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X₃₁₁₃¶

GtX(31)

X₃₁₁₃ = trilinear pole of line X₁₅₇₇ X₁₉₂₄

X₃₁₁₃ (GtX(31)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3113 = GtX(31)."""

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


        def construct_x_03113(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3113 = GtX(31) on reference triangle ABC."""
            X_3113 = eval_trilinear_point(model, A, B, C, '(b**(2) - c**(2))/(a**(2)*(b**(6) - c**(6)))', ID="X_3113", classes=["selected", "target"])
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            X_561 = eval_trilinear_point(model, A, B, C, 'a **(- 4)', ID="X_561", classes=["center", "incident"])
            central_line(model, X_31, X_561, 31, 561, incident=True)
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            X_560 = eval_trilinear_point(model, A, B, C, 'a**(4)', ID="X_560", classes=["center", "incident"])
            central_line(model, X_75, X_560, 75, 560, incident=True)
            X_313 = eval_trilinear_point(model, A, B, C, '(b + c)*b**(3)*c**(3)', ID="X_313", classes=["center", "incident"])
            X_983 = eval_trilinear_point(model, A, B, C, '(1/(b**(2) - b*c + c**(2)))', ID="X_983", classes=["center", "incident"])
            central_line(model, X_313, X_983, 313, 983, incident=True)
            return promote_point_to_top(model, X_3113)


        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_3113 on the given reference triangle."""
            model = create_model('X_3113 = GtX(31)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03113(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-03113.json"))
            write_center_svg(
                model_acute,
                here / "x-03113.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3113¶

X₃₁₁₃¶