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X₁₉₄₂¶

TRILINEAR POLE OF U(17)

X₁₉₄₂ (TRILINEAR POLE OF U(17)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1942 = TRILINEAR POLE OF U(17)."""

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


        def construct_x_01942(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1942 = TRILINEAR POLE OF U(17) on reference triangle ABC."""
            X_450 = eval_trilinear_point(model, A, B, C, '(sec(A))*((cos(A))**(4) - (cos(B)*cos(C))**(2))', ID="X_450", classes=["center"])
            X_1942 = isogonal_conjugate(model, A, B, C, X_450, ID="X_1942", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_1624 = point_from_barycentrics(model, A, B, C, 0.18909568, -0.24246678, 1.0533711, ID="X_1624", classes=["center", "incident"])
            central_line(model, X_6, X_1624, 6, 1624, incident=True)
            X_852 = eval_trilinear_point(model, A, B, C, 'sec(C)*sin(2*B)*sin(C - A) + sec(B)*sin(2*C)*sin(B - A)', ID="X_852", classes=["center", "incident"])
            X_895 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2) - a**(2))/(b**(2) + c**(2) - 2*a**(2))', ID="X_895", classes=["center", "incident"])
            central_line(model, X_852, X_895, 852, 895, incident=True)
            return promote_point_to_top(model, X_1942)


        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_1942 on the given reference triangle."""
            model = create_model('X_1942 = TRILINEAR POLE OF U(17)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01942(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-01942.json"))
            write_center_svg(
                model_acute,
                here / "x-01942.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1942¶

X₁₉₄₂¶