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X₆₅₂¶

CROSSDIFFERENCE OF X₁ AND X₄

X₆₅₂ = crossdifference of every pair of points on line X₁ X₄

X₆₅₂ (CROSSDIFFERENCE OF X₁ AND X₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_652 = CROSSDIFFERENCE OF X_1 AND 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_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00652(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_652 = CROSSDIFFERENCE OF X_1 AND X_4 on reference triangle ABC."""
            X_652 = eval_trilinear_point(model, A, B, C, 'sec(B) - sec(C)', ID="X_652", classes=["selected", "target"])
            X_44 = eval_trilinear_point(model, A, B, C, 'b + c - 2*a', ID="X_44", classes=["center", "incident"])
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center", "incident"])
            central_line(model, X_44, X_513, 44, 513, incident=True)
            X_243 = eval_trilinear_point(model, A, B, C, '(sec(A))*((cos(A))**(2) - cos(B)*cos(C))', ID="X_243", classes=["center", "incident"])
            X_522 = eval_trilinear_point(model, A, B, C, '(cos(B) - cos(C))*(csc(A))', ID="X_522", classes=["center", "incident"])
            central_line(model, X_243, X_522, 243, 522, incident=True)
            X_520 = eval_trilinear_point(model, A, B, C, '(cos(A))*(sin(2*B) - sin(2*C))', ID="X_520", classes=["center", "incident"])
            X_647 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2))', ID="X_647", classes=["center", "incident"])
            central_line(model, X_520, X_647, 520, 647, incident=True)
            return promote_point_to_top(model, X_652)


        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_652 on the given reference triangle."""
            model = create_model('X_652 = CROSSDIFFERENCE OF X_1 AND X_4')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00652(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-00652.json"))
            write_center_svg(
                model_acute,
                here / "x-00652.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X652¶

X₆₅₂¶