{
  "aliases": null,
  "backlinks": [
    {
      "field": "about",
      "target": "5DFMMGGD9Y"
    },
    {
      "field": "uses",
      "target": "5DFMMGGD9Y"
    },
    {
      "field": "defines",
      "target": "KNP5ZEQ458"
    }
  ],
  "body": "\n## Summary\n\nA [[convex polytope|300K6CB1KH]] can be described in two ways.\nA V-representation lists finitely many points whose [[convex hull|0FQSDC2EQ2]] is the polytope.\nAn H-representation lists finitely many linear inequalities, that is closed half-spaces, whose common solutions form the polytope.\nEvery convex polytope has both, and computations with polytopes, as in linear programming and computational geometry, depend on which one is at hand.\n\n## Explanations\n\n### L1 human\n\nTo describe a box you can give its eight corners, or say that each coordinate lies between two bounds.\nThe list of corners is a V-representation, and the list of bounds is an H-representation.\nSome questions are easy with one description and hard with the other.\nChecking that a point lies in the box is easy with the inequalities; finding the corner farthest in a given direction is easy with the corner list.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "52B11",
      "52B55",
      "90C05"
    ],
    "name": "H-representation and V-representation",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Convex_polytope"
      }
    ],
    "tag": "W8P2G5R02N"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/W8P2G5R02N/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/W8P2G5R02N.md",
  "msc": [
    "52B11",
    "52B55",
    "90C05"
  ],
  "name": "H-representation and V-representation",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/W8P/W8P2G5R02N.md",
  "status": null,
  "tag": "W8P2G5R02N",
  "uri": "m2://W8P2G5R02N",
  "url": "https://tamnd.github.io/math2/wiki/h-representation-and-v-representation/",
  "writing": {
    "tag": "W8P2G5R02N",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}