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  "body": "\n## Summary\n\nDe Casteljau's algorithm computes a point of a [[Bézier curve|NEXBTGYYRG]] by repeated linear interpolation between control points.\nIt also evaluates polynomials in [[Bernstein–Bézier form|Z5Y0VH10YR]].\nIt uses only [[convex combinations|21SXYJYC59]], so it is numerically stable.\nThe intermediate points also give the control points of the two halves of the curve, which is the basis of subdivision methods in computer-aided design.\n\n## Explanations\n\n### L1 human\n\nDraw the polygon through the control points and mark the point a fraction $t$ of the way along each edge.\nJoin the marked points to get a polygon with one fewer vertex, and repeat.\nAfter as many rounds as the degree, a single point is left, and it is the point of the curve at parameter $t$.\nFor three points and $t = 1/2$, one takes the two edge midpoints and then the midpoint between them.\n",
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