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X₁₂₉₁¶

COLLINGS TRANSFORM OF X₅₀

X₁₂₉₁ (COLLINGS TRANSFORM OF X₅₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1291 = COLLINGS TRANSFORM OF X_50."""

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


        def construct_x_01291(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1291 = COLLINGS TRANSFORM OF X_50 on reference triangle ABC."""
            X_50 = eval_trilinear_point(model, A, B, C, 'sin(3*A)', ID="X_50", classes=["center"])
            X_512 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))', ID="X_512", classes=["center"])
            X_1291 = cevapoint(model, A, B, C, X_50, X_512, ID="X_1291", classes=["selected", "target"])
            X_477 = eval_trilinear_point(model, A, B, C, '1/(4*cos(A) + cos(A - 2*B) + cos(A - 2*C) - 3*cos(B - C))', ID="X_477", classes=["center", "incident"])
            X_550 = eval_trilinear_point(model, A, B, C, '- cos(B - C) + 4*cos(A)', ID="X_550", classes=["center", "incident"])
            central_line(model, X_477, X_550, 477, 550, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_1141 = eval_trilinear_point(model, A, B, C, 'b*c/(16*D**(2) + (a**(2)+c**(2)-b**(2))*(a**(2)+b**(2)-c**(2)))*(16*D**(2) - 3*(b**(2)+c**(2)-a**(2))**(2))', ID="X_1141", classes=["center", "incident"])
            central_line(model, X_30, X_1141, 30, 1141, incident=True)
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            X_1154 = eval_trilinear_point(model, A, B, C, '(1 - 4*(cos(A))**(2))*cos(B - C)', ID="X_1154", classes=["center", "incident"])
            central_line(model, X_74, X_1154, 74, 1154, incident=True)
            return promote_point_to_top(model, X_1291)


        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_1291 on the given reference triangle."""
            model = create_model('X_1291 = COLLINGS TRANSFORM OF X_50')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01291(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-01291.json"))
            write_center_svg(
                model_acute,
                here / "x-01291.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1291¶

X₁₂₉₁¶