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X₂₄₀₀¶

GIBERT-SIMSON TRANSFORM OF X₁₀₃

X₂₄₀₀ (GIBERT-SIMSON TRANSFORM OF X₁₀₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2400 = GIBERT-SIMSON TRANSFORM OF X_103."""

        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,
            gergonne_point_of,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02400(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2400 = GIBERT-SIMSON TRANSFORM OF X_103 on reference triangle ABC."""
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center"])
            X_522 = eval_trilinear_point(model, A, B, C, '(cos(B) - cos(C))*(csc(A))', ID="X_522", classes=["center"])
            X_103 = eval_trilinear_point(model, A, B, C, 'a/((a - b)*cot(C) + (a - c)*cot(B))', ID="X_103", classes=["center"])
            X_675 = eval_trilinear_point(model, A, B, C, '(b*c/(b**(3) + c**(3) - a*(b**(2) + c**(2))))', ID="X_675", classes=["center"])
            central_line(model, X_7, X_522, 7, 522)
            central_line(model, X_103, X_675, 103, 675)
            X_2400 = intersect_lines(model, X_7, X_522, X_103, X_675, ID="X_2400", classes=["selected", "target"])
            X_677 = eval_trilinear_point(model, A, B, C, '(a/((b - c)*(b**(3) + c**(3) - 2*a**(3) + (b + c)*(a**(2) - b*c))))', ID="X_677", classes=["center", "incident"])
            X_883 = point_from_barycentrics(model, A, B, C, -1.5, 0.1, 2.4, ID="X_883", classes=["center", "incident"])
            central_line(model, X_677, X_883, 677, 883, incident=True)
            return promote_point_to_top(model, X_2400)


        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_2400 on the given reference triangle."""
            model = create_model('X_2400 = GIBERT-SIMSON TRANSFORM OF X_103')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02400(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-02400.json"))
            write_center_svg(
                model_acute,
                here / "x-02400.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2400¶

X₂₄₀₀¶