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X₂₆₅₆¶

TRILINEAR POLE OF PU(82)

X₂₆₅₆ (TRILINEAR POLE OF PU(82)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2656 = TRILINEAR POLE OF PU(82)."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02656(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2656 = TRILINEAR POLE OF PU(82) on reference triangle ABC."""
            X_2655 = eval_trilinear_point(model, A, B, C, '((sec(A) + sec(B))*(sec(A) + sec(C)) - (sec(B) + sec(C))**(2))', ID="X_2655", classes=["center"])
            X_2656 = isogonal_conjugate(model, A, B, C, X_2655, ID="X_2656", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_1047 = point_from_barycentrics(model, A, B, C, 0.47678192, 0.53587009, -0.012652005, ID="X_1047", classes=["center", "incident"])
            central_line(model, X_3, X_1047, 3, 1047, incident=True)
            X_296 = eval_trilinear_point(model, A, B, C, '(cos(A))/((cos(A))**(2) - cos(B)*cos(C))', ID="X_296", classes=["center", "incident"])
            X_851 = eval_trilinear_point(model, A, B, C, 'sin(2*B)*sin(C - A) + sin(2*C)*sin(B - A)', ID="X_851", classes=["center", "incident"])
            central_line(model, X_296, X_851, 296, 851, incident=True)
            X_29 = eval_trilinear_point(model, A, B, C, '(sec(A))/(cos(B) + cos(C))', ID="X_29", classes=["center", "incident"])
            X_2638 = eval_trilinear_point(model, A, B, C, '1/(sec(C) - sec(A)) - 1/(sec(B) - sec(A))', ID="X_2638", classes=["center", "incident"])
            central_line(model, X_29, X_2638, 29, 2638, incident=True)
            return promote_point_to_top(model, X_2656)


        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_2656 on the given reference triangle."""
            model = create_model('X_2656 = TRILINEAR POLE OF PU(82)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02656(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-02656.json"))
            write_center_svg(
                model_acute,
                here / "x-02656.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2656¶

X₂₆₅₆¶