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X₂₄₁₁¶

GIBERT-SIMSON TRANSFORM OF X₄₇₇

X₂₄₁₁ = barycentric quotient X₄₇₇/X₄₇₆

X₂₄₁₁ (GIBERT-SIMSON TRANSFORM OF X₄₇₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2411 = GIBERT-SIMSON TRANSFORM OF X_477."""

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


        def construct_x_02411(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2411 = GIBERT-SIMSON TRANSFORM OF X_477 on reference triangle ABC."""
            X_477 = eval_trilinear_point(model, A, B, C, '1/(4*cos(A) + cos(A - 2*B) + cos(A - 2*C) - 3*cos(B - C))', ID="X_477", classes=["center"])
            X_842 = eval_barycentric_point(model, A, B, C, 'a**(2)/(2*a**(6) - 2*a**(4)*(b**(2) + c**(2)) + a**(2)*(b**(4) + c**(4)) - (b**(2) - c**(2))**(2)*(b**(2) + c**(2)))', ID="X_842", classes=["center"])
            X_249 = eval_trilinear_point(model, A, B, C, '(csc(A))*(csc(B - C))**(2)', ID="X_249", classes=["center"])
            X_2407 = eval_trilinear_point(model, A, B, C, '(csc(C - A)*cos(C) - csc(A - B)*cos(B))*(csc(B - C)/a)**(2)', ID="X_2407", classes=["center"])
            central_line(model, X_477, X_842, 477, 842)
            central_line(model, X_249, X_2407, 249, 2407)
            X_2411 = intersect_lines(model, X_477, X_842, X_249, X_2407, ID="X_2411", classes=["selected", "target"])
            X_323 = eval_trilinear_point(model, A, B, C, 'sin(3*A)*(csc(A))**(2)', ID="X_323", classes=["center", "incident"])
            X_2436 = point_from_barycentrics(model, A, B, C, 0.95620211, -0.024683707, 0.0684816, ID="X_2436", classes=["center", "incident"])
            central_line(model, X_323, X_2436, 323, 2436, incident=True)
            return promote_point_to_top(model, X_2411)


        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_2411 on the given reference triangle."""
            model = create_model('X_2411 = GIBERT-SIMSON TRANSFORM OF X_477')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02411(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-02411.json"))
            write_center_svg(
                model_acute,
                here / "x-02411.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2411¶

X₂₄₁₁¶