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X₁₉₈₀¶

BARYCENTRIC PRODUCT OF PU(42)

X₁₉₈₀ (BARYCENTRIC PRODUCT OF PU(42)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1980 = BARYCENTRIC PRODUCT OF PU(42)."""

        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,
            crosspoint,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01980(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1980 = BARYCENTRIC PRODUCT OF PU(42) on reference triangle ABC."""
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center"])
            X_692 = eval_trilinear_point(model, A, B, C, 'a**(2)/(b - c)', ID="X_692", classes=["center"])
            X_1980 = crosspoint(model, A, B, C, X_32, X_692, ID="X_1980", classes=["selected", "target"])
            X_669 = eval_trilinear_point(model, A, B, C, 'a**(3)*(b**(2) - c**(2))', ID="X_669", classes=["center", "incident"])
            X_688 = eval_trilinear_point(model, A, B, C, '(a**(3)*(b**(4) - c**(4)))', ID="X_688", classes=["center", "incident"])
            central_line(model, X_669, X_688, 669, 688, incident=True)
            X_667 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b - c)', ID="X_667", classes=["center", "incident"])
            X_838 = eval_trilinear_point(model, A, B, C, '(a**(2)*(b**(4) - c**(4)) + a**(3)*(b**(3) - c**(3)))', ID="X_838", classes=["center", "incident"])
            central_line(model, X_667, X_838, 667, 838, incident=True)
            X_813 = eval_trilinear_point(model, A, B, C, '1/(a**(-2)*(b**(1) - c**(1)) + a**(0)*(b**(-1) - c **(-1)))', ID="X_813", classes=["center", "incident"])
            X_929 = point_from_barycentrics(model, A, B, C, -0.17117605, 0.60497835, 0.56619769, ID="X_929", classes=["center", "incident"])
            central_line(model, X_813, X_929, 813, 929, incident=True)
            return promote_point_to_top(model, X_1980)


        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_1980 on the given reference triangle."""
            model = create_model('X_1980 = BARYCENTRIC PRODUCT OF PU(42)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01980(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-01980.json"))
            write_center_svg(
                model_acute,
                here / "x-01980.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1980¶

X₁₉₈₀¶