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X₁₈₇₅¶

ZOSMA TRANSFORM OF X₅₁₅

X₁₈₇₅ = midpoint of X₁₇₈₅ and X₁₈₄₅

X₁₈₇₅ (ZOSMA TRANSFORM OF X₅₁₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1875 = ZOSMA TRANSFORM OF X_515."""

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


        def construct_x_01875(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1875 = ZOSMA TRANSFORM OF X_515 on reference triangle ABC."""
            X_1785 = eval_trilinear_point(model, A, B, C, '(sec(A))*(cos(B) + cos(C) - 1)', ID="X_1785", classes=["center"])
            X_1845 = point_from_barycentrics(model, A, B, C, 0.12337662, 0.012987013, 0.86363636, ID="X_1845", classes=["center"])
            X_1875 = midpoint(model, X_1785, X_1845, ID="X_1875", classes=["selected", "target"], guide=False)
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_34 = eval_trilinear_point(model, A, B, C, '1 - sec(A)', ID="X_34", classes=["center", "incident"])
            central_line(model, X_25, X_34, 25, 34, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            central_line(model, X_4, X_65, 4, 65, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_945 = eval_trilinear_point(model, A, B, C, '(a/(3*a**(4) - 2*a**(3)*(b + c) + (b - c)**(2)*(2*a*b + 2*a*c - 2*b*c - b**(2) - c**(2) - 2*a**(2))))', ID="X_945", classes=["center", "incident"])
            central_line(model, X_1, X_945, 1, 945, incident=True)
            return promote_point_to_top(model, X_1875)


        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_1875 on the given reference triangle."""
            model = create_model('X_1875 = ZOSMA TRANSFORM OF X_515')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01875(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-01875.json"))
            write_center_svg(
                model_acute,
                here / "x-01875.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1875¶

X₁₈₇₅¶