G.523 planes cut right — Code

XI.19

If two planes which cut one another be at right angles to any plane, their common section is at right angles to the same plane.
B E F D A C 
"""Programmatic construction for Book XI, Proposition 19 (XI.19).

        If two planes which cut one another be at right angles to any plane, their
        common section will also be at right angles to the same plane.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for Book XI, Proposition 19 using geometor.model."""
            model = Model("XI.19")

            # Plane of reference boundary corners
            P1 = model.set_point(sp.Rational(-83, 91), sp.Rational(45, 91), label="P1")
            P2 = model.set_point(sp.Rational(81, 91), sp.Rational(45, 91), label="P2")
            P3 = model.set_point(sp.Rational(48, 91), sp.Rational(-55, 91), label="P3")
            P4 = model.set_point(sp.Rational(-106, 91), sp.Rational(-55, 91), label="P4")

            # 1. Let the two planes AB, BC be at right angles to the plane of reference,
            #    and let BD be their common section.
            D = model.set_point(0, 0, classes=["given"], ID="D")
            B = model.set_point(0, 1, classes=["given"], ID="B")
            A = model.set_point(sp.Rational(-63, 91), sp.Rational(-55, 91), classes=["given"], label="A")
            C = model.set_point(sp.Rational(34, 91), sp.Rational(-55, 91), classes=["given"], label="C")

            # Outer corners of planes AB and BC
            A_top = model.set_point(sp.Rational(-63, 91), sp.Rational(57, 91), label="A_top")
            B_right_top = model.set_point(sp.Rational(53, 91), sp.Rational(119, 91), label="B_right_top")
            B_right_bot = model.set_point(sp.Rational(53, 91), sp.Rational(45, 91), label="B_right_bot")

            C_top = model.set_point(sp.Rational(34, 91), sp.Rational(54, 91), label="C_top")
            B_left_top = model.set_point(sp.Rational(-25, 91), sp.Rational(119, 91), label="B_left_top")
            B_left_bot = model.set_point(sp.Rational(-25, 91), sp.Rational(53, 91), label="B_left_bot")

            # 2. From D let DE be drawn in plane AB at right angles to AD, and DF in
            #    plane BC at right angles to CD.
            E = model.set_point(sp.Rational(-16, 91), sp.Rational(53, 91), label="E")
            F = model.set_point(sp.Rational(9, 91), sp.Rational(57, 91), label="F")

            # Segments
            model.set_segment(B, D)
            model.set_segment(A, D)
            model.set_segment(C, D)
            model.set_segment(D, E)
            model.set_segment(D, F)
            model.set_segment(A, B_right_bot)

            # Plane boundaries and polygons
            model.set_segment(P1, P2)
            model.set_segment(P2, P3)
            model.set_segment(P3, P4)
            model.set_segment(P4, P1)
            model.set_polygon([P1, P2, P3, P4])

            model.set_polygon([A, A_top, B_right_top, B_right_bot])
            model.set_polygon([C, C_top, B_left_top, B_left_bot, D])

            return model


        if __name__ == "__main__":
            construct_g1()