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X₁₉₁₂¶

IDEAL POINT OF PU(9)

As the isogonal conjugate of a point on the circumcircle, X₁₉₁₂ lies on the line at infinity.

X₁₉₁₂ (IDEAL POINT OF PU(9)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1912 = IDEAL POINT OF PU(9)."""

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


        def construct_x_01912(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1912 = IDEAL POINT OF PU(9) on reference triangle ABC."""
            X_1912 = eval_trilinear_point(model, A, B, C, '(b - c - a*(b/c + c/b)*(b/c - c/b))', ID="X_1912", classes=["selected", "target"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            X_213 = eval_trilinear_point(model, A, B, C, '(b + c)*a**(2)', ID="X_213", classes=["center", "incident"])
            X_667 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b - c)', ID="X_667", classes=["center", "incident"])
            central_line(model, X_213, X_667, 213, 667, incident=True)
            X_1166 = point_from_barycentrics(model, A, B, C, 0.20424736, 0.33803917, 0.45771347, ID="X_1166", classes=["center", "incident"])
            X_1203 = eval_trilinear_point(model, A, B, C, '(a*((a + b + c)**(2) - b*c))', ID="X_1203", classes=["center", "incident"])
            central_line(model, X_1166, X_1203, 1166, 1203, incident=True)
            return promote_point_to_top(model, X_1912)


        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_1912 on the given reference triangle."""
            model = create_model('X_1912 = IDEAL POINT OF PU(9)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01912(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-01912.json"))
            write_center_svg(
                model_acute,
                here / "x-01912.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1912¶

X₁₉₁₂¶