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Interpolation is a term used to describe the process of finding values ( interpolation process is to find a mean value from a population of a known set of points in a) that lie between a set of known points. Consider the equation of the line passing through points a and B (imagine a straight line connecting point a to point B): 
wHERE P iS ON the any point the Line Vector the iS and from a to B (where AB at any point between the time represented by P):
We can therefore write this equation as (so we can write the equation :) 
It IS Easy to that See When T 0 IS, IS P equal to A; and. 1 When T IS, IS P equal to A + B - A , which is simply B. Such a line is shown in Figure 4.13 ( when the time t is 0, p is equivalent to the point a, the time when the value of t is 1, p is equivalent to point B, shown in Figure 4.13 )
If t lies between 0.0 and 1.0, then P will end up somewhere between A and B (if the value of t between 0 and 1, then p falls somewhere between A and B). Values of t outside this range will push P off the ends of the line. You should be able to see that by smoothly varying t, we can move point P from a to B and back. this is known as linear interpolation (if the value of t is beyond the scope of , then p is also beyond the scope of AB can be seen that, when so slowly vary from 0 to 1 t time, p will move from a to B, called linear interpolation). the values of a and B (and therefore P) can have any number of values (a and B can be any number of dimensions dimensions) For example, they could be scalar values;. two-dimensional values such as points on a graph; three-dimensional values such as coordinates in 3D space, colors, and so on (such as values a and B herein may be a scalar, may be two points may be three points, color, etc.); or even higher-dimension quantities such as matrices, arrays, or even whole images (or even more Dimension of the matrix, or also the entire image array). In many cases, linear interpolation does not make much sense (for example,
Mix vec4 (vec4 A, B vec4, a float T);
of The Mix function Comes in Different dimensionalities Taking Several versions of Vectors The AS or Scalars Inputs A and B and Taking Scalars Vectors for matching or T (function receives the A, B two data, then the variable t, by linear interpolation of the data).
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