On the fast approximation of point clouds using Chebyshev polynomials

Abstract Suppose a large and dense point cloud of an object with complex geometry is available that can be approximated by smooth univariate function. In general, for such clouds the “best” approximation using method least squares usually hard or sometimes even impossible to compute. most cases, however, “near-best” just as good “best”, but much easier faster calculate. Therefore, fast approach Chebyshev polynomials described, which based on interpolation in points second kind. This allows calculate unknown coefficients polynomial means Fast Fourier transform (FFT), extremely efficient, especially high-order polynomials. Thus, focus presented not sparse functions few parameters, rather whose perhaps millions have determined.