{
  "aliases": null,
  "backlinks": [
    {
      "field": "specializes",
      "target": "62AFX32JGT"
    },
    {
      "field": "specializes",
      "target": "HCQWPAHYAT"
    },
    {
      "field": "specializes",
      "target": "V42H0R3EKX"
    },
    {
      "field": "uses",
      "target": "8R4CVVV8WT"
    },
    {
      "field": "uses",
      "target": "B7YND5ZVMF"
    },
    {
      "field": "uses",
      "target": "DHC96EYCN6"
    },
    {
      "field": "uses",
      "target": "E1V8CPXK24"
    },
    {
      "field": "uses",
      "target": "RGT7WEZG8X"
    },
    {
      "field": "uses",
      "target": "Z45HQ5VNF4"
    },
    {
      "field": "about",
      "target": "DHC96EYCN6"
    },
    {
      "field": "defines",
      "target": "KTVJR95GSF"
    }
  ],
  "body": "\n## Summary\n\nA spline is a function made of polynomial pieces on consecutive intervals.\nThe pieces are joined at points called knots, so that the whole function is as smooth as the pieces allow.\nA spline of degree $n$ is usually required to have $n - 1$ continuous derivatives.\nSplines combine the flexibility of piecewise functions with the simplicity of polynomials, and they avoid the oscillations of high-degree polynomial interpolation.\nThey are central in [[spline interpolation|D59HBKKRP9]], in approximation theory and in computer-aided design, where [[B-splines|62AFX32JGT]] give a convenient basis.\n\n## Explanations\n\n### L1 human\n\nThe name comes from the thin flexible strips of wood that draftsmen bent through fixed pegs to draw smooth curves.\nA mathematical spline does the same with polynomial pieces: each piece is simple, and the pieces meet without corners or jumps in bending.\nThe simplest example is a broken line, a spline of degree $1$: straight pieces joined continuously.\nCubic splines use pieces of degree $3$ joined so that position, slope and curvature all match.\nThe [[definition|KTVJR95GSF]] makes the conditions precise.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "41A15",
      "65D07"
    ],
    "name": "Spline",
    "same_as": {
      "wikidata": "Q735256",
      "wikipedia": "Spline (mathematics)"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Spline_(mathematics)"
      }
    ],
    "tag": "84TJ8KQ926"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/84TJ8KQ926/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/84TJ8KQ926.md",
  "msc": [
    "41A15",
    "65D07"
  ],
  "name": "Spline",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/84T/84TJ8KQ926.md",
  "status": null,
  "tag": "84TJ8KQ926",
  "uri": "m2://84TJ8KQ926",
  "url": "https://tamnd.github.io/math2/wiki/spline/",
  "writing": {
    "tag": "84TJ8KQ926",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}