idea to the problem of coordinate transformation, one interprets the lifting of the plate as a displacement of the x or y coordinates within the plane.
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For example, pieces of shot may be placed between the wood pieces to produce indentations when the pieces are clamped together; after the clamp is released, the indentations indicate the center points for drilling. Dowel centers are simple and inexpensive tools for aligning opposing blind holes. Various commercial systems, such as Dowelmax, have been devised to solve this problem. Alternative joinery methods may be used in place of conventional dowel pins, such as Miller dowels, biscuit joiners, spline joints, and proprietary tools such as the Domino jointer.
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Some new single-speed — especially BMX and utility bikes — and lower-end multi-geared bicycles continue to be manufactured and sold with freewheels. Pedaling forces tighten a freewheel onto the hub, so no tool is required to install one. The ratcheting mechanism prevents the freewheel being loosened when the sprockets are turned counter-clockwise. A freewheel can be removed from the hub with one of the many specific freewheel removal tools that engages a spline or set of notches on the outboard end of the freewheel.
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Loop Subdivision of an icosahedron (top) after one and after two refinement steps In computer graphics, Loop subdivision surface is an approximating subdivision scheme developed by Charles Loop in 1987 for triangular meshes. Loop subdivision surfaces are defined recursively, dividing each triangle into four smaller ones. The method is based on a quartic box spline, which generate C2 continuous limit surfaces everywhere except at extraordinary vertices where they are C1 continuous. Geologists have also applied Loop Subdivision Surfaces to erosion on mountain faces, specifically in the Appalachians.
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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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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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Rectangular window The rectangular window (sometimes known as the boxcar or Dirichlet window) is the simplest window, equivalent to replacing all but N values of a data sequence by zeros, making it appear as though the waveform suddenly turns on and off: :w[n] = 1. Other windows are designed to moderate these sudden changes, which reduces scalloping loss and improves dynamic range, as described above (). The rectangular window is the 1st order B-spline window as well as the 0th power Power-of-sine window.
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The game uses an advanced version of Cobra Engine, which is an in-house proprietary engine developed by Frontier previously used by games like Elite Dangerous and RollerCoaster Tycoon 3. Features confirmed for the game include a hybrid spline/piece-by-piece coaster builder, modular structure building, a voxel terrain editor among others detailed through Q&A;'s and "Dev Diaries." On the second live stream, the release date of the alpha was announced. Released on 22 March 2016, the alpha emphasized on modular building and paths.
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Other orthogonal expansions, like Fourier expansions and B-spline expansions may also be employed for the dimension reduction step. The Akaike information criterion (AIC) can be used for selecting the number of included components. Minimization of cross-validation prediction errors is another criterion often used in classification applications. Once the dimension of the predictor process has been reduced, the simplified linear predictor allows to use GLM and quasi-likelihood estimation techniques to obtain estimates of the finite dimensional regression coefficients which in turn provide an estimate of the parameter function \beta in the GFLM.
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Sonique fused a highly stylized aesthetic with a fluid, windowless interface and fully animated menu systems. Additional functionality included a basic playlist editor, a variety of unique output visualization modes via plug-ins, and a robust control set featuring pitch, balance and amplification adjustment, as well as a 20-band equalizer with spline-based level adjustment. It supported many audio formats, including MP3, MP2, Ogg Vorbis, WAV, MOD, XM, IT, S3M, Audio CD and Windows Media Audio. Further audio and visual formats were playable through various plugins, for example AVI video files.
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In kinematics, the motion of a rigid body is defined as a continuous set of displacements. One-parameter motions can be defined as a continuous displacement of moving object with respect to a fixed frame in Euclidean three-space (E3), where the displacement depends on one parameter, mostly identified as time. Rational motions are defined by rational functions (ratio of two polynomial functions) of time. They produce rational trajectories, and therefore they integrate well with the existing NURBS (Non-Uniform Rational B-Spline) based industry standard CAD/CAM systems.
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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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As a consequence of this necessity, they intend to turn Jupiter into a carefully formed singularity and use the precisely specified parameters as a method of encoding information. Miriam Berg is more concerned over the immediate fate of humanity, with the threat of the future Qax, and transmits a 'help' message to the gate designer Michael Poole. The Qax, naturally, panic a little at the escape to the past. A complex, unavoidably fragile species in their huge living Spline spacecraft, the few Qax present are somewhat at a loss.
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New Modeler Features include: "A 'Layout View' viewport shows the current camera view from Layout. In addition, LightWave 2018 Modeler provides new fully interactive tools including Lattice, Smoothing, Array and Spline Bridge to speed up your modeling." In January 2019, LightWave 2019 introduced new integration tools with Unreal Engine, animatable mesh sculpting and painting in Layout, new UV mapping and UDIM tools (as well as support for smoothing groups) in Modeler, improved FBX interchange, shading model customization tools, new shape primitives, OpenVDB creation, shading/rendering enhancements, and workflow/UI improvements.
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Mediator complex architecture with focus on the disordered "spline" of Med 14 The yeast mediator complex is approximately as massive as a small subunit of a eukaryotic ribosome. The yeast mediator is composed of 25 subunits, while the mammalian mediator complexes are slightly larger. Mediator can be divided onto 4 main parts: The head, middle, tail, and the transiently associated CDK8 kinase module. Mediator subunits have many intrinsically disordered regions called "splies", which may be important to allow the structural changes of mediator that change the function of the complex.
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New concepts such as camera and character control presented many drawbacks and required the team to try out a number of approaches before settling on solutions that seemed to work. The team finally settled on the concept that MediEvil would support both analogue and digital camera-related controls for balance reasons. Sorrell stated that a spline camera view was the first attempt, but he disliked it due to the lack of freedom for the player to feel as if he was exploring. It was then changed to a free-form camera view, which "just worked".
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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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Face hallucination enhances facial features improved image resolution using different methods. The simplest way to increase image resolution is a direct interpolation increasing the pixel intensities of input images with such algorithms as nearest-neighbour, bilinear and variants of cubic spline interpolation. Another approach to interpolation is to learn how to interpolate from a set of high resolution training samples, together with the corresponding low resolution versions of them. (pg 4 baker and kanade) However, the results are very poor since no new information is added in the process.
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In vector-based graphics editing, each leaf node in a scene graph represents some atomic unit of the document, usually a shape such as an ellipse or Bezier path. Although shapes themselves (particularly paths) can be decomposed further into nodes such as spline nodes, it is practical to think of the scene graph as composed of shapes rather than going to a lower level of representation. Another useful and user-driven node concept is the layer. A layer acts like a transparent sheet upon which any number of shapes and shape groups can be placed.
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Trilinear interpolation is the extension of linear interpolation, which operates in spaces with dimension D = 1, and bilinear interpolation, which operates with dimension D = 2, to dimension D = 3. These interpolation schemes all use polynomials of order 1, giving an accuracy of order 2, and it requires 2^D = 8 adjacent pre-defined values surrounding the interpolation point. There are several ways to arrive at trilinear interpolation, which is equivalent to 3-dimensional tensor B-spline interpolation of order 1, and the trilinear interpolation operator is also a tensor product of 3 linear interpolation operators.
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Buffa was awarded in 2007 the Bartolozzi Prize and in 2015 the Collatz Prize "for her spectacular use of deep and sophisticated mathematical concepts to obtain outstanding contributions to the development of computer simulations in science and industry" (Laudatio).ICIAM Collatz Prize 2015, news from IMATI In 2014 she was an Invited Speaker at the International Congress of Mathematicians in Seoul with talk Spline differential forms. In 2008 she received an ERC Starting Grant and in 2016 an ERC Advanced Grant. She became a member of the Academia Europaea in 2016.
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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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To do this, he used Photoshop, but later in development he used Cambridge Animation Systems' ANIMO, a spline-based animation software. It took as many as 14,000 frames to draw the worms, and it was estimated that continuing to use Photoshop for the sprites would have required three to four years. In comparison, it took merely months to master ANIMO, and after that the worms were tested five or six times before they were determined to be complete. Holmes was responsible for the game's themes, including their landscapes and background.
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SFNT is a font file format which can contain other fonts, such as PostScript, TrueType, OpenType, Web Open Font Format (WOFF) fonts and other. SFNT stands for spline font or scalable font, and was originally developed for TrueType fonts on the Macintosh and used by Apple Computer's QuickDraw. SFNT was named after the resource tag the Macintosh used internally to track font data. Many existing font formats are based on the table-based SFNT format, such as TrueType, OpenType and Open Font Format, Web Open Font Format (WOFF), SIL Graphite and many other.
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The Mach 1 started with a V8-powered SportsRoof body and added numerous visual and performance enhancing items such as matte black hood treatment with hood pins, hood scoop (including optional Shaker scoop), competition suspension, chrome pop-open gas cap, revised wheels with Goodyear Polyglas tires, chrome exhaust tips (except 351W 2V), deluxe interior, livery and dealer optional chin spoiler, rear deck spoiler, and rear window louvers (SportSlats). Standard equipment was a 351 cu in (5.8 L) Windsor (351W) 2V motor with a 3 speed manual transmission, and a 28 spline open rear axle. A 351W 4V was optional as was a 390 cu in (6.4 L) FE, and the huge 428 cu in (7.0 L) Cobra Jet 4V with or without Ram Air, and even the introduction of the "drag pack" option with the modified 428 cu in (7.0 L) Super Cobra Jet engine. A 4-speed manual or 3-speed FMX (small block)/C6 (big block) automatic transmission was optional, and the 428SCJ added a cast iron tailshaft in place of the regular aluminum one to the C6. A "traction lok" rear axle was optional, and the 428 CJ/SCJ included a "traction lok" with a 3.91 or 4.30 ratio, 31 spline axle shafts and a nodular case.
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A heavy duty rotary hammer drill The rotary hammer (also known as a rotary hammer drill, roto hammer drill or masonry drill) combines a primary dedicated hammer mechanism with a separate rotation mechanism, and is used for more substantial material such as masonry or concrete. Generally, standard chucks and drills are inadequate and chucks such as SDS and carbide drills that have been designed to withstand the percussive forces are used. A rotary hammer uses SDS or Spline Shank bits. These heavy bits are adept at pulverising the masonry and drill into this hard material with relative ease.
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For such systems, the solution can be obtained in O(n) operations instead of O(n^3) required by Gaussian elimination. A first sweep eliminates the a_i's, and then an (abbreviated) backward substitution produces the solution. Examples of such matrices commonly arise from the discretization of 1D Poisson equation and natural cubic spline interpolation. Thomas' algorithm is not stable in general, but is so in several special cases, such as when the matrix is diagonally dominant (either by rows or columns) or symmetric positive definite; for a more precise characterization of stability of Thomas' algorithm, see Higham Theorem 9.12.
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The kriging interpolation, shown in red, runs along the means of the normally distributed confidence intervals shown in gray. The dashed curve shows a spline that is smooth, but departs significantly from the expected intermediate values given by those means. The theoretical basis for the method was developed by the French mathematician Georges Matheron in 1960, based on the Master's thesis of Danie G. Krige, the pioneering plotter of distance-weighted average gold grades at the Witwatersrand reef complex in South Africa. Krige sought to estimate the most likely distribution of gold based on samples from a few boreholes.
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Direct development on Gill ceased around the year 2000, but a fork of its codebase has evolved to Sodipodi, and through it to Inkscape. In 2009, Levien completed a PhD thesis entitled 'From Spiral to Spline: Optimal Techniques in Interactive Curve Design' and published a standalone essay on the mathematical history of Elastica. He calls the Elastica "A beautiful family of curves based on beautiful mathematics and a rich and fascinating history." Beginning in 2010, his work with Google largely focused on introducing high-quality, open licensed, well organized webfonts to the internet through Google's webfont API.
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Jos Stam, 2005 Jos Stam (born 28 December 1965 in The Hague, Netherlands) is a researcher in the field of computer graphics, focusing on the simulation of natural physical phenomena for 3D-computer animation. He achieved technical breakthroughs with the simulation of fluids and gases,Stochastic Dynamics: Simulating the Effects of Turbulence on Flexible Structures, in Computer Graphics Forum (Eurographics'97 Proceedings), Volume 16, Number 3, 1997, p. 159-164 new rendering algorithms and subdivision surfaces,On Subdivision Schemes Generalizing Uniform B-spline Surfaces of Arbitrary Degree, in Computer Aided Geometric Design. Special Edition on Subdivision Surfaces, Volume 18, 2001, p.
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Future purchasers of an FTO should be aware of this. A simple check of the VIN Plate details, or the period of manufacture to be found on the seat-belt tags, should resolve any uncertainty as to the origin of the model-build. Apart from body styling, there are other less apparent differences in the facelift models, including an uprated ECU and also distinct variations to the drive shaft units across the range such as 25 or 27-spline shafts and CV cup variants, as well as fitment for ABS or non-ABS shafts and bearings for same.
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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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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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The evolution of digital color grading tools has advanced to the point where the colorist can use geometric shapes (such as mattes or masks in photo software such as Adobe Photoshop) to isolate color adjustments to specific areas of an image. These tools can highlight a wall in the background and color only that wall, leaving the rest of the frame alone, or color everything but that wall. Subsequent color correctors (typically software-based) have the ability to use spline-based shapes for even greater control over isolating color adjustments. Color keying is also used for isolating areas to adjust.
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On the other hand, software-based systems tend to have more features such as spline-based windows/masks and advanced motion tracking. The line between hardware and software no longer exists as many software-based color correctors (e.g. Pablo , Mistika, SCRATCH, Autodesk Lustre, Nucoda Film Master and FilmLight's Baselight) use multi processor workstations and a GPU (graphics processing unit) as a means of hardware acceleration. As well, some newer software-based systems use a cluster of multiple parallel GPUs on the one computer system to improve performance at the very high resolutions required for feature film grading. e.g.
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In 1975, Computervision introduced an improved database that allowed additional entities and data types to be introduced easily. Other improvements, including a B-spline package and improved refresh performance led to adoption by many large customers, including Boeing, which purchased dozens of systems for the 757/767 aircraft program. Improved 3-D design was added in the early 1980s with the CADDS4 product on the CGP200. This version of CADDS moved display technology from storage tube base displays to raster graphics and introduced the dedicated graphics co-processor board known as the Graphics Processing Unit (GPU).
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Ikarus is a type design and production software developed by URW foundry, for converting existing typefaces and logos into digital format for use on computer driven printing, plotting and sign cutting devices. It was licensed by major foundries such as Agfa-Compugraphic, Autologic, Berthold, ITC International Typeface Corporation, Letraset, Linotype, Monotype, Stempel, and others. Its "IK" format was convertible into diverse vendor representations, including Type3 and Type1 PostScript formats as well as the TrueType format by Apple and Microsoft. Ikarus uses a spline model of the outline shape of each character within a typeface to give a fully scalable representation.
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Catmull–Clark subdivision of a cube with subdivision surface below. (Note that the Catmull-Clark bi-cubic interpolation above cannot approach an actual sphere, as a sphere would be quadric.) The Catmull–Clark algorithm is a technique used in 3D computer graphics to create smooth surfaces by using a type of subdivision surface modeling. It was devised by Edwin Catmull and Jim Clark in 1978 as a generalization of bi-cubic uniform B-spline surfaces to arbitrary topology. In 2005, Edwin Catmull received an Academy Award for Technical Achievement, together with Tony DeRose and Jos Stam (for their invention and application of subdivision surfaces).
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Active contour model, also called snakes, is a framework in computer vision introduced by Michael Kass, Andrew Witkin, and Demetri Terzopoulos for delineating an object outline from a possibly noisy 2D image. The snakes model is popular in computer vision, and snakes are widely used in applications like object tracking, shape recognition, segmentation, edge detection and stereo matching. A snake is an energy minimizing, deformable spline influenced by constraint and image forces that pull it towards object contours and internal forces that resist deformation. Snakes may be understood as a special case of the general technique of matching a deformable model to an image by means of energy minimization.
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Rotating a curve In 3D computer graphics, a lathed object is a 3D model whose vertex geometry is produced by rotating the points of a spline or other point set around a fixed axis. The lathing may be partial; the amount of rotation is not necessarily a full 360 degrees. The point set providing the initial source data can be thought of as a cross section through the object along a plane containing its axis of radial symmetry. The lathe is so named because it produces the same type of object that a real lathe would produce: an object that is symmetrical about an axis of rotation.
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The DCT gearbox retains characteristics of a conventional manual transmission like engine braking and clutch engagement as the internal components are very similar except the clutch operation is controlled by an electric motor and computer rather than the rider. Both models feature a slipper clutch to reduce wheel spin during hard engine braking and a shaft-drive system to transmit power to the rear wheel. The shaft-drive system is bolted to the frame on a swinging pivot mount. Engineers developed a two-part shaft connected by a spline that allows the system to flex under load mimicking the feel and performance benefits of a traditional chain drive.
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The class covered Bezier curves, Bezier to B-spline and surfaces. The first public presentation of our NURBS work was at a Seattle CASA/SME seminar in March of 1982. The staff had progressed quite far by then. They could take a rather simple NURBS surface definition of an aircraft and slice it with a plane surface to generate an interesting outline of some of the wing, body and engines. The staff were allowed great freedom in pursuing our ideas and Boeing correctly promoted NURBS, but the task of developing that technology into a useable form was too much for Boeing, which abandoned the TIGER task late in ’84.
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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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When approximating a mathematical function or a surface by a spline, the accuracy of the approximation is usually determined by the piece size -- the bigger the pieces, the larger the error. Thus it is often necessary to split large pieces into smaller ones, in order to achieve a prescribed accuracy. In theory, BCS could be used for that purpose, since it has the property that the longest edge of any piece is smaller than the longest edge of the original polytope by a factor less than n/(n + 1). Therefore, by applying BCS sufficiently many times, the largest edge can be made as small as desired.
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Several manufacturers have built bottom brackets with titanium spindles and alloy cups but their durability was lower than that of steel. Early Campagnolo Super Record titanium spindles (which were hollow) were replaced by a later version that used solid, nutted spindles for improved reliability. In recent years Shimano has migrated much of their product line away from square taper to a spline attachment called Octalink and to external bearing types. In late 2006, Campagnolo announced that it was abandoning the square taper interface for double chainsets in favor of an outboard bearing design called Ultra-Torque, which uses a splined interface between spindle halves.
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Non-climate factors include soil, tree age, fire, tree-to-tree competition, genetic differences, logging or other human disturbance, herbivore impact (particularly sheep grazing), pest outbreaks, disease, and CO2 concentration. For factors which vary randomly over space (tree to tree or stand to stand), the best solution is to collect sufficient data (more samples) to compensate for confounding noise. Tree age is corrected for with various statistical methods: either fitting spline curves to the overall tree record or using similar aged trees for comparison over different periods (regional curve standardization). Careful examination and site selection helps to limit some confounding effects, for example picking sites undisturbed by modern man.
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Then there is the nature of transitions between points: are they abrupt or gradual. Finally, there is whether a method is global (it uses the entire data set to form the model), or local where an algorithm is repeated for a small section of terrain. Interpolation is a justified measurement because of a spatial autocorrelation principle that recognizes that data collected at any position will have a great similarity to, or influence of those locations within its immediate vicinity. Digital elevation models, triangulated irregular networks, edge-finding algorithms, Thiessen polygons, Fourier analysis, (weighted) moving averages, inverse distance weighting, kriging, spline, and trend surface analysis are all mathematical methods to produce interpolative data.
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Harmonic Drive SE strain wave gear set consisting of wave generator bearing (top left), flexspline cup (top right) and circular spline ring (bottom). Strain wave gearing also known as harmonic gearing is a type of mechanical gear system that can improve certain characteristics compared to traditional gearing systems such as helical gears or planetary gears. Harmonic Drive is the brand name of strain wave gear trademarked by the Harmonic Drive company. It was invented in 1957 by C.W. Musser while he was a research advisor at United Shoe Machinery (USM) and is commonly implemented in robotics, and used in aerospace as well, for gear reduction but may also be used to increase rotational speed, or for differential gearing.
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In computing, D3DX (Direct3D Extension) is a deprecated high level API library which is written to supplement Microsoft's Direct3D graphics API. The D3DX library was introduced in Direct3D 7, and subsequently was improved in Direct3D 9. It provides classes for common calculations on vectors, matrices and colors, calculating look-at and projection matrices, spline interpolations, and several more complicated tasks, such as compiling or assembling shaders used for 3D graphic programming, compressed skeletal animation storage and matrix stacks. There are several functions that provide complex operations over 3D meshes like tangent-space computation, mesh simplification, precomputed radiance transfer, optimizing for vertex cache friendliness and strip reordering, and generators for 3D text meshes.
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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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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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Meanwhile, aided by Jasoft Parz's internal sabotage, Poole succeeds in ramming the Hermit Crab into the second Spline, killing the sapience of the vessel and the entangled Qax, second Governor of Earth, with it. Harry takes over in lieu of the higher intelligence and, at the direction of Poole, steers it back into the wormhole: when inside, Poole intends to activate the hyperdrive, shattering the fragile dimensional warping of the wormhole, and of all wormholes connecting to it, thus saving humanity from further interference by the future. Poole's audacious plan succeeds, but with an unexpected side effect. As the hyperdrive activates, it somewhat shatters space-time, forming a long series of interconnected wormholes that hurl Poole 5 million years forward into the far future.
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The broaching machine elevator, which is the part of the machine that moves the broach above the workholder, then lowers the broach through the workpiece. Once through, the broaching machine's puller, essentially a hook, grabs the pilot of the broach. The elevator then releases the top of the follower and the puller pulls the broach through the workpiece completely. The workpiece is then removed from the machine and the broach is raised back up to reengage with the elevator.. The broach usually only moves linearly, but sometimes it is also rotated to create a spiral spline or gun-barrel rifling.. Cutting fluids are used for three reasons: # to cool the workpiece and broach # to lubricate cutting surfaces # to flush the chips from the teeth.
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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 photograph was actually of much lower resolution: The entire Betelgeuse image fit entirely within a 10x10 pixel area on the Hubble Space Telescope's Faint Object Camera. The actual images were oversampled by a factor of 5 with bicubic spline interpolation, then deconvolved (see Plate L2).). In another false-color image obtained by infrared interferometry two large, bright star spots spanning ~10 milliarcseconds are visible on the surface of Betelgeuse, possibly representing enormous convective cells rising from below the supergiant's surface. Because of these, Betelgeuse appears to change shape periodically, with a complex, asymmetric envelope that is the product of a colossal ongoing loss of mass, as huge plumes of gas are continuously expelled from its surface (see "Tony and the Beetles" by Philip K. Dick, below).
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Standard sizes of square drives around the world include , , , , 1, , and -inch square drive sizes (a de facto international standard with no metric equivalents) along with some lesser used drivers such as -inch square drive, and both No. 4 and No. 5 spline drives specified in ANSI B107 specifications. This wide range of square drive sizes provides for a wide variety of socket types and sizes to suit small to very large nuts and bolts. Some square drivers have a through hole to attach the socket to the driver (using a retaining ring with O-ring and pin type, or single piece molded retaining rings), a locking pin, or friction ball. Some common hand ratchets employ a quick release button on their top for quick socket release of smaller sockets.
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If the forecast from the three versions is similar, then the forecaster can conclude that there is minimal uncertainty, but if the versions vary by a great deal, then the forecaster has less confidence in the track predicted due to the greater uncertainty. Large differences between model predictions can also indicate wind shear in the atmosphere, which could affect the intensity forecast as well. Tested in 1989 and 1990, The Vic Ooyama Barotropic (VICBAR) model used a cubic-B spline representation of variables for the objective analysis of observations and solutions to the shallow-water prediction equations on nested domains, with the boundary conditions defined as the global forecast model. It was implemented operationally as the Limited Area Sine Transform Barotropic (LBAR) model in 1992, using the GFS for boundary conditions.
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Dr. Ruptash suggested to Paul that a computer be used to execute the technical drawings of the Pysanka. He made some phone calls and recommended to Paul an old friend of his, Dr. Ron Resch and his team of mathematicians at the University of Utah. Though the surface area of an egg can be difficult to solve mathematically, the enigma of how to assemble two-dimensional tiles onto a three-dimensional egg was eventually solved by Ronald Resch, a computer science professor from the University of Utah, and his team that included Robert McDermott, who wrote an algorithm to cast a periodic B-spline curve that was used to define and manufacture the egg. It was the first physical structure designed entirely with computer-aided geometric modeling software.
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SRTM void filling with spline interpolation in GRASS GIS. The elevation datasets are affected by mountain and desert no-data areas. These amount to no more than 0.2% of the total area surveyed,Reuter H.I, A. Nelson, A. Jarvis, 2007, An evaluation of void filling interpolation methods for SRTM data, International Journal of Geographical Information Science, 21:9, 983–1008 – 'the ‘finished’ grade version of the data (also referred to as Version 2) still contains data voids (some 836,000 km^2)'; 836,000 is 0.164% of the Earth's 5.1×10^8 km^2 surface but can be a problem in areas of very high relief. They affect all summits over 8,000 meters, most summits over 7,000 meters, many Alpine and similar summits and ridges, and many gorges and canyons.
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The angles of movement are "left and right" and "into the depth" (while still capable of doing so technically, this game did not allow making a U-turn or going into reverse, therefore moving "out of the depth", as this did not make sense to the high- speed game play and tense time limit). Notice the view is comparable to that which a driver would have in reality when driving a car. The position and size of any billboard is generated by a (complete 3D) perspective transformation as are the vertices of the poly-line representing the center of the street. Often the center of the street is stored as a spline and sampled in a way that on straight streets every sampling point corresponds to one scan-line on the screen.
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Male bit drivers are sometimes incorrectly referred to as "sockets", but are in fact the opposite of a socket - a socket is a female recess or opening which receives another object. Common male bit drivers of this type include Allen hex wrenches (in both metric and fractional inch sizes), Torx (T-3 through T-50) spline wrenches, 4-point (square), and 12-point (triple square) male bit drivers. Other specialized screw heads that are often installed or removed with screwdriver type handles and appropriate type tip have socket varieties that fit the various screw head types and a can be attached to a socket wrench. Conversely, for low torque situations, a "socket spinner" screwdriver handle with a socket wrench type fitting on one end can be attached to many different types of sockets, bit drivers and extensions.
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For the 1972 model year, AMC began to purchase a variation of the Chrysler-developed TorqueFlite transmission and named it TorqueCommand. All TorqueCommand automatics used 23-spline output shafts. Later on, as AMC revised their mainstay engines to have lighter casting technology, these transmissions were available in both the Chevrolet small V6 engine pattern (used on the AMC 150 I4) and the AMC late model pattern that was used on their I6 and V8 engines. Other than the bell housing pattern (main transmission case) and the torque converter, the AMC version is the same as other Chrysler transmissions—all parts interchange (torque converters do not interchange - unlike the Chrysler torque converters which have a pressed on ring gear for the starter teeth AMC uses a traditional 164 tooth flexplate similar in design to those used by Ford.
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Advanced Graphics Programming Techniques Using OpenGL. Siggraph 1999. (see: Multitexture) Procedural textures (created from adjusting parameters of an underlying algorithm that produces an output texture), and bitmap textures (created in an image editing application or imported from a digital camera) are, generally speaking, common methods of implementing texture definition on 3D models in computer graphics software, while intended placement of textures onto a model's surface often requires a technique known as UV mapping (arbitrary, manual layout of texture coordinates) for polygon surfaces, while non-uniform rational B-spline (NURB) surfaces have their own intrinsic parameterization used as texture coordinates. Texture mapping as a discipline also encompasses techniques for creating normal maps and bump maps that correspond to a texture to simulate height and specular maps to help simulate shine and light reflections, as well as environment mapping to simulate mirror-like reflectivity, also called gloss.
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In the best possible case, one has data streams of measurements of all the system variables, equally spaced in time, say :s1(t), s2(t), ... , sk(t) for : t = t1, t2,..., tn, beginning at several different initial conditions. Then the task of finding a vector field, and thus a differential equation model consists of fitting functions, for instance, a cubic spline, to the data to obtain a set of continuous time functions :x1(t), x2(t), ... , xk(t), computing time derivatives dx1/dt, dx2/dt,...,dxk/dt of the functions, then making a least squares fit using some sort of orthogonal basis functions (orthogonal polynomials, radial basis functions, etc.) to each component of the tangent vectors to find a global vector field. A differential equation then can be read off the global vector field. There are various methods of creating the basis functions for the least squares fit.
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The up-shift and down- shift process is the same, with the hub toggling between gears; there is a consequent risk of overshooting the desired gear. The S2 has no equivalent to the sliding clutch seen in 3- and 4-speed Sturmey-Archer hub designs, there is indeed no lateral movement within the hub in use. To achieve this radically different mode of shifting gears, the hub featured a unique driver with a 4 spline keyed socket in the middle (similar to, though not interchangeable with, later 'No Intermediate Gear' AW drivers), into which sat a selector sleeve. The 4 cuttings on the selector sleeve (2 shallow and 2 deep, arranged alternately) enabled the selector sleeve to transmit drive from the driver to the backs of the two unique high gear pawls, with said pawls either allowed to engage the hub shell for direct drive (deep selector sleeve cutting) or tripped out such that drive is transmitted only to the gear ring (shallow selector sleeve cutting).
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Another early line of research by Grinbergs at the Computer Center concerned the automated design of ship hulls, and the computations with spline curves and surfaces needed in this design. The goal of this research was to calculate patterns for cutting and then bending flat steel plates so that they could be welded together to form ship hulls without the need for additional machining after the bending step; the methods developed by Grinbergs were later used throughout the Soviet Union. In graph theory, Grinbergs is best known for Grinberg's theorem, a necessary condition for a planar graph to have a Hamiltonian cycle that has been frequently used to find non-Hamiltonian planar graphs with other special properties.. His researches in graph theory also concerned graph coloring, graph isomorphism, cycles in directed graphs, and a counterexample to a conjecture of András Ádám on the number of cycles in tournaments. Other topics in Grinbergs' research include Steiner triple systems, magnetohydrodynamics, operations research, and the mathematical modeling of hydrocarbon exploration.
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They decide to build their own Interface, with major human-collaborator assistance (headed by Ambassador Jasoft Parz), to create a link to their future to gain aid in resolving the problem – with more modern GUT-engine spacecraft they can make a 500-year link in just eighteen months. A startling high-technology future vessel (in truth, one of the legendary Xeelee nightfighters, an advanced and long-range fast scout ship), with a future Qax comes through the gate. Its first act is to execute the Qax Governor of Earth and gather up Parz, before passing through the original portal after the Friends and all humanity. The future Qax takes two Spline ships (presumably leaving behind the nightfighter; this might be the nightfighter that is discovered by the crew of The Great Northern millennia later in Ring) through the gate and on the journey reveals to Parz the reason behind its desire to completely destroy the human race.
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The close-fitting bumper was actually a rear bumper that had been cut, narrowed, V'ed in the center, and filled on the ends to create a crude air dam, further improving the aerodynamics of the car at high speeds. Semon E "Bunkie" Knudsen's custom built Talladega In another well kept secret design move, the rocker panels of the Talladega were reshaped and rolled to allow Ford teams to run their racing cars about an inch closer to the ground while staying within NASCAR rules; this also greatly enhanced the top speed of the car by lowering its center of gravity, and further reducing its wind resistance. The cars were also equipped with an engine oil cooler, a power steering oil cooler, staggered shocks, a 3.25:1 Ford 9 inch 31 spline nodular open rear end, and most surprisingly: a heavy duty C-6 (cast iron tailshaft) automatic transmission that was column shifted. These other special performance parts were normally only available when ordering a "drag pack car" which would have been equipped with a 4 speed and a limited slip rear end.
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Drive shaft with universal joints at each end and a spline in the centre Škoda 422 rear axle, suspension and drive shaft on display at the Škoda Museum A drive shaft, driveshaft, driving shaft, tailshaft (Australian English), propeller shaft (prop shaft), or Cardan shaft (after Girolamo Cardano) is a mechanical component for transmitting torque and rotation, usually used to connect other components of a drive train that cannot be connected directly because of distance or the need to allow for relative movement between them. As torque carriers, drive shafts are subject to torsion and shear stress, equivalent to the difference between the input torque and the load. They must therefore be strong enough to bear the stress, while avoiding too much additional weight as that would in turn increase their inertia. To allow for variations in the alignment and distance between the driving and driven components, drive shafts frequently incorporate one or more universal joints, jaw couplings, or rag joints, and sometimes a splined joint or prismatic joint.
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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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