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First, consider bi-linear interpolation. In order to determine the color at a position lying between four grid samples. Each grid sample at a position has an influence of

on .

Given: Light Field
Let be the coordinates of the four pixels around on the camera plane and the coordinates of the four pixels around on the object plane.

For each , we compute an interpolated color value from the four neighboring samples on the object plane based on the position .
Then, we compute a interpolated color value from the , based on the position .
Since we do a linear interpolation twice, this is called quad-linear interpolation.

GPU Implementation
Obtaining coordinates for every pixel
Draw two quads: One for the object plane, one for the camera plane. As a texture, use a smooth color gradient from lower left to upper right. The rasterized colors are the coordinates for every pixel.

Bi-Linear Interpolation on the Object Plane
We get this for free through texture interpolation: For each camera plane pixel, render one quad. As texture coordinates for the quad, use the respective coordinates at that position.

Quad-Linear Interpolation
Instead of rendering one quad per camera plane pixel, render four quads surrounding the pixel with alpha blending and fade out the contribution towards the outer edges.