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X₁₃₁₀¶

COLLINGS TRANSFORM OF X₉₄₀

X₁₃₁₀ (COLLINGS TRANSFORM OF X₉₄₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1310 = COLLINGS TRANSFORM OF X_940."""

        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,
            cevapoint,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01310(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1310 = COLLINGS TRANSFORM OF X_940 on reference triangle ABC."""
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center"])
            X_940 = eval_trilinear_point(model, A, B, C, '(a**(2) + a*(b + c) + 2*b*c)', ID="X_940", classes=["center"])
            X_1310 = cevapoint(model, A, B, C, X_513, X_940, ID="X_1310", classes=["selected", "target"])
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_336 = eval_trilinear_point(model, A, B, C, 'csc(A)*cot(A)*sec(A +  omega  )', ID="X_336", classes=["center", "incident"])
            central_line(model, X_98, X_336, 98, 336, incident=True)
            X_108 = eval_trilinear_point(model, A, B, C, 'a/(sec(B) - sec(C))', ID="X_108", classes=["center", "incident"])
            X_664 = eval_trilinear_point(model, A, B, C, '1/(a*(b - c)*(b + c - a))', ID="X_664", classes=["center", "incident"])
            central_line(model, X_108, X_664, 108, 664, incident=True)
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center", "incident"])
            X_662 = eval_trilinear_point(model, A, B, C, '1/(cot(B) - cot(C))', ID="X_662", classes=["center", "incident"])
            central_line(model, X_112, X_662, 112, 662, incident=True)
            return promote_point_to_top(model, X_1310)


        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_1310 on the given reference triangle."""
            model = create_model('X_1310 = COLLINGS TRANSFORM OF X_940')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01310(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-01310.json"))
            write_center_svg(
                model_acute,
                here / "x-01310.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1310¶

X₁₃₁₀¶