{
  "id": "frame-rotation",
  "title": "Frame rotation and geodetic conversion",
  "summary": "The two transformations between the representations of a position: the Cartesian rotation about the pole, and the ellipsoidal conversion.",
  "nodes": [
    {
      "id": "angle",
      "label": "Earth Rotation Angle from UT1",
      "kind": "data",
      "group": "input",
      "summary": "A linear function of the days of UT1 since J2000.0, in turns.",
      "api": "EarthRotationAngle",
      "label_zh": "由 UT1 求地球自转角",
      "summary_zh": "自 J2000.0 起 UT1 天数的线性函数，单位为圈。"
    },
    {
      "id": "eci",
      "label": "Eci",
      "kind": "data",
      "group": "frames",
      "summary": "A Cartesian position in the inertial frame, in meters.",
      "api": "Eci",
      "summary_zh": "惯性系中的直角坐标位置，单位为米。"
    },
    {
      "id": "ecef",
      "label": "Ecef",
      "kind": "data",
      "group": "frames",
      "summary": "A Cartesian position in the Earth-fixed frame, in meters.",
      "api": "Ecef",
      "summary_zh": "地固系中的直角坐标位置，单位为米。"
    },
    {
      "id": "matrix",
      "label": "Build the rotation matrix",
      "kind": "step",
      "group": "rotate",
      "summary": "A clockwise turn about the third axis, whose transpose is the inverse.",
      "api": "rotation_eci_to_ecef",
      "label_zh": "构造旋转矩阵",
      "summary_zh": "绕第三轴的顺时针转动，其转置即逆变换。"
    },
    {
      "id": "to_ecef",
      "label": "Rotate inertial to Earth-fixed",
      "kind": "step",
      "group": "rotate",
      "summary": "Apply the rotation to the vector. The length is preserved.",
      "api": "Eci",
      "label_zh": "惯性系旋转到地固系",
      "summary_zh": "对矢量施加旋转。长度保持不变。"
    },
    {
      "id": "to_eci",
      "label": "Rotate Earth-fixed to inertial",
      "kind": "step",
      "group": "rotate",
      "summary": "Apply the transposed rotation. The length is preserved.",
      "api": "Ecef",
      "label_zh": "地固系旋转到惯性系",
      "summary_zh": "施加转置后的旋转。长度保持不变。"
    },
    {
      "id": "cartesian",
      "label": "Cartesian to geodetic",
      "kind": "step",
      "group": "geodetic",
      "summary": "Solve for latitude, longitude, and height on an ellipsoid. Iterative, because no elementary closed form exists.",
      "api": "geodetic_from_cartesian",
      "label_zh": "直角坐标转大地坐标",
      "summary_zh": "在椭球上求解纬度、经度与高。因无初等闭式解而采用迭代。"
    },
    {
      "id": "polar",
      "label": "On the rotation axis?",
      "kind": "decision",
      "group": "geodetic",
      "summary": "No longitude is defined on the axis.",
      "label_zh": "位于自转轴上？",
      "summary_zh": "轴上经度无定义。"
    },
    {
      "id": "undefined",
      "label": "No longitude",
      "kind": "terminal",
      "group": "error",
      "summary": "The conversion returns no value rather than an arbitrary longitude.",
      "label_zh": "经度无定义",
      "summary_zh": "转换返回空值，而不是任意经度。"
    },
    {
      "id": "geodetic",
      "label": "Geodetic",
      "kind": "terminal",
      "group": "output",
      "summary": "Latitude and longitude in radians, height in meters above the WGS 84 ellipsoid.",
      "api": "Geodetic",
      "summary_zh": "纬度与经度单位为弧度，高为 WGS 84 椭球面以上的米数。"
    },
    {
      "id": "forward",
      "label": "Geodetic to Cartesian",
      "kind": "step",
      "group": "geodetic",
      "summary": "Closed form, using the prime vertical radius of curvature.",
      "api": "cartesian_from_geodetic",
      "label_zh": "大地坐标转直角坐标",
      "summary_zh": "闭式解，使用卯酉圈曲率半径。"
    },
    {
      "id": "direct",
      "label": "Geodetic to Ecef",
      "kind": "terminal",
      "group": "output",
      "summary": "The Earth-fixed Cartesian position on the WGS 84 ellipsoid.",
      "api": "Geodetic",
      "label_zh": "大地坐标转 Ecef",
      "summary_zh": "WGS 84 椭球上的地固系直角坐标。"
    }
  ],
  "edges": [
    {
      "source": "angle",
      "target": "matrix",
      "kind": "flow",
      "label": null
    },
    {
      "source": "matrix",
      "target": "to_ecef",
      "kind": "flow",
      "label": null
    },
    {
      "source": "matrix",
      "target": "to_eci",
      "kind": "flow",
      "label": null
    },
    {
      "source": "eci",
      "target": "to_ecef",
      "kind": "flow",
      "label": null
    },
    {
      "source": "ecef",
      "target": "to_eci",
      "kind": "flow",
      "label": null
    },
    {
      "source": "to_ecef",
      "target": "ecef",
      "kind": "flow",
      "label": "Earth-fixed"
    },
    {
      "source": "to_eci",
      "target": "eci",
      "kind": "flow",
      "label": "inertial"
    },
    {
      "source": "to_ecef",
      "target": "cartesian",
      "kind": "flow",
      "label": null
    },
    {
      "source": "cartesian",
      "target": "polar",
      "kind": "flow",
      "label": null
    },
    {
      "source": "polar",
      "target": "undefined",
      "kind": "branch",
      "label": "yes"
    },
    {
      "source": "polar",
      "target": "geodetic",
      "kind": "branch",
      "label": "no"
    },
    {
      "source": "geodetic",
      "target": "forward",
      "kind": "flow",
      "label": null
    },
    {
      "source": "forward",
      "target": "direct",
      "kind": "flow",
      "label": null
    }
  ],
  "title_zh": "参考系旋转与大地坐标转换",
  "summary_zh": "位置各表示之间的两种变换：绕极轴的直角坐标旋转，以及椭球坐标转换。"
}