How does linear interpolation work

All points on the line other than the original two can be considered interpolated values. The use of interpolation in astronomy dates as far back as BC. Early in its history, interpolation served as a tool to study and predict the positions and movements of celestial bodies. Hipparchus of Rhodes used linear interpolation to construct chord function tables around BC. Over the next 2, years, civilizations across several continents developed many different uses for linear interpolation in astronomy, mathematics and beyond.

Linear interpolation found common usage in computer graphics during the twentieth century. By: Justin Stoltzfus Contributor, Reviewer. By: Satish Balakrishnan. Dictionary Dictionary Term of the Day. Gorilla Glass. Techopedia Terms. Connect with us. Sign up. Term of the Day. Best of Techopedia weekly. The points are simply joined by straight line segments. Know the formula for the linear interpolation process.

A gardener planted a tomato plant and she measured and kept track of its growth every other day. This gardener is a curious person, and she would like to estimate how tall her plant was on the fourth day. The linear pattern means the points created a straight line. We could even estimate by plotting the data on a graph. But what if the plant was not growing with a convenient linear pattern? What if its growth looked more like this? What would the gardener do in order to make an estimation based on the above curve?

Well, that is where the interpolation formula would come in handy. 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 , , and , and that one wanted to estimate the population in Linear interpolation is an easy way to do this. The technique of using linear interpolation for tabulation was believed to be used by Babylonian astronomers and mathematicians in Seleucid Mesopotamia last three centuries BC , and by the Greek astronomer and mathematician, Hipparchus 2nd century BC.

A description of linear interpolation can be found in the Almagest 2nd century AD by Ptolemy. The basic operation of linear interpolation between two values is commonly used in computer graphics. The term can be used as a verb or noun for the operation. 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, bilinear interpolation can be accomplished in three lerps. Let us say that we have two known points x 1 , y 1 x1,y1 and x 2 , y 2 x2,y2.

Now we want to estimate what y y value we would get for some x x value that is between x 1 x1 and x 2 x2. Call this y y value estimate — an interpolated value. Two simple methods for choosing y y come to mind. The first is to see whether x x is closer to x 1 x1 or to x 2 x2.