# bilinear interpolation

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## bilinear interpolation

A texture mapping technique that produces a reasonably realistic image, also known as "bilinear filtering" and "bilinear texture mapping." An algorithm is used to map a screen pixel location to a corresponding point on the texture map. A weighted average of the attributes (color, alpha, etc.) of the four surrounding texels is computed and applied to the screen pixel. This process is repeated for each pixel forming the object being textured.

The term bilinear refers to the performing of interpolations in two dimensions (horizontal and vertical). The top and bottom pairs of each texel quadrant are averaged (horizontal) and then their results are averaged (vertical). This method is often used in conjunction with MIP mapping. See texture map, MIP mapping, point sampling and trilinear interpolation.

Bilinear Mapping Each screen pixel of the object is mapped onto the corresponding texel in the texture map. The red dots are an example of one pixel. The attributes of the weighted average of the four nearest texels is applied to the screen pixel. Two horizontal interpolations are made (texels 1-2 and 3-4), and then the results are averaged together for the vertical interpolation. (Redrawn from illustration courtesy of Intergraph Computer Systems.)
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The triangle filter, also known as the bilinear interpolation filter, gives a smooth, natural gradient pass between pixels when upsampling, in contrast to the box filter (Thyssen, 2017).
Next, the prediction value is produced by the bilinear interpolation method, and the difference between the current embedding pixel and the prediction value is calculated for each block.
Another complicated methodology is named bilinear interpolation [10]
Bilinear Interpolation determines the value of a new pixel based on piecewise linear function and bicubic interpolation determines the new pixel value on the basis of cubic function [3].
In short summary, the linear (more formally, bilinear interpolation in the context of two-dimensional array data) involves a simple point-slope imputation of data at points intermediate to true observation; the cubic spline (more formally, bicubic spline) involves a summed, iterative approximation through fitting a third-order polynomial [12].
Popular methods of interpolation by convolution include nearest neighbor interpolation, bilinear interpolation, cubic B-spline interpolation, and piecewise-cubic convolution (Lehmann et al.
Step 4: Use bilinear interpolation to convert [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] into a 3-D linear phase grating.
In order to determine whether there were large differences in the results when using other interpolation techniques or not, we created DEMs using the nearest-neighbours interpolation and the bilinear interpolation algorithm.
Bilinear interpolation generally is not conformal, so grid shift transform can be considered nearly conformal if the shift vectors are small.
Bilinear interpolation is used for the coordinates, displacements and rotations.
The following re-sampling methods are commonly used and are supported in IMAGINE: nearest neighbor, cubic convolution, and bilinear interpolation.
The stress, the velocity components and the temperature are interpolated inside each element by the bilinear interpolation function while the pressure is piecewise-constantly in each element.

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