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X₆₆₉¶

CROSSDIFFERENCE OF X₂ AND X₃₉

X₆₆₉ = crossdifference of every pair of points on line {2, 39}

X₆₆₉ (CROSSDIFFERENCE OF X₂ AND X₃₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_669 = CROSSDIFFERENCE OF X_2 AND X_39."""

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


        def construct_x_00669(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_669 = CROSSDIFFERENCE OF X_2 AND X_39 on reference triangle ABC."""
            X_669 = eval_trilinear_point(model, A, B, C, 'a**(3)*(b**(2) - c**(2))', ID="X_669", classes=["selected", "target"])
            X_23 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4) - b**(2)*c**(2))', ID="X_23", classes=["center", "incident"])
            X_385 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(4) - b**(2)*c**(2))', ID="X_385", classes=["center", "incident"])
            central_line(model, X_23, X_385, 23, 385, incident=True)
            X_187 = eval_trilinear_point(model, A, B, C, 'a*(2*a**(2) - b**(2) - c**(2))', ID="X_187", classes=["center", "incident"])
            X_237 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A +  omega  )', ID="X_237", classes=["center", "incident"])
            central_line(model, X_187, X_237, 187, 237, incident=True)
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_878 = point_from_barycentrics(model, A, B, C, -0.14706477, 1.0752646, 0.071800149, ID="X_878", classes=["center", "incident"])
            central_line(model, X_25, X_878, 25, 878, incident=True)
            return promote_point_to_top(model, X_669)


        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_669 on the given reference triangle."""
            model = create_model('X_669 = CROSSDIFFERENCE OF X_2 AND X_39')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00669(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-00669.json"))
            write_center_svg(
                model_acute,
                here / "x-00669.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X669¶

X₆₆₉¶