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X₁₁₂₀¶

X₂-BLAIKIE TRANSFORM OF X₁

For the definition of Blaikie transform, see X₉₀₃.

X₁₁₂₀ (X₂-BLAIKIE TRANSFORM OF X₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1120 = X_2-BLAIKIE TRANSFORM OF X_1."""

        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,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01120(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1120 = X_2-BLAIKIE TRANSFORM OF X_1 on reference triangle ABC."""
            X_1120 = eval_trilinear_point(model, A, B, C, '(b*c/(b**(2) + c**(2) + b*a + c*a - 4*b*c))', ID="X_1120", classes=["selected", "target"])
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            central_line(model, X_56, X_100, 56, 100, incident=True)
            X_106 = eval_trilinear_point(model, A, B, C, 'a/(2*a - b - c)', ID="X_106", classes=["center", "incident"])
            X_519 = eval_trilinear_point(model, A, B, C, '(2*a - b - c)/a', ID="X_519", classes=["center", "incident"])
            central_line(model, X_106, X_519, 106, 519, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_644 = eval_trilinear_point(model, A, B, C, '((b + c - a)/(b - c))', ID="X_644", classes=["center", "incident"])
            central_line(model, X_6, X_644, 6, 644, incident=True)
            return promote_point_to_top(model, X_1120)


        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_1120 on the given reference triangle."""
            model = create_model('X_1120 = X_2-BLAIKIE TRANSFORM OF X_1')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01120(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-01120.json"))
            write_center_svg(
                model_acute,
                here / "x-01120.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1120¶

X₁₁₂₀¶