{
  "$id": "https://github.com/Geo-AID/Geo-AID/blob/v0.4/figure.schema.json",
  "title": "Geo-AID JSON Figure",
  "description": "Geo-AID's JSON export format",
  "type": "object",
  "properties": {
    "width": {
      "description": "The width of the image",
      "type": "number",
      "exclusiveMinimum": 0
    },
    "height": {
      "description": "The height of the image",
      "type": "number",
      "exclusiveMinimum": 0
    },
    "expressions": {
      "description": "Expressions used by the image",
      "type": "array",
      "items": {
        "type": "object",
        "description": "A single expression",
        "properties": {
          "hint": {
            "description": "The calculated value of this expression",
            "$ref": "#/$defs/value"
          },
          "kind": {
            "description": "The kind of expression this is",
            "oneOf": [
              {
                "type": "object",
                "description": "An entity",
                "properties": {
                  "type": {
                    "const": "entity"
                  },
                  "id": {
                    "description": "The index of the entity",
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "id"
                ]
              },
              {
                "type": "object",
                "description": "Intersection of k and l",
                "properties": {
                  "type": {
                    "const": "line-line-intersection"
                  },
                  "k": {
                    "$ref": "#/$defs/index"
                  },
                  "l": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "k",
                  "l"
                ]
              },
              {
                "type": "object",
                "description": "The arithmetic average of points as complex numbers",
                "properties": {
                  "type": {
                    "const": "average-point"
                  },
                  "items": {
                    "type": "array",
                    "items": {
                      "$ref": "#/$defs/index"
                    },
                    "minItems": 1
                  }
                },
                "required": [
                  "type",
                  "items"
                ]
              },
              {
                "type": "object",
                "description": "Center of a circle",
                "properties": {
                  "type": {
                    "const": "circle-center"
                  },
                  "circle": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "circle"
                ]
              },
              {
                "type": "object",
                "description": "Convert a complex number to a point",
                "properties": {
                  "type": {
                    "const": "complex-to-point"
                  },
                  "number": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "number"
                ]
              },
              {
                "type": "object",
                "description": "Summation of numbers",
                "properties": {
                  "type": {
                    "const": "sum"
                  },
                  "plus": {
                    "type": "array",
                    "items": {
                      "$ref": "#/$defs/index"
                    }
                  },
                  "minus": {
                    "type": "array",
                    "items": {
                      "$ref": "#/$defs/index"
                    }
                  }
                },
                "required": [
                  "type",
                  "plus",
                  "minus"
                ]
              },
              {
                "type": "object",
                "description": "Multiplication of numbers",
                "properties": {
                  "type": {
                    "const": "product"
                  },
                  "times": {
                    "type": "array",
                    "items": {
                      "$ref": "#/$defs/index"
                    }
                  },
                  "by": {
                    "type": "array",
                    "items": {
                      "$ref": "#/$defs/index"
                    }
                  }
                },
                "required": [
                  "type",
                  "times",
                  "by"
                ]
              },
              {
                "type": "object",
                "description": "A constant number value",
                "properties": {
                  "type": {
                    "const": "const"
                  },
                  "value": {
                    "$ref": "#/$defs/complex"
                  }
                },
                "required": [
                  "type",
                  "value"
                ]
              },
              {
                "type": "object",
                "description": "Raising a value to a rational power",
                "properties": {
                  "type": {
                    "const": "power"
                  },
                  "value": {
                    "$ref": "#/$defs/index"
                  },
                  "exponent": {
                    "$ref": "#/$defs/ratio"
                  }
                },
                "required": [
                  "type",
                  "value",
                  "exponent"
                ]
              },
              {
                "type": "object",
                "description": "Distance between `p` and `q`",
                "properties": {
                  "type": {
                    "const": "point-point-distance"
                  },
                  "p": {
                    "$ref": "#/$defs/index"
                  },
                  "q": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "p",
                  "q"
                ]
              },
              {
                "type": "object",
                "description": "Distance between `point` and `line`",
                "properties": {
                  "type": {
                    "const": "point-line-distance"
                  },
                  "point": {
                    "$ref": "#/$defs/index"
                  },
                  "line": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "point",
                  "line"
                ]
              },
              {
                "type": "object",
                "description": "Angle `abc`",
                "properties": {
                  "type": {
                    "const": "three-point-angle"
                  },
                  "a": {
                    "$ref": "#/$defs/index"
                  },
                  "b": {
                    "$ref": "#/$defs/index"
                  },
                  "c": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "a",
                  "b",
                  "c"
                ]
              },
              {
                "type": "object",
                "description": "Directed angle `abc`",
                "properties": {
                  "type": {
                    "const": "three-point-angle-dir"
                  },
                  "a": {
                    "$ref": "#/$defs/index"
                  },
                  "b": {
                    "$ref": "#/$defs/index"
                  },
                  "c": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "a",
                  "b",
                  "c"
                ]
              },
              {
                "type": "object",
                "description": "Angle between `k` and `l`",
                "properties": {
                  "type": {
                    "const": "two-line-angle"
                  },
                  "k": {
                    "$ref": "#/$defs/index"
                  },
                  "l": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "k",
                  "l"
                ]
              },
              {
                "type": "object",
                "description": "X coordinate of a point",
                "properties": {
                  "type": {
                    "const": "point-x"
                  },
                  "point": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "point"
                ]
              },
              {
                "type": "object",
                "description": "Y coordinate of a point",
                "properties": {
                  "type": {
                    "const": "point-y"
                  },
                  "point": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "point"
                ]
              },
              {
                "type": "object",
                "description": "Convert a point to a complex number",
                "properties": {
                  "type": {
                    "const": "point-to-complex"
                  },
                  "point": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "point"
                ]
              },
              {
                "type": "object",
                "description": "The real part of a number",
                "properties": {
                  "type": {
                    "const": "real"
                  },
                  "number": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "number"
                ]
              },
              {
                "type": "object",
                "description": "The imaginary part of a number",
                "properties": {
                  "type": {
                    "const": "imaginary"
                  },
                  "number": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "number"
                ]
              },
              {
                "type": "object",
                "description": "Natural logarithm (base e)",
                "properties": {
                  "type": {
                    "const": "log"
                  },
                  "number": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "number"
                ]
              },
              {
                "type": "object",
                "description": "Exponential function (e^this)",
                "properties": {
                  "type": {
                    "const": "exp"
                  },
                  "number": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "number"
                ]
              },
              {
                "type": "object",
                "description": "Sine of an angle",
                "properties": {
                  "type": {
                    "const": "sin"
                  },
                  "angle": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "angle"
                ]
              },
              {
                "type": "object",
                "description": "Cosine of an angle",
                "properties": {
                  "type": {
                    "const": "cos"
                  },
                  "angle": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "angle"
                ]
              },
              {
                "type": "object",
                "description": "Arcsine function",
                "properties": {
                  "type": {
                    "const": "asin"
                  },
                  "value": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "value"
                ]
              },
              {
                "type": "object",
                "description": "Arccosine function",
                "properties": {
                  "type": {
                    "const": "acos"
                  },
                  "value": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "value"
                ]
              },
              {
                "type": "object",
                "description": "Arctan function",
                "properties": {
                  "type": {
                    "const": "atan"
                  },
                  "value": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "value"
                ]
              },
              {
                "type": "object",
                "description": "Arctan2 function",
                "properties": {
                  "type": {
                    "const": "atan2"
                  },
                  "y": {
                    "$ref": "#/$defs/index"
                  },
                  "x": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "y",
                  "x"
                ]
              },
              {
                "type": "object",
                "description": "Direction vector of a line.",
                "properties": {
                  "type": {
                    "const": "direction-vector"
                  },
                  "line": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "line"
                ]
              },
              {
                "type": "object",
                "description": "Line `pq`",
                "properties": {
                  "type": {
                    "const": "point-point-line"
                  },
                  "p": {
                    "$ref": "#/$defs/index"
                  },
                  "q": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "p",
                  "q"
                ]
              },
              {
                "type": "object",
                "description": "Line from a point and a direction vector",
                "properties": {
                  "type": {
                    "const": "point-vector-line"
                  },
                  "point": {
                    "$ref": "#/$defs/index"
                  },
                  "vector": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "point",
                  "vector"
                ]
              },
              {
                "type": "object",
                "description": "Bisector of angle `abc`",
                "properties": {
                  "type": {
                    "const": "angle-bisector"
                  },
                  "a": {
                    "$ref": "#/$defs/index"
                  },
                  "b": {
                    "$ref": "#/$defs/index"
                  },
                  "c": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "a",
                  "b",
                  "c"
                ]
              },
              {
                "type": "object",
                "description": "Perpendicular line going through point",
                "properties": {
                  "type": {
                    "const": "perpendicular-through"
                  },
                  "point": {
                    "$ref": "#/$defs/index"
                  },
                  "line": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "point",
                  "line"
                ]
              },
              {
                "type": "object",
                "description": "Parallel line going through `point`",
                "properties": {
                  "type": {
                    "const": "parallel-through"
                  },
                  "point": {
                    "$ref": "#/$defs/index"
                  },
                  "line": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "point",
                  "line"
                ]
              },
              {
                "type": "object",
                "description": "A circle with center and radius",
                "properties": {
                  "type": {
                    "const": "construct-circle"
                  },
                  "center": {
                    "$ref": "#/$defs/index"
                  },
                  "radius": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "center",
                  "radius"
                ]
              }
            ]
          }
        },
        "required": [
          "hint",
          "kind"
        ]
      }
    },
    "entities": {
      "description": "Entities in the image",
      "type": "array",
      "items": {
        "type": "object",
        "description": "A single entity",
        "properties": {
          "hint": {
            "description": "The calculated value of this expression",
            "$ref": "#/$defs/value"
          },
          "kind": {
            "description": "The kind of an entity this is",
            "oneOf": [
              {
                "type": "object",
                "description": "A free point",
                "properties": {
                  "type": {
                    "const": "free-point"
                  }
                },
                "required": [
                  "type"
                ]
              },
              {
                "type": "object",
                "description": "Point on a line",
                "properties": {
                  "type": {
                    "const": "point-on-line"
                  },
                  "line": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "line"
                ]
              },
              {
                "type": "object",
                "description": "Point on a circle",
                "properties": {
                  "type": {
                    "const": "point-on-circle"
                  },
                  "circle": {
                    "$ref": "#/$defs/index"
                  }
                },
                "required": [
                  "type",
                  "circle"
                ]
              },
              {
                "type": "object",
                "description": "A free real",
                "properties": {
                  "type": {
                    "const": "free-real"
                  }
                },
                "required": [
                  "type"
                ]
              }
            ]
          }
        },
        "required": [
          "hint",
          "kind"
        ]
      }
    },
    "items": {
      "type": "array",
      "description": "Items drawn on the image",
      "items": {
        "oneOf": [
          {
            "type": "object",
            "description": "A point item",
            "properties": {
              "type": {
                "const": "point"
              },
              "position": {
                "$ref": "#/$defs/position",
                "description": "Where the point should be displayed"
              },
              "label": {
                "$ref": "#/$defs/label"
              },
              "id": {
                "$ref": "#/$defs/index",
                "description": "The defining expression index"
              },
              "display-dot": {
                "type": "boolean",
                "description": "Whether the point circle should be drawn",
                "default": false
              }
            },
            "required": [
              "type",
              "position",
              "id"
            ]
          },
          {
            "type": "object",
            "description": "A line item",
            "properties": {
              "type": {
                "const": "line"
              },
              "points": {
                "type": "array",
                "description": "Delimiting points of the drawn line segment",
                "items": {
                  "$ref": "#/$defs/position"
                },
                "minItems": 2,
                "maxItems": 2
              },
              "label": {
                "$ref": "#/$defs/label"
              },
              "id": {
                "$ref": "#/$defs/index",
                "description": "The defining expression index"
              },
              "style": {
                "$ref": "#/$defs/style",
                "description": "How the line should be drawn",
                "default": "solid"
              }
            },
            "required": [
              "type",
              "points",
              "id"
            ]
          },
          {
            "type": "object",
            "description": "A ray item",
            "properties": {
              "type": {
                "const": "ray"
              },
              "points": {
                "type": "array",
                "description": "Delimiting points of the drawn ray segment",
                "items": {
                  "$ref": "#/$defs/position"
                },
                "minItems": 2,
                "maxItems": 2
              },
              "label": {
                "$ref": "#/$defs/label"
              },
              "p-id": {
                "$ref": "#/$defs/index",
                "description": "The origin expression index"
              },
              "q-id": {
                "$ref": "#/$defs/index",
                "description": "The guiding expression index"
              },
              "style": {
                "$ref": "#/$defs/style",
                "description": "How the ray should be drawn",
                "default": "solid"
              }
            },
            "required": [
              "type",
              "points",
              "p-id",
              "q-id"
            ]
          },
          {
            "type": "object",
            "description": "A segment item",
            "properties": {
              "type": {
                "const": "segment"
              },
              "points": {
                "type": "array",
                "description": "Delimiting points of the drawn segment segment",
                "items": {
                  "$ref": "#/$defs/position"
                },
                "minItems": 2,
                "maxItems": 2
              },
              "label": {
                "$ref": "#/$defs/label"
              },
              "p-id": {
                "$ref": "#/$defs/index",
                "description": "The first point's expression index"
              },
              "q-id": {
                "$ref": "#/$defs/index",
                "description": "The second point's expression index"
              },
              "style": {
                "$ref": "#/$defs/style",
                "description": "How the segment should be drawn",
                "default": "solid"
              }
            },
            "required": [
              "type",
              "points",
              "p-id",
              "q-id"
            ]
          },
          {
            "type": "object",
            "description": "A circle item",
            "properties": {
              "type": {
                "const": "circle"
              },
              "center": {
                "description": "The center of the drawn circle",
                "$ref": "#/$defs/position"
              },
              "radius": {
                "description": "The radius of the drawn circle",
                "type": "number",
                "minimum": 0
              },
              "label": {
                "$ref": "#/$defs/label"
              },
              "id": {
                "$ref": "#/$defs/index",
                "description": "The defining expression index"
              },
              "style": {
                "$ref": "#/$defs/style",
                "description": "How the line should be drawn",
                "default": "solid"
              }
            },
            "required": [
              "type",
              "center",
              "radius",
              "id"
            ]
          }
        ]
      }
    }
  },
  "required": [
    "width",
    "height",
    "expressions",
    "entities",
    "items"
  ],
  "$defs": {
    "index": {
      "type": "integer",
      "minimum": 0,
      "description": "Index of an expression or an entity"
    },
    "complex": {
      "type": "object",
      "description": "A complex number real + i*imaginary",
      "properties": {
        "real": {
          "type": "number",
          "default": 0,
          "description": "The real component"
        },
        "imaginary": {
          "type": "number",
          "default": 0,
          "description": "The imaginary component"
        }
      }
    },
    "ratio": {
      "type": "object",
      "properties": {
        "nom": {
          "type": "integer"
        },
        "denom": {
          "type": "integer",
          "default": 1,
          "exclusiveMinimum": 0
        }
      },
      "required": [
        "nom"
      ]
    },
    "value": {
      "description": "A value of an expression or an entity",
      "oneOf": [
        {
          "type": "object",
          "description": "A complex number",
          "properties": {
            "type": {
              "const": "complex"
            },
            "value": {
              "$ref": "#/$defs/complex"
            }
          },
          "required": [
            "type",
            "value"
          ]
        },
        {
          "type": "object",
          "description": "A line",
          "properties": {
            "type": {
              "const": "line"
            },
            "value": {
              "type": "object",
              "properties": {
                "origin": {
                  "$ref": "#/$defs/complex"
                },
                "direction": {
                  "$ref": "#/$defs/complex"
                }
              },
              "required": [
                "origin",
                "direction"
              ]
            }
          },
          "required": [
            "type",
            "value"
          ]
        },
        {
          "type": "object",
          "description": "A circle",
          "properties": {
            "type": {
              "const": "circle"
            },
            "value": {
              "type": "object",
              "properties": {
                "center": {
                  "$ref": "#/$defs/complex"
                },
                "radius": {
                  "$ref": "#/$defs/complex"
                }
              },
              "required": [
                "center",
                "radius"
              ]
            }
          },
          "required": [
            "type",
            "value"
          ]
        }
      ]
    },
    "style": {
      "enum": [
        "solid",
        "dotted",
        "dashed",
        "bold"
      ],
      "default": "solid",
      "description": "Defines how a line should be drawn"
    },
    "label": {
      "type": "object",
      "description": "Label-related information",
      "properties": {
        "position": {
          "$ref": "#/$defs/position",
          "description": "Where the label should be drawn (figure space)"
        },
        "content": {
          "type": "string",
          "description": "The label contents"
        }
      },
      "required": [
        "position",
        "content"
      ]
    },
    "position": {
      "type": "object",
      "description": "Represents a figure space position",
      "properties": {
        "x": {
          "type": "number"
        },
        "y": {
          "type": "number"
        }
      },
      "required": [
        "x",
        "y"
      ]
    }
  }
}