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X₁₉₁₀¶

TRILINEAR POLE OF PU(23)

X₁₉₁₀ (TRILINEAR POLE OF PU(23)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1910 = TRILINEAR POLE OF PU(23)."""

        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,
            incenter_of,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01910(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1910 = TRILINEAR POLE OF PU(23) on reference triangle ABC."""
            X_1910 = eval_trilinear_point(model, A, B, C, '(a/(a**(2)*cos(B)*cos(C) - b*c*(cos(A))**(2)))', ID="X_1910", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            central_line(model, X_10, X_98, 10, 98, incident=True)
            X_48 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C)', ID="X_48", classes=["center", "incident"])
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            central_line(model, X_48, X_75, 48, 75, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_163 = eval_trilinear_point(model, A, B, C, '(sin(2*A))/(sin(2*B) - sin(2*C))', ID="X_163", classes=["center", "incident"])
            central_line(model, X_1, X_163, 1, 163, incident=True)
            return promote_point_to_top(model, X_1910)


        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_1910 on the given reference triangle."""
            model = create_model('X_1910 = TRILINEAR POLE OF PU(23)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01910(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-01910.json"))
            write_center_svg(
                model_acute,
                here / "x-01910.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1910¶

X₁₉₁₀¶