G.571 cylinder cut plane — Code

XII.13

If a cylinder be cut by a plane which is parallel to its opposite planes, then, as the cylinder is to the cylinder, so will the axis be to the axis.
P L Q R N S A E B G K H C F D T O U V M W 
"""Programmatic construction for Book XII, Proposition 13 (XII.13).

        Cylinder AD cut by plane GH parallel to opposite planes AB, CD, with axis EF
        produced to L and M, and circles PQ, RS, AB, GH, CD, TU, VW about centers
        L, N, E, K, F, O, M.
        """

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0421.g1 using geometor.model."""
            model = Model("XII.13")

            # Axis centers from left to right
            L = model.set_point(41.0, -60.5, classes=["given"], ID="L")
            N = model.set_point(96.0, -60.5, classes=["given"], ID="N")
            E = model.set_point(158.0, -60.5, classes=["given"], ID="E")
            K = model.set_point(221.0, -60.5, classes=["given"], ID="K")
            F = model.set_point(256.0, -60.5, classes=["given"], ID="F")
            O = model.set_point(289.0, -60.5, classes=["given"], ID="O")
            M = model.set_point(321.0, -60.5, classes=["given"], ID="M")

            # Top generator points
            P = model.set_point(41.0, -25.0, classes=["given"], ID="P")
            R = model.set_point(96.0, -25.0, classes=["given"], ID="R")
            A = model.set_point(158.0, -25.0, classes=["given"], ID="A")
            G = model.set_point(221.0, -25.0, classes=["given"], ID="G")
            C = model.set_point(256.0, -25.0, classes=["given"], ID="C")
            T = model.set_point(289.0, -25.0, classes=["given"], ID="T")
            V = model.set_point(321.0, -25.0, classes=["given"], ID="V")

            # Bottom generator points
            Q = model.set_point(41.0, -96.0, classes=["given"], ID="Q")
            S = model.set_point(96.0, -96.0, classes=["given"], ID="S")
            B = model.set_point(158.0, -96.0, classes=["given"], ID="B")
            H = model.set_point(221.0, -96.0, classes=["given"], ID="H")
            D = model.set_point(256.0, -96.0, classes=["given"], ID="D")
            U = model.set_point(289.0, -96.0, classes=["given"], ID="U")
            W = model.set_point(321.0, -96.0, classes=["given"], ID="W")

            # Circular sections (modeled as circles in 3D, rendered as ellipses in SVG)
            for center, top in [
                (L, P), (N, R), (E, A), (K, G), (F, C), (O, T), (M, V),
            ]:
                model.construct_circle(center, top)

            # Generator segments and axis sub-segments
            for p1, p2 in [
                (P, V), (Q, W),
                (L, N), (N, E), (E, K), (K, F), (F, O), (O, M),
                (E, F), (L, M), (K, L), (K, M),
            ]:
                model.set_segment(p1, p2)

            # Cylindrical sub-regions
            model.set_polygon([A, B, D, C])  # Cylinder AD
            model.set_polygon([A, B, H, G])  # Cylinder BG / GB
            model.set_polygon([G, H, D, C])  # Cylinder GD
            model.set_polygon([P, Q, W, V])  # Cylinder PW
            model.set_polygon([P, Q, S, R])  # Cylinder QR
            model.set_polygon([R, S, B, A])  # Cylinder RB
            model.set_polygon([P, Q, H, G])  # Cylinder QG
            model.set_polygon([G, H, W, V])  # Cylinder WG / GW

            return model


        if __name__ == "__main__":
            construct_g1()