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A spline is a type of function used to replicate smooth curves. It has been adopted from numerical analysis, a branch of mathematics, for a variety of applications in geographic information science (GISci), from the graphical representation of curvilinear features to the interpolation of sampled attributes. While there are several types of splines and techniques for creating them, all splines are piecewise polynomial functions. That is, a spline decomposes a curve into short sections, each of which is approximated by a polynomial. These polynomials can be of any order; in fact, the segmented line fundamental to the vector data model can be considered a first-order spline. However, when splines are used explicitly in GISci, cubic (third-order) polynomials are the most common. Also, splines can ...

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