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X₂₁₀₆¶

POINT KEPLER I

X₂₁₀₆ (POINT KEPLER I) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2106 = POINT KEPLER I."""

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


        def construct_x_02106(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2106 = POINT KEPLER I on reference triangle ABC."""
            X_2106 = eval_trilinear_point(model, A, B, C, '((a + b)*(a + c)*(b**(2)*c**(2) - a**(2)*b**(2) - a**(2)*c**(2) + a*b*c*(b + c - a)))', ID="X_2106", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_2, X_6, 2, 6, incident=True)
            X_105 = eval_trilinear_point(model, A, B, C, '1/(b**(2) + c**(2) - a*(b + c))', ID="X_105", classes=["center", "incident"])
            X_805 = eval_trilinear_point(model, A, B, C, '(1/(a **(-3)*(b**(2) - c**(2)) + a**(1)*(b **(-2) - c **(-2))))', ID="X_805", classes=["center", "incident"])
            central_line(model, X_105, X_805, 105, 805, incident=True)
            X_238 = eval_trilinear_point(model, A, B, C, 'a**(2) - b*c', ID="X_238", classes=["center", "incident"])
            X_741 = eval_trilinear_point(model, A, B, C, '(1/(a **(-2)*(b**(1) + c**(1)) - a**(0)*(b **(-1) + c **(-1))))', ID="X_741", classes=["center", "incident"])
            central_line(model, X_238, X_741, 238, 741, incident=True)
            return promote_point_to_top(model, X_2106)


        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_2106 on the given reference triangle."""
            model = create_model('X_2106 = POINT KEPLER I')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02106(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-02106.json"))
            write_center_svg(
                model_acute,
                here / "x-02106.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2106¶

X₂₁₀₆¶