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X₁₂₉₃¶

COLLINGS TRANSFORM OF X₁₂₁

X₁₂₉₃ (COLLINGS TRANSFORM OF X₁₂₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1293 = COLLINGS TRANSFORM OF X_121."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01293(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1293 = COLLINGS TRANSFORM OF X_121 on reference triangle ABC."""
            X_1293 = eval_trilinear_point(model, A, B, C, '(a/((b - c)*(3*a - b - c)))', ID="X_1293", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_106 = eval_trilinear_point(model, A, B, C, 'a/(2*a - b - c)', ID="X_106", classes=["center", "incident"])
            central_line(model, X_3, X_106, 3, 106, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_121 = eval_trilinear_point(model, A, B, C, '(b*c*(b + c - 2*a)*(b**(3) + c**(3) + a*(b**(2) + c**(2)) - 2*b*c*(b + c)))', ID="X_121", classes=["center", "incident"])
            central_line(model, X_4, X_121, 4, 121, incident=True)
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            X_104 = eval_trilinear_point(model, A, B, C, '1/(-1 + cos(B) + cos(C))', ID="X_104", classes=["center", "incident"])
            central_line(model, X_40, X_104, 40, 104, incident=True)
            return promote_point_to_top(model, X_1293)


        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_1293 on the given reference triangle."""
            model = create_model('X_1293 = COLLINGS TRANSFORM OF X_121')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01293(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-01293.json"))
            write_center_svg(
                model_acute,
                here / "x-01293.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1293¶

X₁₂₉₃¶