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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. 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 ...
A spline is a ridge or tooth [1] [2] [3] 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.
The next most simple spline has degree 1. 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. A cubic spline has degree 3 with continuity C 2, i.e. the values and first and second derivatives are continuous. Natural ...
For example, if there are 202 teeth on the circular spline and 200 on the flex spline, the reduction ratio is (200 − 202)/200 = −0.01 Thus the flex spline spins at 1/100 the speed of the wave generator plug and in the opposite direction. Different reduction ratios are set by changing the number of teeth.
is used to calculate the tangents. The parameter c is a tension parameter that must be in the interval [0, 1]. In some sense, this can be interpreted as the "length" of the tangent. Choosing c = 1 yields all zero tangents, and choosing c = 0 yields a Catmull–Rom spline in the uniform parameterization case.
Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing. "A spline is a function defined by polynomials in a piecewise manner." [1] [2] They were introduced to geometric design by Duchon. [3] They are an important special case of a polyharmonic spline. Robust Point Matching (RPM) is a common extension and ...
To determine the weights, a dense linear system of equations must be solved. Solving a dense linear system becomes impractical if the dimension N {\displaystyle N} is large, since the memory required is O ( N 2 ) {\displaystyle O(N^{2})} and the number of operations required is O ( N 3 ) . {\displaystyle O(N^{3}).}
A B-spline function is a combination of flexible bands that is controlled by a number of points that are called control points, creating smooth curves. These functions are used to create and manage complex shapes and surfaces using a number of points. B-spline function and Bézier functions are applied extensively in shape optimization methods. [5]