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X₁₆₃₇¶

TRIPOLAR CENTROID OF X₄

X₁₆₃₇ is the tripolar centroid of X₄.

X₁₆₃₇ (TRIPOLAR CENTROID OF X₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1637 = TRIPOLAR CENTROID OF X_4."""

        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_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01637(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1637 = TRIPOLAR CENTROID OF X_4 on reference triangle ABC."""
            X_1637 = eval_barycentric_point(model, A, B, C, 'tan(A)*(tan(B) - tan(C))*(tan(B) + tan(C) - 2*tan(A))', ID="X_1637", classes=["selected", "target"])
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center", "incident"])
            central_line(model, X_98, X_111, 98, 111, incident=True)
            X_107 = eval_trilinear_point(model, A, B, C, '1/(cos(A)*(sin(2*B) - sin(2*C)))', ID="X_107", classes=["center", "incident"])
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center", "incident"])
            central_line(model, X_107, X_112, 107, 112, incident=True)
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_125 = eval_trilinear_point(model, A, B, C, 'cos(A)*(sin(B - C))**(2)', ID="X_125", classes=["center", "incident"])
            central_line(model, X_115, X_125, 115, 125, incident=True)
            return promote_point_to_top(model, X_1637)


        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_1637 on the given reference triangle."""
            model = create_model('X_1637 = TRIPOLAR CENTROID OF X_4')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01637(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-01637.json"))
            write_center_svg(
                model_acute,
                here / "x-01637.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1637¶

X₁₆₃₇¶