G.536 describe on a given segment a parallelepipedal solid — Code

XI.27

Describe on a given segment a parallelepipedal solid similar and similarly situated to a given parallelepipedal solid.
D F G C E L H M K A B 
"""Programmatic construction for Book XI, Proposition 27 (XI.27).

        On a given straight line AB describe a parallelepipedal solid AL similar and
        similarly situated to a given parallelepipedal solid CD.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for Book XI, Proposition 27 using geometor.model."""
            model = Model("XI.27")

            # Given parallelepipedal solid CD
            C = model.set_point(sp.Rational(32, 100), sp.Rational(-128, 100), classes=["given"], label="C")
            E = model.set_point(sp.Rational(171, 100), sp.Rational(-128, 100), classes=["given"], label="E")
            F = model.set_point(sp.Rational(18, 100), sp.Rational(-52, 100), classes=["given"], label="F")
            Fr = model.set_point(sp.Rational(157, 100), sp.Rational(-52, 100), label="Fr")
            G = model.set_point(sp.Rational(49, 100), sp.Rational(-97, 100), classes=["given"], label="G")
            Db = model.set_point(sp.Rational(188, 100), sp.Rational(-97, 100), label="Db")
            Gt = model.set_point(sp.Rational(35, 100), sp.Rational(-28, 100), label="Gt")
            D = model.set_point(sp.Rational(174, 100), sp.Rational(-28, 100), classes=["given"], label="D")

            # Constructed parallelepipedal solid AL on AB
            A = model.set_point(sp.Rational(292, 100), sp.Rational(-119, 100), classes=["given"], label="A")
            B = model.set_point(sp.Rational(375, 100), sp.Rational(-119, 100), classes=["given"], label="B")
            H = model.set_point(sp.Rational(285, 100), sp.Rational(-77, 100), label="H")
            M = model.set_point(sp.Rational(368, 100), sp.Rational(-77, 100), label="M")
            K = model.set_point(sp.Rational(302, 100), sp.Rational(-104, 100), label="K")
            Lb = model.set_point(sp.Rational(385, 100), sp.Rational(-104, 100), label="Lb")
            Kt = model.set_point(sp.Rational(295, 100), sp.Rational(-62, 100), label="Kt")
            L = model.set_point(sp.Rational(378, 100), sp.Rational(-62, 100), label="L")

            # Edges
            for u, v in [
                (C, E), (C, F), (C, G), (F, Fr), (Fr, E), (G, Db), (Db, E), (Gt, D), (D, Db), (Gt, G), (Gt, F), (D, Fr),
                (A, B), (A, H), (A, K), (H, M), (M, B), (K, Lb), (Lb, B), (Kt, L), (L, Lb), (Kt, K), (Kt, H), (L, M),
            ]:
                model.set_segment(u, v)

            # Faces
            for poly in [
                [C, G, Db, E],
                [C, F, Gt, G],
                [C, F, Fr, E],
                [A, K, Lb, B],
                [A, H, Kt, K],
                [A, H, M, B],
            ]:
                model.set_polygon(poly)

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

            return model


        if __name__ == "__main__":
            construct_g1()