|
In mathematics, linear interpolation is a method of curve fitting using linear polynomials. ==Linear interpolation between two known points== If the two known points are given by the coordinates and , the linear interpolant is the straight line between these points. For a value ''x'' in the interval , the value ''y'' along the straight line is given from the equation : which can be derived geometrically from the figure on the right. It is a special case of polynomial interpolation with ''n'' = 1. Solving this equation for ''y'', which is the unknown value at ''x'', gives : which is the formula for linear interpolation in the interval . Outside this interval, the formula is identical to linear extrapolation. This formula can also be understood as a weighted average. The weights are inversely related to the distance from the end points to the unknown point; the closer point has more influence than the farther point. Thus, the weights are and , which are normalized distances between the unknown point and each of the end points. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「linear interpolation」の詳細全文を読む スポンサード リンク
|