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X₂₀₅₆¶

ORION TRANSFORM OF X₆

X₂₀₅₆ = perspector of ABC and orthic triangle of symmedial triangle

X₂₀₅₆ (ORION TRANSFORM OF X₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2056 = ORION TRANSFORM OF X_6."""

        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,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02056(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2056 = ORION TRANSFORM OF X_6 on reference triangle ABC."""
            X_2056 = eval_trilinear_point(model, A, B, C, 'a*(a**(4) - 2*a**(2)*b**(2) - 2*a**(2)*c**(2) + b**(2)*c**(2))', ID="X_2056", classes=["selected", "target"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            X_251 = eval_trilinear_point(model, A, B, C, 'a**(2)*csc(A +  omega  )', ID="X_251", classes=["center", "incident"])
            central_line(model, X_110, X_251, 110, 251, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_1196 = eval_trilinear_point(model, A, B, C, '(a*(b**(4) + c**(4) + a**(2)*b**(2) + a**(2)*c**(2) - 2*b**(2)*c**(2)))', ID="X_1196", classes=["center", "incident"])
            central_line(model, X_6, X_1196, 6, 1196, incident=True)
            X_184 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A)', ID="X_184", classes=["center", "incident"])
            X_1613 = eval_trilinear_point(model, A, B, C, '(a*(b**(2)*c**(2) - c**(2)*a**(2) - a**(2)*b**(2)))', ID="X_1613", classes=["center", "incident"])
            central_line(model, X_184, X_1613, 184, 1613, incident=True)
            return promote_point_to_top(model, X_2056)


        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_2056 on the given reference triangle."""
            model = create_model('X_2056 = ORION TRANSFORM OF X_6')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02056(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-02056.json"))
            write_center_svg(
                model_acute,
                here / "x-02056.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2056¶

X₂₀₅₆¶