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X₃₂₈₃¶

PERSPECTOR OF TRIANGLES S1S2S3 AND N1N2N3

X₃₂₈₃ is the perspector of triangles s1s2s3 and n1n2n3.

X₃₂₈₃ (PERSPECTOR OF TRIANGLES S1S2S3 AND N1N2N3) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3283 = PERSPECTOR OF TRIANGLES S1S2S3 AND N1N2N3."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03283(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3283 = PERSPECTOR OF TRIANGLES S1S2S3 AND N1N2N3 on reference triangle ABC."""
            X_3283 = eval_trilinear_point(model, A, B, C, '(cos(A) - 2*sin(B/3)*sin(C/3) + sin(A/3 -  pi  /6))', ID="X_3283", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_3277 = eval_trilinear_point(model, A, B, C, 'cos(A/3 - 4*pi  /3) + 2*cos(B/3 - 4*pi  /3)*cos(C/3 - 4*pi  /3)', ID="X_3277", classes=["center", "incident"])
            central_line(model, X_3, X_3277, 3, 3277, incident=True)
            X_1135 = eval_trilinear_point(model, A, B, C, 'cos(A/3 + 2*pi  /3)', ID="X_1135", classes=["center", "incident"])
            X_3279 = eval_trilinear_point(model, A, B, C, '(cos(B/3)*cos(C/3) + sin(A/3)*sin(2*A/3))', ID="X_3279", classes=["center", "incident"])
            central_line(model, X_1135, X_3279, 1135, 3279, incident=True)
            X_1137 = eval_trilinear_point(model, A, B, C, '(cos(A/3 + 4*pi  /3))', ID="X_1137", classes=["center", "incident"])
            X_3281 = eval_trilinear_point(model, A, B, C, '(2*cos(A/3) + cos(A) - 2*cos(B/3)*cos(C/3))', ID="X_3281", classes=["center", "incident"])
            central_line(model, X_1137, X_3281, 1137, 3281, incident=True)
            return promote_point_to_top(model, X_3283)


        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_3283 on the given reference triangle."""
            model = create_model('X_3283 = PERSPECTOR OF TRIANGLES S1S2S3 AND N1N2N3')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03283(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-03283.json"))
            write_center_svg(
                model_acute,
                here / "x-03283.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3283¶

X₃₂₈₃¶