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X₁₂₈₇¶

COLLINGS TRANSFORM OF X₂₃

X₁₂₈₇ (COLLINGS TRANSFORM OF X₂₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1287 = COLLINGS TRANSFORM OF X_23."""

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


        def construct_x_01287(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1287 = COLLINGS TRANSFORM OF X_23 on reference triangle ABC."""
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center"])
            X_842 = eval_barycentric_point(model, A, B, C, 'a**(2)/(2*a**(6) - 2*a**(4)*(b**(2) + c**(2)) + a**(2)*(b**(4) + c**(4)) - (b**(2) - c**(2))**(2)*(b**(2) + c**(2)))', ID="X_842", classes=["center"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center"])
            X_826 = eval_trilinear_point(model, A, B, C, 'a **(-1)*(b**(4) - c**(4)) + a**(3)*(b**(0) - c**(0))', ID="X_826", classes=["center"])
            central_line(model, X_5, X_842, 5, 842)
            central_line(model, X_110, X_826, 110, 826)
            X_1287 = intersect_lines(model, X_5, X_842, X_110, X_826, ID="X_1287", classes=["selected", "target"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center", "incident"])
            X_827 = eval_trilinear_point(model, A, B, C, '1/(a**(-1)*(b**(4) - c**(4)) + a**(3)*(b**(0) - c**(0)))', ID="X_827", classes=["center", "incident"])
            central_line(model, X_523, X_827, 523, 827, incident=True)
            return promote_point_to_top(model, X_1287)


        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_1287 on the given reference triangle."""
            model = create_model('X_1287 = COLLINGS TRANSFORM OF X_23')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01287(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-01287.json"))
            write_center_svg(
                model_acute,
                here / "x-01287.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1287¶

X₁₂₈₇¶