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X₁₃₀₂¶

COLLINGS TRANSFORM OF X₃₈₁

X₁₃₀₂ (COLLINGS TRANSFORM OF X₃₈₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1302 = COLLINGS TRANSFORM OF X_381."""

        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,
            centroid_of,
            cevapoint,
            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_01302(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1302 = COLLINGS TRANSFORM OF X_381 on reference triangle ABC."""
            X_381 = eval_trilinear_point(model, A, B, C, '2*cos(B - C) - cos(A)', ID="X_381", classes=["center"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center"])
            X_1302 = cevapoint(model, A, B, C, X_381, X_523, ID="X_1302", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            central_line(model, X_2, X_74, 2, 74, incident=True)
            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_477 = eval_trilinear_point(model, A, B, C, '1/(4*cos(A) + cos(A - 2*B) + cos(A - 2*C) - 3*cos(B - C))', ID="X_477", classes=["center", "incident"])
            central_line(model, X_23, X_477, 23, 477, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_841 = point_from_barycentrics(model, A, B, C, 1.0412972, 0.27499895, -0.31629615, ID="X_841", classes=["center", "incident"])
            central_line(model, X_30, X_841, 30, 841, incident=True)
            return promote_point_to_top(model, X_1302)


        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_1302 on the given reference triangle."""
            model = create_model('X_1302 = COLLINGS TRANSFORM OF X_381')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01302(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-01302.json"))
            write_center_svg(
                model_acute,
                here / "x-01302.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1302¶

X₁₃₀₂¶