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X₂₄₀₂¶

GIBERT-SIMSON TRANSFORM OF X₁₀₅

X₂₄₀₂ (GIBERT-SIMSON TRANSFORM OF X₁₀₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2402 = GIBERT-SIMSON TRANSFORM OF X_105."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02402(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2402 = GIBERT-SIMSON TRANSFORM OF X_105 on reference triangle ABC."""
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_650 = eval_trilinear_point(model, A, B, C, 'cos(B) - cos(C)', ID="X_650", classes=["center"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center"])
            X_885 = eval_barycentric_point(model, A, B, C, '(b - c)*(a - b - c)/(b**(2) + c**(2) - a*b - a*c)', ID="X_885", classes=["center"])
            central_line(model, X_2, X_650, 2, 650)
            central_line(model, X_523, X_885, 523, 885)
            X_2402 = intersect_lines(model, X_2, X_650, X_523, X_885, ID="X_2402", classes=["selected", "target"])
            X_514 = eval_trilinear_point(model, A, B, C, '(b - c)/a', ID="X_514", classes=["center", "incident"])
            X_1024 = eval_trilinear_point(model, A, B, C, '((b - c)*(b + c - a)/(b**(2) + c**(2) - a*(b + c)))', ID="X_1024", classes=["center", "incident"])
            central_line(model, X_514, X_1024, 514, 1024, incident=True)
            return promote_point_to_top(model, X_2402)


        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_2402 on the given reference triangle."""
            model = create_model('X_2402 = GIBERT-SIMSON TRANSFORM OF X_105')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02402(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-02402.json"))
            write_center_svg(
                model_acute,
                here / "x-02402.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2402¶

X₂₄₀₂¶