G.532 segment point construct — Code

XI.26

On a given segment, and at a given point on it, to construct a solid angle equal to a given solid angle.
H F L K C D G B E A 
"""Programmatic construction for Book XI, Proposition 26 (XI.26).

        On a given straight line AB and at point A on it, construct a solid angle A-BLH
        equal to a given solid angle D-CEF.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for Book XI, Proposition 26 using geometor.model."""
            model = Model("XI.26")

            # Plane of reference boundary
            P1 = model.set_point(sp.Rational(42, 100), sp.Rational(-97, 100), label="P1")
            P2 = model.set_point(sp.Rational(388, 100), sp.Rational(-97, 100), label="P2")
            P3 = model.set_point(sp.Rational(362, 100), sp.Rational(-238, 100), label="P3")
            P4 = model.set_point(sp.Rational(16, 100), sp.Rational(-238, 100), label="P4")
            model.set_polygon([P1, P2, P3, P4])

            # Given solid angle at D
            D = model.set_point(sp.Rational(68, 100), sp.Rational(-184, 100), classes=["given"], label="D")
            C = model.set_point(sp.Rational(134, 100), sp.Rational(-138, 100), classes=["given"], label="C")
            E = model.set_point(sp.Rational(138, 100), sp.Rational(-218, 100), classes=["given"], label="E")
            F = model.set_point(sp.Rational(156, 100), sp.Rational(-56, 100), classes=["given"], label="F")
            G = model.set_point(sp.Rational(156, 100), sp.Rational(-184, 100), label="G")

            # Constructed solid angle at A on AB
            A = model.set_point(sp.Rational(251, 100), sp.Rational(-218, 100), classes=["given"], label="A")
            B = model.set_point(sp.Rational(345, 100), sp.Rational(-168, 100), classes=["given"], label="B")
            L = model.set_point(sp.Rational(233, 100), sp.Rational(-125, 100), label="L")
            K = model.set_point(sp.Rational(306, 100), sp.Rational(-125, 100), label="K")
            H = model.set_point(sp.Rational(325, 100), sp.Rational(-22, 100), label="H")

            # Segments
            for u, v in [
                (D, C), (D, E), (D, F), (D, G),
                (F, C), (F, E), (F, G), (C, G), (E, G),
                (A, B), (A, L), (A, K), (A, H),
                (H, L), (H, K), (H, B), (L, K), (K, B),
            ]:
                model.set_segment(u, v)

            # Polygons
            for poly in [
                [E, D, C], [E, D, F], [F, D, C], [F, G, D], [F, G, E], [G, D, E],
                [B, A, L], [B, A, H], [H, A, L], [H, K, A], [H, K, B], [K, A, B],
            ]:
                model.set_polygon(poly)

            # Angles
            model.set_wedge(D, E, E, C)
            model.set_wedge(D, E, E, F)
            model.set_wedge(D, F, F, C)
            model.set_wedge(D, E, E, G)
            model.set_wedge(G, F, F, D)
            model.set_wedge(G, F, F, E)
            model.set_wedge(A, B, B, L)
            model.set_wedge(A, B, B, K)
            model.set_wedge(A, B, B, H)
            model.set_wedge(A, H, H, L)
            model.set_wedge(K, H, H, A)
            model.set_wedge(K, H, H, B)

            return model


        if __name__ == "__main__":
            construct_g1()