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X₂₆₅₀¶

SUM OF PU(81)

X₂₆₅₀ = reflection of X₂₂₉₂ in X₁

X₂₆₅₀ (SUM OF PU(81)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2650 = SUM OF PU(81)."""

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


        def construct_x_02650(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2650 = SUM OF PU(81) on reference triangle ABC."""
            X_2292 = point_from_barycentrics(model, A, B, C, 0.31565657, 0.34032634, 0.34401709, ID="X_2292", classes=["center"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_2650 = reflection_in_point(model, X_2292, X_1, ID="X_2650", classes=["selected", "target"], guide=False)
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            central_line(model, X_1, X_21, 1, 21, incident=True)
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            central_line(model, X_42, X_65, 42, 65, incident=True)
            X_72 = eval_trilinear_point(model, A, B, C, '(b + c)*cot(A)', ID="X_72", classes=["center", "incident"])
            X_756 = eval_trilinear_point(model, A, B, C, '(b + c)**(2)', ID="X_756", classes=["center", "incident"])
            central_line(model, X_72, X_756, 72, 756, incident=True)
            return promote_point_to_top(model, X_2650)


        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_2650 on the given reference triangle."""
            model = create_model('X_2650 = SUM OF PU(81)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02650(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-02650.json"))
            write_center_svg(
                model_acute,
                here / "x-02650.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2650¶

X₂₆₅₀¶