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X₁₉₀₈¶

MIDPOINT OF PU(8)

X₁₉₀₈ is the midpoint of pu(8).

X₁₉₀₈ (MIDPOINT OF PU(8)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1908 = MIDPOINT OF PU(8)."""

        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_01908(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1908 = MIDPOINT OF PU(8) on reference triangle ABC."""
            X_1908 = eval_trilinear_point(model, A, B, C, '(a**(2)*(b**(3) + c**(3)) + 2*a*b*c*(a**(2) + b*c))', ID="X_1908", classes=["selected", "target"])
            X_171 = eval_trilinear_point(model, A, B, C, 'a**(2) + b*c', ID="X_171", classes=["center", "incident"])
            X_292 = eval_trilinear_point(model, A, B, C, 'a/(a**(2) - b*c)', ID="X_292", classes=["center", "incident"])
            central_line(model, X_171, X_292, 171, 292, incident=True)
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            X_649 = eval_trilinear_point(model, A, B, C, 'a*(b - c)', ID="X_649", classes=["center", "incident"])
            central_line(model, X_42, X_649, 42, 649, incident=True)
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            X_1155 = eval_trilinear_point(model, A, B, C, '(cos(B) + cos(C) - 2*cos(A))', ID="X_1155", classes=["center", "incident"])
            central_line(model, X_39, X_1155, 39, 1155, incident=True)
            return promote_point_to_top(model, X_1908)


        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_1908 on the given reference triangle."""
            model = create_model('X_1908 = MIDPOINT OF PU(8)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01908(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-01908.json"))
            write_center_svg(
                model_acute,
                here / "x-01908.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1908¶

X₁₉₀₈¶