Abstract
The most popular problem in data reconstruction is fitting a curve or a surface. Data fitting has two meanings: interpolation and approximation. Interpolation means fitting the data exactly on the sample values while approximation means a fitted function can be set near the sample values. In this chapter, to introduce data reconstruction, we do a comprehensive review on basic numerical and computational methods for data fitting. We will cover the the following topics: (1) Piece-wise linear interpolation and approximation; (2) Delaunay triangulation; (3) Lagrange curve interpolations and smooth curve approximation; and (4) Coons surfaces and spline surface fitting. In curve and surface fitting, we briefly introduce some of the advanced methods including B-Spline and Bernstein polynomial approximation.
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