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X₂₁₃₂¶

EIGENTRANSFORM OF X₃₀

X₂₁₃₂ is the tangential of X₇₄ on the Neuberg cubic (K001).

X₂₁₃₂ (EIGENTRANSFORM OF X₃₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2132 = EIGENTRANSFORM OF X_30."""

        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,
            intersect_lines,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02132(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2132 = EIGENTRANSFORM OF X_30 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_1138 = eval_trilinear_point(model, A, B, C, '(1/(5*cos(A) - 4*cos(B)*cos(C) - 8*(cos(A))**(2)*sin(B)*sin(C)))', ID="X_1138", classes=["center"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center"])
            X_2133 = point_from_barycentrics(model, A, B, C, -0.66648885, 0.7236793, 0.94280955, ID="X_2133", classes=["center"])
            central_line(model, X_4, X_1138, 4, 1138)
            central_line(model, X_30, X_2133, 30, 2133)
            X_2132 = intersect_lines(model, X_4, X_1138, X_30, X_2133, ID="X_2132", classes=["selected", "target"])
            X_3065 = eval_trilinear_point(model, A, B, C, '(1/(1 + 2*(cos(A) - cos(B) - cos(C))))', ID="X_3065", classes=["center", "incident"])
            X_3466 = point_from_barycentrics(model, A, B, C, 0.75049052, 1.2119032, -0.96239372, ID="X_3466", classes=["center", "incident"])
            central_line(model, X_3065, X_3466, 3065, 3466, incident=True)
            return promote_point_to_top(model, X_2132)


        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_2132 on the given reference triangle."""
            model = create_model('X_2132 = EIGENTRANSFORM OF X_30')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02132(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-02132.json"))
            write_center_svg(
                model_acute,
                here / "x-02132.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2132¶

X₂₁₃₂¶