Approximation of Smooth Surfaces and Adaptive Sampling by Piecewise-linear Interpolants

Publisher Summary This chapter describes the approximation of smooth surfaces and adaptive sampling by piecewise-linear interpolates. The general problem of approximating a smooth two-dimensional function by a piecewise-linear surface (PLS) arises in a variety of applications where surface samples are either given, or obtainable at will. Examples include the reconstruction of terrain surfaces from random digital terrain models extracted by automatic methods, such as matching stereo image pairs. The methods obtain terrain elevation samples wherever possible, usually at feature points, resulting in a data set consisting of points at essentially random locations in the plane. The reason the approximation is done with a PLS, namely, a collection of triangles, is that it is the simplest method possible. Triangles are standard geometric primitives in modern graphics engine hardware. Terrain visualization by texture-mapped aerial imagery onto surface triangles is a popular graphics application in visual simulation environments. In some applications, the surface sample set is not given, and it is up to the user to decide where to sample the surface.

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