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X₂₁₂₆¶

EIGENTRANSFORM OF X₁₀

X₂₁₂₆ (EIGENTRANSFORM OF X₁₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2126 = EIGENTRANSFORM OF X_10."""

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


        def construct_x_02126(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2126 = EIGENTRANSFORM OF X_10 on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_229 = point_from_barycentrics(model, A, B, C, 0.21061481, 0.29086323, 0.49852195, ID="X_229", classes=["center"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center"])
            X_572 = eval_trilinear_point(model, A, B, C, '(cos(A - U))', ID="X_572", classes=["center"])
            central_line(model, X_1, X_229, 1, 229)
            central_line(model, X_5, X_572, 5, 572)
            X_2126 = intersect_lines(model, X_1, X_229, X_5, X_572, ID="X_2126", classes=["selected", "target"])
            X_49 = eval_trilinear_point(model, A, B, C, 'cos(3*A)', ID="X_49", classes=["center", "incident"])
            X_970 = eval_trilinear_point(model, A, B, C, 'a*(a**(3)*(b + c)**(2) + a*(a*b + a*c - 2*b*c)*(b**(2) + c**(2)) - b*c*(b**(3) + c**(3)) - a*(b**(4) + c**(4)) - (b**(5) + c**(5)))', ID="X_970", classes=["center", "incident"])
            central_line(model, X_49, X_970, 49, 970, incident=True)
            return promote_point_to_top(model, X_2126)


        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_2126 on the given reference triangle."""
            model = create_model('X_2126 = EIGENTRANSFORM OF X_10')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02126(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-02126.json"))
            write_center_svg(
                model_acute,
                here / "x-02126.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2126¶

X₂₁₂₆¶