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  "body": "\n## Summary\n\nBicubic interpolation builds a smooth surface over a rectangular grid from values and derivatives at the grid points.\nOn each cell it uses a polynomial $\\sum_{i,j=0}^{3} a_{ij} x^i y^j$, fixed by the values, the two first partial derivatives and the mixed derivative at the four corners.\nThe patches join with continuous first derivatives, giving smoother results than [[bilinear interpolation|5QJYCNRYMQ]], which is why it is common in image resampling.\n\n## Explanations\n\n### L1 human\n\nBilinear interpolation produces visible creases along grid lines because its slopes jump there.\nBicubic interpolation also matches slopes at the grid points, so neighboring patches meet smoothly.\nEach patch is a cubic in each direction, with sixteen coefficients determined by sixteen pieces of corner data.\nWhen the derivatives are unknown, as in image processing, they are estimated from neighboring values by finite differences.\n",
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