Editing Linear interpolation (section)

==History and applications==
Linear interpolation has been used since antiquity for filling the gaps in tables. Suppose that one has a table listing the population of some country in 1970, 1980, 1990 and 2000, and that one wanted to estimate the population in 1994. Linear interpolation is an easy way to do this. 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). A description of linear interpolation can be found in the ancient [[Chinese mathematics|Chinese mathematical]] text called ''[[The Nine Chapters on the Mathematical Art]]'' ({{lang|zh|九章算術}}),<ref name="Needham1959">{{cite book|author=Joseph Needham|title=Science and Civilisation in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth|url=https://books.google.com/books?id=jfQ9E0u4pLAC&pg=PA147|date=1 January 1959|  publisher=Cambridge University Press| isbn=978-0-521-05801-8| pages=147–}}</ref> 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]]. In that field's jargon it is sometimes called a '''lerp''' (from '''l'''inear int'''erp'''olation). The term can be used as a [[verb]] or [[noun]] for the operation. e.g. "[[Bresenham's algorithm]] lerps incrementally between the two endpoints of the line."

Lerp operations are built into the hardware of all modern computer graphics processors. They are often used as building blocks for more complex operations: for example, a [[bilinear interpolation]] can be accomplished in three lerps. Because this operation is cheap, it's also a good way to implement accurate [[lookup table]]s with quick lookup for [[smooth function]]s without having too many table entries.