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X₂₀₆₅¶

ORION TRANSFORM OF X₉₈

X₂₀₆₅ (ORION TRANSFORM OF X₉₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2065 = ORION TRANSFORM OF X_98."""

        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,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02065(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2065 = ORION TRANSFORM OF X_98 on reference triangle ABC."""
            X_114 = eval_trilinear_point(model, A, B, C, 'b*c*(b*sec(B +  omega  ) + c*sec(C +  omega  ))', ID="X_114", classes=["center"])
            X_2065 = isogonal_conjugate(model, A, B, C, X_114, ID="X_2065", classes=["selected", "target"])
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_325 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)', ID="X_325", classes=["center", "incident"])
            central_line(model, X_98, X_325, 98, 325, incident=True)
            X_460 = eval_trilinear_point(model, A, B, C, '(sec(A))*(a**(2)*(2*a**(2) - b**(2) - c**(2)) + (b**(2) - c**(2))**(2))', ID="X_460", classes=["center", "incident"])
            X_685 = eval_trilinear_point(model, A, B, C, '(1/(sec(B)*(sin(C))**(3) - sec(C)*(sin(B))**(3)))', ID="X_685", classes=["center", "incident"])
            central_line(model, X_460, X_685, 460, 685, incident=True)
            X_248 = eval_trilinear_point(model, A, B, C, 'sin(2*A)*sec(A +  omega  )', ID="X_248", classes=["center", "incident"])
            X_1570 = eval_trilinear_point(model, A, B, C, 'a*(cot(A) + cot(omega)  - 4*tan(omega)  )', ID="X_1570", classes=["center", "incident"])
            central_line(model, X_248, X_1570, 248, 1570, incident=True)
            return promote_point_to_top(model, X_2065)


        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_2065 on the given reference triangle."""
            model = create_model('X_2065 = ORION TRANSFORM OF X_98')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02065(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-02065.json"))
            write_center_svg(
                model_acute,
                here / "x-02065.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2065¶

X₂₀₆₅¶