G.577 spheres center inscribe — Code

XII.17

Given two spheres about the same center, to inscribe in the greater sphere a polyhedral solid which does not touch the lesser sphere at its surface.
O R U Q T P S X Z B V W K G C H A F E M L N D 
"""Programmatic construction for Book XII, Proposition 17 (XII.17).

        Two concentric spheres about center A, with great circle BCDE in the outer
        sphere, circle FGH in the inner sphere, perpendicular semicircles BOD and KON,
        and polyhedral facets KBPS, SPQT, TQRU, URO.
        """

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0429.g1 using geometor.model."""
            model = Model("XII.17")

            # Center A and main poles/diameters
            A = model.set_point(250.0, -252.5, classes=["given"], ID="A")
            O = model.set_point(250.0, -23.5, classes=["given"], ID="O")
            B = model.set_point(479.0, -252.5, classes=["given"], ID="B")
            D = model.set_point(21.0, -252.5, classes=["given"], ID="D")

            # Inner sphere circle FGH points
            G = model.set_point(386.0, -252.5, classes=["given"], ID="G")
            H = model.set_point(281.9, -205.0, classes=["given"], ID="H")
            F = model.set_point(218.1, -300.0, classes=["given"], ID="F")

            # Equatorial ellipse BCDE points
            C = model.set_point(312.0, -160.1, classes=["given"], ID="C")
            E = model.set_point(188.0, -344.9, classes=["given"], ID="E")
            M = model.set_point(265.0, -348.3, classes=["given"], ID="M")
            L = model.set_point(340.0, -340.8, classes=["given"], ID="L")
            K = model.set_point(412.4, -320.2, classes=["given"], ID="K")
            N = model.set_point(87.6, -184.8, classes=["given"], ID="N")

            # Quadrant BO points
            R = model.set_point(337.6, -40.9, classes=["given"], ID="R")
            Q = model.set_point(411.9, -90.6, classes=["given"], ID="Q")
            P = model.set_point(461.6, -164.9, classes=["given"], ID="P")

            # Quadrant KO points
            U = model.set_point(331.0, -51.2, classes=["given"], ID="U")
            T = model.set_point(388.0, -118.9, classes=["given"], ID="T")
            S = model.set_point(416.8, -207.2, classes=["given"], ID="S")

            # Foot of perpendiculars and auxiliary points V, W, Z, X
            V = model.set_point(461.6, -252.5, classes=["given"], ID="V")
            W = model.set_point(401.6, -315.7, classes=["given"], ID="W")
            Z = model.set_point(456.0, -252.5, classes=["given"], ID="Z")
            X = model.set_point(445.0, -232.0, classes=["given"], ID="X")

            # Concentric spheres / circles
            model.construct_circle(A, B)
            model.construct_circle(A, G)

            # Segments
            for p1, p2 in [
                (D, A), (A, G), (G, Z), (Z, V), (V, B),
                (D, B), (A, B), (A, V), (B, V), (D, Z), (B, Z), (A, Z),
                (C, H), (H, A), (A, F), (F, E), (C, E),
                (N, A), (A, W), (W, K), (A, K), (K, N),
                (A, O),
                (B, K), (K, L), (L, M), (M, E),
                (B, P), (P, Q), (Q, R), (R, O),
                (K, S), (S, T), (T, U), (U, O),
                (S, P), (T, Q), (U, R),
                (P, V), (S, W), (W, V),
                (A, X), (B, X), (K, X),
                (K, Z), (K, D),
            ]:
                model.set_segment(p1, p2)

            # Polyhedral facets
            model.set_polygon([K, B, P, S])
            model.set_polygon([S, P, Q, T])
            model.set_polygon([T, Q, R, U])
            model.set_polygon([U, R, O])

            return model


        if __name__ == "__main__":
            construct_g1()