G.506 segment set right — Code

XI.4

If a segment be set up at right angles to two segments which cut one another, at their common point of section, it is at right angles to the plane through them.
F A G D E C H B 
"""Programmatic construction for Book XI, Proposition 4 (XI.4)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0282.g1 using geometor.model."""
            model = Model("XI.4")

            # Plane of reference corners
            P1 = model.set_point(33.0, -60.0, classes=["plane_corner"])
            P2 = model.set_point(228.0, -60.0, classes=["plane_corner"])
            P3 = model.set_point(192.0, -155.0, classes=["plane_corner"])
            P4 = model.set_point(11.0, -155.0, classes=["plane_corner"])

            # Points in the plane of reference and elevated point F
            E = model.set_point(119.0, -107.0, classes=["given"], ID="E")
            F = model.set_point(119.0, -22.0, classes=["given"], ID="F")
            A = model.set_point(71.0, -86.0, classes=["given"], ID="A")
            B = model.set_point(162.0, -125.81, classes=["given"], ID="B")
            D = model.set_point(71.0, -131.0, classes=["given"], ID="D")
            C = model.set_point(162.0, -85.5, classes=["given"], ID="C")
            G = model.set_point(71.0, -103.0, ID="G")
            H = model.set_point(162.0, -110.58, ID="H")

            # Construction lines in the plane of reference
            model.construct_line(A, B)
            model.construct_line(C, D)
            model.construct_line(G, H)

            # Segments in the plane of reference
            model.set_segment(A, B)
            model.set_segment(A, E)
            model.set_segment(E, B)
            model.set_segment(C, D)
            model.set_segment(C, E)
            model.set_segment(E, D)
            model.set_segment(G, H)
            model.set_segment(G, E)
            model.set_segment(E, H)
            model.set_segment(A, D)
            model.set_segment(A, G)
            model.set_segment(G, D)
            model.set_segment(C, B)
            model.set_segment(C, H)
            model.set_segment(H, B)

            # Segments from F
            model.set_segment(E, F)
            model.set_segment(F, A)
            model.set_segment(F, G)
            model.set_segment(F, D)
            model.set_segment(F, C)
            model.set_segment(F, H)
            model.set_segment(F, B)

            # Sections
            model.set_section([G, E, H])
            model.set_section([A, E, B])
            model.set_section([C, E, D])

            # Polygons (triangles and plane of reference)
            model.set_polygon([P1, P2, P3, P4])
            model.set_polygon([A, E, D])
            model.set_polygon([C, E, B])
            model.set_polygon([A, G, E])
            model.set_polygon([B, E, H])
            model.set_polygon([A, E, F])
            model.set_polygon([B, E, F])
            model.set_polygon([C, E, F])
            model.set_polygon([D, E, F])
            model.set_polygon([F, A, D])
            model.set_polygon([F, B, C])
            model.set_polygon([F, A, G])
            model.set_polygon([F, B, H])
            model.set_polygon([F, E, G])
            model.set_polygon([F, E, H])

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

            return model


        if __name__ == "__main__":
            construct_g1()