![]() ![]() Their heights above the ground correspond to their values. Because this operation is cheap, it's also a good way to implement accurate lookup tables with quick lookup for smooth functions without having too many table entries.Ĭomparison of linear and bilinear interpolation some 1- and 2-dimensional interpolations.īlack and red/ yellow/ green/ blue dots correspond to the interpolated point and neighbouring samples, respectively. They are often used as building blocks for more complex operations: for example, a bilinear interpolation can be accomplished in three lerps. Lerp operations are built into the hardware of all modern computer graphics processors. " Bresenham's algorithm lerps incrementally between the two endpoints of the line." The term can be used as a verb or noun for the operation. In that field's jargon it is sometimes called a lerp (from linear int erpolation). The basic operation of linear interpolation between two values is commonly used in computer graphics. 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), dated from 200 BC to AD 100 and the Almagest (2nd century AD) by Ptolemy. ![]() It is believed that it was used in the Seleucid Empire (last three centuries BC) and by the Greek astronomer and mathematician Hipparchus (second century BC). Linear interpolation is an easy way to do this. Suppose that one has a table listing the population of some country in 1970, 1980, 19, and that one wanted to estimate the population in 1994. Linear interpolation has been used since antiquity for filling the gaps in tables. This is intuitively correct as well: the "curvier" the function is, the worse the approximations made with simple linear interpolation become. That is, the approximation between two points on a given function gets worse with the second derivative of the function that is approximated. ![]()
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