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A description of linear interpolation can be found in the ancient Chinese mathematical text called The Nine Chapters on the Mathematical Art (九章算術), [1] dated from 200 BC to AD 100 and the Almagest (2nd century AD) by Ptolemy. The basic operation of linear interpolation between two values is commonly used in computer graphics.
One good solution is linear interpolation, which draws a line between the two points in the table on either side of the value and locates the answer on that line. This is still quick to compute, and much more accurate for smooth functions such as the sine function. Here is an example using linear interpolation:
The simplest interpolation method is to locate the nearest data value, and assign the same value. In simple problems, this method is unlikely to be used, as linear interpolation (see below) is almost as easy, but in higher-dimensional multivariate interpolation, this could be a favourable choice for its speed and simplicity.
The key points, placed by the artist, are used by the computer algorithm to form a smooth curve either through, or near these points. For a typical example of 2-D interpolation through key points see cardinal spline. For examples which go near key points see nonuniform rational B-spline, or Bézier curve. This is extended to the forming of ...
set terminal svg fname "Vera" fsize 25 set output "Interpolation_example_linear.svg" set key off set xzeroaxis set xtics axis 1,1 set ytics nomirror 1 set border 2 set samples 2 plot "-" with lines linetype 3 linewidth 4, \ "-" with points linetype 1 pointtype 7 pointsize 0.7, \ 0 with lines linetype -1 linewidth 1 0 0 1 0.8415 2 0.9093 3 0.1411 4 -0.7568 5 -0.9589 6 -0.2794 e 0 0 1 0.8415 2 0 ...
Fitting of a noisy curve by an asymmetrical peak model, with an iterative process (Gauss–Newton algorithm with variable damping factor α).Curve fitting [1] [2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints.