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  "body": "\n## Summary\n\nDe Boor's algorithm evaluates a spline written in the [[B-spline|62AFX32JGT]] basis at a point.\nIt replaces the coefficients of the B-splines that are active at the point by repeated [[convex combinations|21SXYJYC59]], until a single value remains.\nIt needs no explicit B-spline values, is numerically stable, and generalizes [[de Casteljau's algorithm|HT4Q9K3P2Z]] for Bézier curves.\n\n## Explanations\n\n### L1 human\n\nA spline curve is controlled by a list of control points, but only a few of them affect a given parameter value.\nDe Boor's algorithm takes those few points and repeatedly replaces each pair of neighbours by a point on the segment between them.\nAfter as many rounds as the degree, one point is left, and that point lies on the curve.\nFor a quadratic spline, three control points are blended into two, and the two into one.\n",
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