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X₅₃₉¶

DIRECTION OF VECTOR AX + BX + CX, where X = X₅₄

X₅₃₉ (DIRECTION OF VECTOR AX + BX + CX, where X = X₅₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_539 = DIRECTION OF VECTOR AX + BX + CX, where X = X_54."""

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


        def construct_x_00539(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_539 = DIRECTION OF VECTOR AX + BX + CX, where X = X_54 on reference triangle ABC."""
            X_539 = eval_barycentric_point(model, A, B, C, '(a**(2) - b**(2) - c**(2))*(2*a**(8) - 4*a**(6)*(b**(2) + c**(2)) + 3*a**(4)*(b**(4) + c**(4)) - 2*a**(2)*(b**(2) - c**(2))**(2)*(b**(2) + c**(2)) + (b**(2) - c**(2))**(4))', ID="X_539", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            central_line(model, X_2, X_54, 2, 54, incident=True)
            X_155 = eval_trilinear_point(model, A, B, C, '(cos(A))*((cos(B))**(2) + (cos(C))**(2) - (cos(A))**(2))', ID="X_155", classes=["center", "incident"])
            X_195 = eval_trilinear_point(model, A, B, C, 'a*(a**(8) + b**(8) + c**(8) - 4*a**(6)*(b**(2) + c**(2)) + a**(4)*(6*b**(4) + 6*c**(4) + 5*b**(2)*c**(2)) - a**(2)*(4*b**(6) + 4*c**(6) - b**(4)*c**(2) - b**(2)*c**(4)) - 2*b**(2)*c**(2)*(b**(4) + c**(4) - b**(2)*c**(2)))', ID="X_195", classes=["center", "incident"])
            central_line(model, X_155, X_195, 155, 195, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            return promote_point_to_top(model, X_539)


        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_539 on the given reference triangle."""
            model = create_model('X_539 = DIRECTION OF VECTOR AX + BX + CX, where X = X_54')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00539(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-00539.json"))
            write_center_svg(
                model_acute,
                here / "x-00539.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X539¶

X₅₃₉¶