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X₂₁₂₂¶

EIGENTRANSFORM OF X₈

X₂₁₂₂ (EIGENTRANSFORM OF X₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2122 = EIGENTRANSFORM OF X_8."""

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


        def construct_x_02122(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2122 = EIGENTRANSFORM OF X_8 on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_84 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C) - cos(A) - 1)', ID="X_84", classes=["center"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center"])
            X_1035 = point_from_barycentrics(model, A, B, C, 9.6083789, 14.775956, -23.384335, ID="X_1035", classes=["center"])
            central_line(model, X_1, X_84, 1, 84)
            central_line(model, X_109, X_1035, 109, 1035)
            X_2122 = intersect_lines(model, X_1, X_84, X_109, X_1035, ID="X_2122", classes=["selected", "target"])
            X_34 = eval_trilinear_point(model, A, B, C, '1 - sec(A)', ID="X_34", classes=["center", "incident"])
            X_1767 = point_from_barycentrics(model, A, B, C, -16.139785, -20.043011, 37.182796, ID="X_1767", classes=["center", "incident"])
            central_line(model, X_34, X_1767, 34, 1767, incident=True)
            return promote_point_to_top(model, X_2122)


        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_2122 on the given reference triangle."""
            model = create_model('X_2122 = EIGENTRANSFORM OF X_8')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02122(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-02122.json"))
            write_center_svg(
                model_acute,
                here / "x-02122.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2122¶

X₂₁₂₂¶