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X₁₉₄₅¶

TRILINEAR POLE OF PU(18)

X₁₉₄₅ (TRILINEAR POLE OF PU(18)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1945 = TRILINEAR POLE OF PU(18)."""

        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_01945(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1945 = TRILINEAR POLE OF PU(18) on reference triangle ABC."""
            X_1944 = eval_trilinear_point(model, A, B, C, '(b*c*((cos(A))**(2) - cos(B)*cos(C)))', ID="X_1944", classes=["center"])
            X_1945 = isogonal_conjugate(model, A, B, C, X_1944, ID="X_1945", classes=["selected", "target"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center", "incident"])
            X_284 = eval_trilinear_point(model, A, B, C, '(sin(A))/(cos(B) + cos(C))', ID="X_284", classes=["center", "incident"])
            central_line(model, X_109, X_284, 109, 284, incident=True)
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            X_800 = eval_trilinear_point(model, A, B, C, 'sin(A)*((cos(B))**(2) + (cos(C))**(2))', ID="X_800", classes=["center", "incident"])
            central_line(model, X_19, X_800, 19, 800, incident=True)
            X_333 = eval_trilinear_point(model, A, B, C, 'b*c*(b + c - a)/(b + c)', ID="X_333", classes=["center", "incident"])
            X_664 = eval_trilinear_point(model, A, B, C, '1/(a*(b - c)*(b + c - a))', ID="X_664", classes=["center", "incident"])
            central_line(model, X_333, X_664, 333, 664, incident=True)
            return promote_point_to_top(model, X_1945)


        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_1945 on the given reference triangle."""
            model = create_model('X_1945 = TRILINEAR POLE OF PU(18)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01945(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-01945.json"))
            write_center_svg(
                model_acute,
                here / "x-01945.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1945¶

X₁₉₄₅¶