{
  "$id": "https://github.com/Geo-AID/Geo-AID/blob/v0.4/figure.schema.json",
  "title": "Geo-AID JSON Figure",
  "description": "Geo-AID's JSON export format",
  "type": "object",
  "properties": {
    "width": {
      "description": "The width of the image",
      "type": "number",
      "exclusiveMinimum": 0
    },
    "height": {
      "description": "The height of the image",
      "type": "number",
      "exclusiveMinimum": 0
    },
    "expressions": {
      "description": "Expressions used by the image",
      "type": "array",
      "items": {
        "type": "object",
        "description": "A single expression",
        "properties": {
          "hint": {
            "description": "The calculated value of this expression",
            "$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": "#/$defs/index" }
                },
                "required": ["type", "circle"]
              },
              {
                "type": "object",
                "description": "Summation of numbers",
                "properties": {
                  "type": {"const": "sum"},
                  "plus": {
                    "type": "array",
                    "items": {
                      "$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": "#/$defs/index" }
                },
                "required": ["type", "point"]
              },
              {
                "type": "object",
                "description": "Line `pq`",
                "properties": {
                  "type": { "const": "point-point-line" },
                  "p": { "$ref": "#/$defs/index" },
                  "q": { "$ref": "#/$defs/index" }
                },
                "required": ["type", "p", "q"]
              },
              {
                "type": "object",
                "description": "Bisector of angle `abc`",
                "properties": {
                  "type": { "const": "angle-bisector" },
                  "a": { "$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"]
    }
  }
}