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X₂₃₉₆¶

GIBERT-SIMSON TRANSFORM OF X₉₉

X₂₃₉₆ = trilinear pole of line X₁₁₄ X₃₂₅ (the Simson line of X₉₉)

X₂₃₉₆ (GIBERT-SIMSON TRANSFORM OF X₉₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2396 = GIBERT-SIMSON TRANSFORM OF X_99."""

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


        def construct_x_02396(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2396 = GIBERT-SIMSON TRANSFORM OF X_99 on reference triangle ABC."""
            X_2396 = eval_barycentric_point(model, A, B, C, '(b**(4) + c**(4) - a**(2)*b**(2) - a**(2)*c**(2))/(b**(2) - c**(2))', ID="X_2396", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            central_line(model, X_2, X_39, 2, 39, incident=True)
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_99, X_110, 99, 110, incident=True)
            X_325 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)', ID="X_325", classes=["center", "incident"])
            X_868 = eval_trilinear_point(model, A, B, C, 'sin(2*B)*sin(A - C)*csc(A - B) - sin(2*C)*sin(A - B)*csc(A - C)', ID="X_868", classes=["center", "incident"])
            central_line(model, X_325, X_868, 325, 868, incident=True)
            return promote_point_to_top(model, X_2396)


        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_2396 on the given reference triangle."""
            model = create_model('X_2396 = GIBERT-SIMSON TRANSFORM OF X_99')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02396(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-02396.json"))
            write_center_svg(
                model_acute,
                here / "x-02396.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2396¶

X₂₃₉₆¶