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X₁₁₀₁¶

TRILINEAR SQUARE OF X₁₁₀

X₁₁₀₁ (TRILINEAR SQUARE OF X₁₁₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1101 = TRILINEAR SQUARE OF X_110."""

        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_01101(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1101 = TRILINEAR SQUARE OF X_110 on reference triangle ABC."""
            X_1101 = eval_trilinear_point(model, A, B, C, '((csc(B - C))**(2))', ID="X_1101", classes=["selected", "target"])
            X_59 = eval_trilinear_point(model, A, B, C, '1/(1 - cos(B - C))', ID="X_59", classes=["center", "incident"])
            X_60 = eval_trilinear_point(model, A, B, C, '1/(1 + cos(B - C))', ID="X_60", classes=["center", "incident"])
            central_line(model, X_59, X_60, 59, 60, incident=True)
            X_163 = eval_trilinear_point(model, A, B, C, '(sin(2*A))/(sin(2*B) - sin(2*C))', ID="X_163", classes=["center", "incident"])
            X_798 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b**(2) - c**(2))', ID="X_798", classes=["center", "incident"])
            central_line(model, X_163, X_798, 163, 798, incident=True)
            X_656 = eval_trilinear_point(model, A, B, C, 'tan(B) - tan(C)', ID="X_656", classes=["center", "incident"])
            X_662 = eval_trilinear_point(model, A, B, C, '1/(cot(B) - cot(C))', ID="X_662", classes=["center", "incident"])
            central_line(model, X_656, X_662, 656, 662, incident=True)
            return promote_point_to_top(model, X_1101)


        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_1101 on the given reference triangle."""
            model = create_model('X_1101 = TRILINEAR SQUARE OF X_110')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01101(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-01101.json"))
            write_center_svg(
                model_acute,
                here / "x-01101.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1101¶

X₁₁₀₁¶