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  "body": "\n## Summary\n\nA cubic Hermite spline is a piecewise cubic function that matches prescribed values and prescribed first derivatives at given nodes.\nOn each interval between nodes it is the cubic [[Hermite interpolant|9Z50M2WPTP]] of the data at the two ends.\nIt is continuously differentiable, and each piece depends only on local data, which makes it the basis of many curve tools in graphics and animation.\n\n## Explanations\n\n### L1 human\n\nOn each gap between two nodes, prescribe a height and a slope at both ends.\nExactly one cubic matches these four numbers.\nA cubic Hermite spline joins these cubics end to end.\nSince neighbouring pieces share the value and the slope at each node, the curve has no corners.\nFor example, data $p_0 = 0$, $m_0 = 0$ at $x = 0$ and $p_1 = 1$, $m_1 = 0$ at $x = 1$ give the smooth step $3x^2 - 2x^3$.\n",
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