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X₁₉₃₉¶

MIDPOINT OF PU(15)

X₁₉₃₉ is the midpoint of pu(15).

X₁₉₃₉ (MIDPOINT OF PU(15)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1939 = MIDPOINT OF PU(15)."""

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


        def construct_x_01939(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1939 = MIDPOINT OF PU(15) on reference triangle ABC."""
            X_1939 = eval_trilinear_point(model, A, B, C, '((a*cos(B) + b*cos(C) + c*cos(A))*cos(C) + (a*cos(C) + b*cos(A) + c*cos(B))*cos(B))', ID="X_1939", classes=["selected", "target"])
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            X_650 = eval_trilinear_point(model, A, B, C, 'cos(B) - cos(C)', ID="X_650", classes=["center", "incident"])
            central_line(model, X_65, X_650, 65, 650, incident=True)
            X_169 = eval_trilinear_point(model, A, B, C, '- (sin(A))*(cos(A/2))**(2) + (sin(B))*(cos(B/2))**(2) + (sin(C))*(cos(C/2))**(2)', ID="X_169", classes=["center", "incident"])
            X_1575 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2)) - b*c*(b + c)', ID="X_1575", classes=["center", "incident"])
            central_line(model, X_169, X_1575, 169, 1575, incident=True)
            X_1385 = eval_trilinear_point(model, A, B, C, '16*( area )**(2) + a*(a + b + c)*(b**(2) + c**(2) - a**(2))', ID="X_1385", classes=["center", "incident"])
            X_2649 = eval_trilinear_point(model, A, B, C, '((a*(cos(B) + cos(A)) + b*(cos(C) + cos(B)) + c*(cos(A) + cos(C)))*(cos(C) + cos(A)) + (a*(cos(C) + cos(A)) + b*(cos(A) + cos(B)) + c*(cos(B) + cos(C)))*(cos(B) + cos(A)))', ID="X_2649", classes=["center", "incident"])
            central_line(model, X_1385, X_2649, 1385, 2649, incident=True)
            return promote_point_to_top(model, X_1939)


        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_1939 on the given reference triangle."""
            model = create_model('X_1939 = MIDPOINT OF PU(15)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01939(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-01939.json"))
            write_center_svg(
                model_acute,
                here / "x-01939.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1939¶

X₁₉₃₉¶