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Time series analysis and forecasting
Published in Amithirigala Widhanelage Jayawardena, Fluid Mechanics, Hydraulics, Hydrology and Water Resources for Civil Engineers, 2021
Amithirigala Widhanelage Jayawardena
Spline, in the ordinary sense, refers to a flexible strip used in drafting to draw a smooth curve through a set of points. In the mathematical sense too it has the same meaning. Spline methods can be used for interpolation as well as for regression. The basic objective in spline interpolation is to connect a set of data points by a smooth curve via a combination of several piecewise low order curves. The interpolation (or regression) functions can be polynomial, sinusoidal, exponential or their combinations. The cubic spline which consists of N polynomial functions each of which has order not greater than three is by far the most widely used. It is of the form y=ai+bix+cix2+dix3
Time series analysis and forecasting
Published in A. W. Jayawardena, Environmental and Hydrological Systems Modelling, 2013
Spline in the ordinary sense refers to a flexible strip used in drafting to draw a smooth curve through a set of points. Also in the mathematical sense, it has the same meaning. Spline methods can be used for interpolation and regression. The basic objective in spline interpolation is to connect a set of data points by a smooth curve via a combination of several piecewise low-order curves. The interpolation (or regression) functions can be polynomial, sinusoidal, exponential, or their combinations. The cubic spline, which consists of N polynomial functions each of which has order not greater than three, is by far the most widely used. It is of the form () y=ai+bix+cix2+dix3
Strip Adjustment and Registration
Published in Jie Shan, Charles K. Toth, Topographic Laser Ranging and Scanning, 2017
Spline interpolation fits a mathematical function, defined by piecewise polynomials of varying orders, to some neighboring measured points to determine the value at the unknown locations, which may be compared to bending a sheet of rubber through the measured points (Loan and Charles, 1997). The lowest order spline is equivalent to linear interpolation, or bilinear transformation for surfaces. Spline interpolation results in a smooth surface that passes through the sample points and, in general, gives a good representation of smoothly changing terrain (no sudden elevation changes, such as buildings and other man-made objects). This is a very useful method if the goal is to derive good quality contours.
Spatial Distribution and Potential Ecological Risk Assessment of Trace Metals in Reclaimed Mine Soils in Abuakwa South Municipal, Ghana
Published in Soil and Sediment Contamination: An International Journal, 2023
Douglas Siaw Baah, Gordon Foli, Emmanuel Gikunoo, Solomon S. R. Gidigasu
The data obtained contained both the coordinates of the locations and also the concentrations of the various trace metals such as As, Cr, Ni, and Pb. Both data were imported into the ARC GIS software specifically ARC Map. Spline interpolation within the spatial analyst tools was used to generate the various concentrations of each trace metal. Spline interpolation makes use of a mathematical function that minimizes the overall surface curvature resulting in a smooth surface that passes exactly through the input points. Due to the curvature and continuous nature of the soil sample, spline interpolation was best for such depiction, hence its use. Maps of the various concentrations generated were produced as an outcome and presented in Figure 5.
Development of automated feature extraction and convolutional neural network optimization for real-time warping monitoring in 3D printing
Published in International Journal of Computer Integrated Manufacturing, 2022
Jiarui Xie, Aditya Saluja, Amirmohammad Rahimizadeh, Kazem Fayazbakhsh
Spline interpolation is a numerical approximation method that uses a piecewise polynomial named spline. Taking three points A(xi-1, yi-1), B(xi, yi), and C(xi+1, yi+1), where xi-1< xi< xi+1, two polynomial curves, described by functions L1 and L2, were created to connect them smoothly. Point B is the intercept of L1 and L2.
Research on Effects of Groove Shape Optimization on Cavitation and Lubricating Characteristics for Microgroove Rotary Seal
Published in Tribology Transactions, 2018
Bing Xue, Chao Wei, Ji Bin Hu, Yi Min Zhao
Spline interpolation has a higher degree of smoothness and better adaptability to the interpolation points and is widely used in engineering design. In this article, a spline interpolation method is used to fit the groove shape molded line and describe the evolution of the optimization process. By using a three-moment construction method (Burden and Faires (23)), a cubed spline interpolation polynomial can be obtained as follows: where Mi is a second derivative value of Pi; that is, the bending moment value.