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  "body": "\n## Summary\n\nThe Bernstein–Bézier form writes a polynomial in the [[Bernstein basis|0JT92VK307]] adapted to an interval, or to a simplex in several variables.\nIts coefficients, the Bézier coefficients, behave like control points.\nThe polynomial lies between their minimum and maximum, and it agrees with the end coefficients at the endpoints.\nThis form is numerically stable and is the standard way to store and manipulate polynomial pieces of splines and Bézier curves.\n\n## Explanations\n\n### L1 human\n\nThe usual way to write a polynomial uses powers $1, x, x^2, \\dots$.\nThe Bernstein–Bézier form instead uses the blending weights $\\binom{n}{k}(1-u)^{n-k}u^k$, where $u$ measures the position in the interval.\nThen each coefficient has a geometric meaning, a height that the graph is pulled toward.\nFor example, on $[0, 1]$ the polynomial $x$ of degree $2$ has Bézier coefficients $0, 1/2, 1$, equally spaced heights along the line.\n",
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