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X₂₉₆₄¶

TRILINEAR PRODUCT X₆₁*X₆₂

X₂₉₆₄ (TRILINEAR PRODUCT X₆₁*X₆₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2964 = TRILINEAR PRODUCT X_61*X_62."""

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


        def construct_x_02964(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2964 = TRILINEAR PRODUCT X_61*X_62 on reference triangle ABC."""
            X_2962 = eval_trilinear_point(model, A, B, C, '(csc(A +  pi  /6)*csc(A -  pi  /6))', ID="X_2962", classes=["center"])
            X_2964 = isogonal_conjugate(model, A, B, C, X_2962, ID="X_2964", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            central_line(model, X_1, X_21, 1, 21, incident=True)
            X_484 = eval_trilinear_point(model, A, B, C, '1 + 2*(cos(A) - cos(B) - cos(C))', ID="X_484", classes=["center", "incident"])
            X_580 = point_from_barycentrics(model, A, B, C, 0.002197609, 0.25263713, 0.74516526, ID="X_580", classes=["center", "incident"])
            central_line(model, X_484, X_580, 484, 580, incident=True)
            X_36 = eval_trilinear_point(model, A, B, C, '1 - 2*cos(A)', ID="X_36", classes=["center", "incident"])
            X_1399 = eval_trilinear_point(model, A, B, C, '(cos(A) - cos(2*A))', ID="X_1399", classes=["center", "incident"])
            central_line(model, X_36, X_1399, 36, 1399, incident=True)
            return promote_point_to_top(model, X_2964)


        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_2964 on the given reference triangle."""
            model = create_model('X_2964 = TRILINEAR PRODUCT X_61*X_62')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02964(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-02964.json"))
            write_center_svg(
                model_acute,
                here / "x-02964.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2964¶

X₂₉₆₄¶