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X₃₅₆₆¶

2nd MOSES INFINITY POINT

X₃₅₆₆ = crossdifference of every pair of points on line X₆ X₁₁₉₆

X₃₅₆₆ (2nd MOSES INFINITY POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3566 = 2nd MOSES INFINITY POINT."""

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


        def construct_x_03566(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3566 = 2nd MOSES INFINITY POINT on reference triangle ABC."""
            X_3565 = eval_trilinear_point(model, A, B, C, '(a/((3*a**(2) - b**(2) - c**(2))*(b**(2) - c**(2))))', ID="X_3565", classes=["center"])
            X_3566 = isogonal_conjugate(model, A, B, C, X_3565, ID="X_3566", 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_64 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - cos(B)*cos(C))', ID="X_64", classes=["center", "incident"])
            X_879 = eval_barycentric_point(model, A, B, C, '(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2))/(b**(4) + c**(4) - a**(2)*b**(2) - a**(2)*c**(2))', ID="X_879", classes=["center", "incident"])
            central_line(model, X_64, X_879, 64, 879, incident=True)
            X_1640 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))*(2*a**(6) - b**(6) - c**(6) - 2*a**(4)*b**(2) - 2*a**(4)*c**(2) + a**(2)*b**(4) + a**(2)*c**(4) + b**(4)*c**(2) + b**(2)*c**(4))', ID="X_1640", classes=["center", "incident"])
            X_1853 = point_from_barycentrics(model, A, B, C, -0.10818713, -0.21754386, 1.325731, ID="X_1853", classes=["center", "incident"])
            central_line(model, X_1640, X_1853, 1640, 1853, incident=True)
            return promote_point_to_top(model, X_3566)


        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_3566 on the given reference triangle."""
            model = create_model('X_3566 = 2nd MOSES INFINITY POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03566(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-03566.json"))
            write_center_svg(
                model_acute,
                here / "x-03566.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3566¶

X₃₅₆₆¶