{
  "schema": "OMEGA_MARKED_REFERENCE_GEOMETRY/1.2",
  "paper_version": "OMEGA_Paper_VII_v1.6.0",
  "numeric_model": "IEEE-754 binary64 approximation",
  "normative_layer": "exact_formulas",
  "construction_inputs": {
    "radius_scale": "a>0",
    "seed_angle": "epsilon=pi/648000 rad=1 arcsecond",
    "frame": "ordered orthonormal pair (u,v)",
    "bilateral_steps": [
      "a",
      "a*phi"
    ],
    "circular_component": "oriented major arc from b to d"
  },
  "exact_formulas": {
    "phi": "(1+sqrt(5))/2",
    "epsilon": "pi/648000",
    "delta": "epsilon/2",
    "s": "sin(delta)",
    "c": "cos(delta)",
    "x0": "s",
    "x1": "1+s",
    "x2": "phi^2+s",
    "golden_accumulation": "a+a*phi=a*(1+phi)=a*phi^2",
    "point": "alpha+a*(c*u+sigma*x_j*v)",
    "major_arc": "alpha+a*(cos(t)*u+sin(t)*v), delta<=t<=2*pi-delta",
    "left_foot": "d-a*lambda*v, 0<=lambda<=phi^2",
    "right_foot": "b+a*lambda*v, 0<=lambda<=phi^2",
    "gram_factorization": "G=c^2*1*1^T+z*z^T",
    "intrinsic_to_cartesian": "(xi_u,xi_v)->(xi_v,-xi_u)"
  },
  "constants_approx": {
    "epsilon_rad": 4.84813681109536e-06,
    "epsilon_arcsec": 1.0,
    "delta_rad": 2.42406840554768e-06,
    "phi": 1.618033988749895,
    "s": 2.424068405545306e-06,
    "c": 0.9999999999970619,
    "x_levels": [
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      1.0000024240684056,
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    ]
  },
  "transform": {
    "scale": 1.0,
    "translation": [
      0.0,
      0.0,
      0.0
    ],
    "rotation_deg_xyz": [
      0.0,
      0.0,
      0.0
    ],
    "rotation_convention": "active Rz(rz) Ry(ry) Rx(rx)",
    "rotation_matrix": [
      [
        1.0,
        0.0,
        0.0
      ],
      [
        0.0,
        1.0,
        0.0
      ],
      [
        0.0,
        0.0,
        1.0
      ]
    ]
  },
  "frame_approx": {
    "u": [
      0.0,
      -1.0,
      0.0
    ],
    "v": [
      1.0,
      0.0,
      0.0
    ],
    "n": [
      0.0,
      0.0,
      1.0
    ]
  },
  "landmarks_approx": {
    "alpha": [
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      0.0,
      0.0
    ],
    "d2": [
      -2.6180364128183005,
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      0.0
    ],
    "d1": [
      -1.0000024240684056,
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      0.0
    ],
    "d": [
      -2.424068405545306e-06,
      -0.9999999999970619,
      0.0
    ],
    "b": [
      2.424068405545306e-06,
      -0.9999999999970619,
      0.0
    ],
    "b1": [
      1.0000024240684056,
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      0.0
    ],
    "b2": [
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      0.0
    ]
  },
  "signed_bearings_rad_approx": {
    "d2": -1.20593280731939,
    "d1": -0.7853993754316511,
    "d": -2.42406840554768e-06,
    "b": 2.42406840554768e-06,
    "b1": 0.7853993754316511,
    "b2": 1.20593280731939
  },
  "center_angle_matrix_rad_approx": [
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  ],
  "invariants": {
    "baseline_affine_dimension": 1,
    "center_augmented_affine_dimension": 2,
    "center_relative_matrix_shape": [
      3,
      6
    ],
    "gram_matrix_shape": [
      6,
      6
    ],
    "center_relative_matrix_rank": 2,
    "gram_matrix_rank": 2,
    "ambient_export_dimension": 3,
    "ordered_landmarks": [
      "d2",
      "d1",
      "d",
      "b",
      "b1",
      "b2"
    ],
    "obj_circle_samples": 4096,
    "major_arc_traversal": "counterclockwise from b to d in canonical Cartesian coordinates"
  }
}