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docs/bilinear_interpolation.md

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+## Coding Bilinear Interpolation ##
+
+Source: [The Supercomputing Blog](http://supercomputingblog.com/graphics/coding-bilinear-interpolation/)
+
+When performing image transformation and manipulation techniques, it is often
+necessary to employ some sort of interpolation or filtering in order to obtain
+a good image quality. For example, if you scale an image, you can determine
+the final color of each pixel by either some basic nearest neighbor method, or
+a more advanced interpolation method. However, an interpolation method will
+invariably offer better final image quality. In this tutorial, we’ll be
+writing a function to rotate an image, using bilinear interpolation. This
+tutorial also demonstrates how to perform a high quality image rotate
+transformation, however, that is not the focus of this tutorial, but rather
+the example transform being performed.
+
+
+### Why interpolation is used after image transforms ###
+
+Image transforms like scaling, rotating, twisting or otherwise warping,
+effectively move pixels around in the image. The result is that the pixels in
+the final image do not directly map to a single original pixel in the original
+image. Suppose after rotation, a pixel should have the same color as pixel
+(3.4, 5.6) in the original image. The only problem is that there is no such
+thing as fractional pixels! Instead of simply choosing the color of the
+nearest available pixel, (3,6), we can get better results by intelligently
+averaging the colors of the four closest pixels. In this case, the values of
+pixels (3,5) (3,6) (4,5) and (4,6) would be intelligently averaged together to
+estimate the color of an imaginary pixel at (3.4, 5.6). This is called
+interpolation, and it is used after image transforms to provide a smooth,
+accurate and visually appealing images.
+
+
+### Understanding bilinear interpolation ###
+
+We can best understand bilinear interpolation by looking at the graphic here.
+The green P dot represents the point where we want to estimate the color. The
+four red Q dots represent the nearest pixels from the original image. The
+color of these four Q pixels is known. In this example, P lies closest to Q12,
+so it is only appropriate that the color of Q12 contributes more to the final
+color of P than the 3 other Q pixels.
+
+
+### Calculating bilinear interpolation ###
+
+There are several ways equivalent ways to calculate the value of P. An easy
+way to calculate the value of P would be to first calculate the value of the
+two blue dots, R2, and R1. R2 is effectively a weighted average of Q12 and
+Q22, while R1 is a weighted average of Q11 and Q21.
+
+``` R1 = ((x2 – x)/(x2 – x1))*Q11 + ((x – x1)/(x2 – x1))*Q21 R2 = ((x2 –
+x)/(x2 – x1))*Q12 + ((x – x1)/(x2 – x1))*Q22 ```
+
+After the two R values are calculated, the value of P can finally be
+calculated by a weighted average of R1 and R2.
+
+``` P = ((y2 – y)/(y2 – y1))*R1 + ((y – y1)/(y2 – y1))*R2 ```
+
+The calculation will have to be repeated for the red, green, blue, and
+optionally the alpha component of.