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X₁₉₄₄¶

CROSSDIFFERENCE OF PU(18)

X₁₉₄₄ = perspector of conic {{A, B, C,X₃₃₃,X₆₆₄}}

X₁₉₄₄ (CROSSDIFFERENCE OF PU(18)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1944 = CROSSDIFFERENCE 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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            gergonne_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01944(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1944 = CROSSDIFFERENCE 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=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_2, X_7, 2, 7, incident=True)
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            X_219 = eval_trilinear_point(model, A, B, C, 'cos(A)*cot(A/2)', ID="X_219", classes=["center", "incident"])
            central_line(model, X_75, X_219, 75, 219, incident=True)
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            X_281 = eval_trilinear_point(model, A, B, C, 'sec(A)*cot(A/2)', ID="X_281", classes=["center", "incident"])
            central_line(model, X_69, X_281, 69, 281, incident=True)
            return promote_point_to_top(model, X_1944)


        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_1944 on the given reference triangle."""
            model = create_model('X_1944 = CROSSDIFFERENCE OF PU(18)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01944(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-01944.json"))
            write_center_svg(
                model_acute,
                here / "x-01944.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1944¶

X₁₉₄₄¶