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  "body": "\n## Summary\n\nBilinear interpolation estimates a function of two variables inside a rectangle from its values at the four corners.\nIt uses the unique function of the form $a + bx + cy + dxy$ that matches the four values.\nIt is the two-dimensional analogue of linear interpolation and a basic tool for resampling images and gridded data.\n\n## Explanations\n\n### L1 human\n\nSuppose the temperature is known at the four corners of a rectangular field.\nTo estimate it at a point inside, first interpolate linearly along the bottom edge and along the top edge, and then interpolate linearly between those two results.\nDoing it in the other order, first along the vertical edges, gives the same answer.\nFor example, on the unit square with corner values $0$, $0$, $0$ and $1$ (the last at $(1, 1)$), the estimate at $(x, y)$ is $xy$, so the center gets $1/4$.\n",
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