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X₂₆₄₀¶

CROSSSUM OF PU(78)

X₂₆₄₀ (CROSSSUM OF PU(78)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2640 = CROSSSUM OF PU(78)."""

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


        def construct_x_02640(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2640 = CROSSSUM OF PU(78) on reference triangle ABC."""
            X_2640 = eval_trilinear_point(model, A, B, C, '(cot(A) - cot(B))*(cot(A) - cot(C)) - (cot(B) - cot(C))**(2)', ID="X_2640", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_662 = eval_trilinear_point(model, A, B, C, '1/(cot(B) - cot(C))', ID="X_662", classes=["center", "incident"])
            central_line(model, X_1, X_662, 1, 662, incident=True)
            X_45 = eval_trilinear_point(model, A, B, C, '2*b + 2*c - a', ID="X_45", classes=["center", "incident"])
            X_846 = eval_trilinear_point(model, A, B, C, '(- a**(2) + b**(2) + c**(2) + b*c + c*a + a*b)', ID="X_846", classes=["center", "incident"])
            central_line(model, X_45, X_846, 45, 846, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_1247 = point_from_barycentrics(model, A, B, C, 0.47979502, 0.29838347, 0.22182151, ID="X_1247", classes=["center", "incident"])
            central_line(model, X_3, X_1247, 3, 1247, incident=True)
            return promote_point_to_top(model, X_2640)


        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_2640 on the given reference triangle."""
            model = create_model('X_2640 = CROSSSUM OF PU(78)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02640(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-02640.json"))
            write_center_svg(
                model_acute,
                here / "x-02640.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2640¶

X₂₆₄₀¶