|
Splines (mathematics)
Spline may refer to: Mathematics * Spline (mathematics), a mathematical function used for interpolation or smoothing * Spline interpolation, a type of interpolation * Smoothing spline, a method of smoothing using a spline function Devices * Spline (mechanical), a mating feature for rotating elements * Flat spline, a device to draw curves * Spline drive, a type of screw drive * Spline cord, a type of thin rubber cord used to secure a window screen to its frame * Spline (or star filler A star filler (also known as cross filler, splines, separators and crossweb fillers) is a type of plastic insert in Cat 5 and Cat 6 cable which separates the individual stranded pair sets from each other while inside of the cable. It increases th ...), a type of plastic cable filler for CAT cable Other * Spline (alien beings), in Stephen Baxter's Xeelee Sequence novels See also * {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spline (mathematics)
In mathematics, a spline is a 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. 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. Introduction 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spline Interpolation
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. That is, instead of fitting a single, high-degree polynomial to all of the values at once, spline interpolation fits low-degree polynomials to small subsets of the values, for example, fitting nine cubic polynomials between each of the pairs of ten points, instead of fitting a single degree-nine polynomial to all of them. 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 also avoids the problem of Runge's phenomenon, in which oscillation can occur between points when interpolating using high-degree polynomials. Introduction Originally, '' spline'' was a term for elastic rulers that were bent to pass through a number of predefined points, or ''knots''. These we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smoothing Spline
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. Cubic spline definition Let \ be a set of observations, modeled by the relation Y_i = f(x_i) + \epsilon_i where the \epsilon_i are independent, zero mean random variables. The cubic smoothing spline estimate \hat f of the function f is defined to be the unique minimizer, in the Sobolev space W^2_2 on a compact interval, of : \sum_^n \^2 + \lambda \int \hat^(x)^2 \,dx. Remarks: * \lambda \ge 0 is a smoothing parameter, controlling the trade-off between fidelity to the data and roughness of the function estimate. This is oft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spline (mechanical)
A spline is a ridge or tooth on a drive shaft that matches with a groove in a mating piece and transfers 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. Adjacent images in the section below show a transmission input shaft with male splines and a clutch plate with mating female splines in the center hub, where the smooth tip of the axle would be supported in a pilot bearing in the flywheel (not pictured). 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. Types There are several types of splines: ;Parallel key spline: where the sides of the equally spaced grooves are parallel in both directions, radial and axial. ;Involute spline: where the sides of the equally spaced grooves are involute, as with an involute gear, but not as tall. The c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flat Spline
A spline 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). 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spline Drive
At a minimum, a screw drive is a set of shaped cavities and protrusions on the screw head that allows torque to be applied to it. Usually, it also involves a mating tool, such as a screwdriver, that is used to turn it. Some of the less-common drives are classified as being "tamper-resistant". Most heads come in a range of sizes, typically distinguished by a number, such as "Phillips #00". Overview Slotted drives Slot Slot screw drives have a single horizontal indentation (the ''slot'') in the fastener head and is driven by a "common blade" or flat-bladed screwdriver. This form was the first type of screw drive to be developed, and, for centuries, it was the simplest and cheapest to make because it can just be sawed or filed. Blunt or damaged tools can easily be re-ground as required in any workshop. It is unique because the slot head is straightforward to manufacture, and because it can be driven by a simple handtool. The ''slotted screw'' is commonly found in existing p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
