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Delaunay triangulation; Bitmap resampling is the application of 2D multivariate interpolation in image processing. Three of the methods applied on the same dataset, from 25 values located at the black dots. The colours represent the interpolated values.
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications
Krakiwsky, "A synthesis of recent advances in the method of least squares", Lecture Notes #42, Department of Geodesy and Geomatics Engineering, University of New Brunswick, 1975 Cross, P.A. "Advanced least squares applied to position-fixing" , University of East London , School of Surveying, Working Paper No. 6, ISSN 0260-9142 , January 1994.
The astronomer Tycho Brahe applied the method in Scandinavia, completing a detailed triangulation in 1579 of the island of Hven, where his observatory was based, with reference to key landmarks on both sides of the Øresund, producing an estate plan of the island in 1584. [3]
The method is an exact interpolator, in that the original data values are retained at the reference data points. The method creates a smooth surface free from any discontinuities. The method is entirely local, as it is based on a minimal subset of data locations that excludes locations that, while close, are more distant than another location ...
Not every triangulation method assures invariance, at least not for general types of coordinate transformations. For a homogeneous representation of 3D coordinates, the most general transformation is a projective transformation, represented by a 4 × 4 {\displaystyle 4\times 4} matrix T {\displaystyle \mathbf {T} } .
Inverse Distance Weighting as a sum of all weighting functions for each sample point. Each function has the value of one of the samples at its sample point and zero at every other sample point. Inverse distance weighting ( IDW ) is a type of deterministic method for multivariate interpolation with a known scattered set of points.
This distribution for a = 0, b = 1 and c = 0.5—the mode (i.e., the peak) is exactly in the middle of the interval—corresponds to the distribution of the mean of two standard uniform variables, that is, the distribution of X = (X 1 + X 2) / 2, where X 1, X 2 are two independent random variables with standard uniform distribution in [0, 1]. [1]