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X₂₀₆₂¶

ORION TRANSFORM OF X₆₃

X₂₀₆₂ (ORION TRANSFORM OF X₆₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2062 = ORION TRANSFORM OF X_63."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02062(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2062 = ORION TRANSFORM OF X_63 on reference triangle ABC."""
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_77 = eval_trilinear_point(model, A, B, C, '1/(1 + sec(A))', ID="X_77", classes=["center"])
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center"])
            X_307 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)*(b + c)*(cos(A))/(b + c - a)', ID="X_307", classes=["center"])
            central_line(model, X_3, X_77, 3, 77)
            central_line(model, X_21, X_307, 21, 307)
            X_2062 = intersect_lines(model, X_3, X_77, X_21, X_307, ID="X_2062", classes=["selected", "target"])
            X_284 = eval_trilinear_point(model, A, B, C, '(sin(A))/(cos(B) + cos(C))', ID="X_284", classes=["center", "incident"])
            X_2003 = eval_trilinear_point(model, A, B, C, 'sin(3*A/2)*sec(A/2)', ID="X_2003", classes=["center", "incident"])
            central_line(model, X_284, X_2003, 284, 2003, incident=True)
            return promote_point_to_top(model, X_2062)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_2062 on the given reference triangle."""
            model = create_model('X_2062 = ORION TRANSFORM OF X_63')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02062(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-02062.json"))
            write_center_svg(
                model_acute,
                here / "x-02062.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2062¶

X₂₀₆₂¶