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X₂₀₆₄¶

ORION TRANSFORM OF X₇₅

X₂₀₆₄ (ORION TRANSFORM OF X₇₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2064 = ORION TRANSFORM OF X_75."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02064(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2064 = ORION TRANSFORM OF X_75 on reference triangle ABC."""
            X_2064 = eval_trilinear_point(model, A, B, C, '(b**(2)*c**(2)*(a**(4) - b**(4) - c**(4) + a**(2)*b*c - b**(3)*c - b*c**(3)))', ID="X_2064", classes=["selected", "target"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            X_85 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)/(b + c - a)', ID="X_85", classes=["center", "incident"])
            central_line(model, X_76, X_85, 76, 85, incident=True)
            X_81 = eval_trilinear_point(model, A, B, C, '1/(b + c)', ID="X_81", classes=["center", "incident"])
            X_314 = eval_trilinear_point(model, A, B, C, '(b**(2)*c**(2)*(b + c - a)/(b + c))', ID="X_314", classes=["center", "incident"])
            central_line(model, X_81, X_314, 81, 314, incident=True)
            X_278 = eval_trilinear_point(model, A, B, C, 'sec(A)*tan(A/2)', ID="X_278", classes=["center", "incident"])
            X_345 = eval_trilinear_point(model, A, B, C, '(csc(A))/(1 - sec(A))', ID="X_345", classes=["center", "incident"])
            central_line(model, X_278, X_345, 278, 345, incident=True)
            return promote_point_to_top(model, X_2064)


        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_2064 on the given reference triangle."""
            model = create_model('X_2064 = ORION TRANSFORM OF X_75')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02064(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-02064.json"))
            write_center_svg(
                model_acute,
                here / "x-02064.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2064¶

X₂₀₆₄¶