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X₁₂₉₉¶

COLLINGS TRANSFORM OF X₁₃₅

X₁₂₉₉ = reflection of X₄ in X₁₃₅

X₁₂₉₉ (COLLINGS TRANSFORM OF X₁₃₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1299 = COLLINGS TRANSFORM OF X_135."""

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


        def construct_x_01299(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1299 = COLLINGS TRANSFORM OF X_135 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_135 = eval_trilinear_point(model, A, B, C, '(sec(A))*((sin(2*B))/(sec(2*C) - sec(2*A)) + (sin(2*C))/(sec(2*A) - sec(2*B)))', ID="X_135", classes=["center"])
            X_1299 = reflection_in_point(model, X_4, X_135, ID="X_1299", classes=["selected", "target"], guide=False)
            X_24 = eval_trilinear_point(model, A, B, C, 'sec(A)*cos(2*A)', ID="X_24", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_24, X_110, 24, 110, incident=True)
            X_131 = point_from_barycentrics(model, A, B, C, 0.57236082, 0.12379803, 0.30384114, ID="X_131", classes=["center", "incident"])
            central_line(model, X_4, X_131, 4, 131, incident=True)
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_317 = eval_trilinear_point(model, A, B, C, 'sec(A)*cos(2*A)*(csc(A))**(2)', ID="X_317", classes=["center", "incident"])
            central_line(model, X_99, X_317, 99, 317, incident=True)
            return promote_point_to_top(model, X_1299)


        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_1299 on the given reference triangle."""
            model = create_model('X_1299 = COLLINGS TRANSFORM OF X_135')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01299(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-01299.json"))
            write_center_svg(
                model_acute,
                here / "x-01299.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1299¶

X₁₂₉₉¶