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X₆₅₆¶

CROSSDIFFERENCE OF X₁ AND X₁₉

X₆₅₆ = crossdifference of every pair of points on line {1, 19}

X₆₅₆ (CROSSDIFFERENCE OF X₁ AND X₁₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_656 = CROSSDIFFERENCE OF X_1 AND X_19."""

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


        def construct_x_00656(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_656 = CROSSDIFFERENCE OF X_1 AND X_19 on reference triangle ABC."""
            X_162 = eval_trilinear_point(model, A, B, C, '1/(sin(2*B) - sin(2*C))', ID="X_162", classes=["center"])
            X_656 = isogonal_conjugate(model, A, B, C, X_162, ID="X_656", 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_240 = eval_trilinear_point(model, A, B, C, 'sec(A)*cos(A +  omega  )', ID="X_240", 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_240, X_522, 240, 522, incident=True)
            X_521 = eval_trilinear_point(model, A, B, C, '(sec(B) - sec(C))*(csc(A))', ID="X_521", classes=["center", "incident"])
            X_810 = eval_trilinear_point(model, A, B, C, 'sin(2*A)*((cos(B))**(2) - (cos(C))**(2))', ID="X_810", classes=["center", "incident"])
            central_line(model, X_521, X_810, 521, 810, incident=True)
            return promote_point_to_top(model, X_656)


        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_656 on the given reference triangle."""
            model = create_model('X_656 = CROSSDIFFERENCE OF X_1 AND X_19')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00656(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-00656.json"))
            write_center_svg(
                model_acute,
                here / "x-00656.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X656¶

X₆₅₆¶