"""Programmatic construction for Book XI, Proposition 16 (XI.16).
If two parallel planes be cut by any plane, their common sections are parallel.
"""
from __future__ import annotations
import sympy as sp
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure for Book XI, Proposition 16 using geometor.model."""
model = Model("XI.16")
# 1. Let the two parallel planes AB, CD be cut by the plane EFGH,
# and let EF, GH be their common sections.
E = model.set_point(0, 1, classes=["given"], ID="E")
F = model.set_point(sp.Rational(100, 106), 1, classes=["given"], label="F")
G = model.set_point(sp.Rational(25, 106), 0, classes=["given"], label="G")
H = model.set_point(sp.Rational(146, 106), 0, classes=["given"], label="H")
# 2. Suppose EF, GH produced meet at K.
K = model.set_point(sp.Rational(366, 106), sp.Rational(36, 106), label="K")
# Plane AB corners
B1 = model.set_point(sp.Rational(9, 106), sp.Rational(142, 106), label="B1")
B = model.set_point(sp.Rational(110, 106), sp.Rational(142, 106), classes=["given"], label="B")
B3 = model.set_point(sp.Rational(95, 106), sp.Rational(89, 106), label="B3")
A = model.set_point(sp.Rational(-4, 106), sp.Rational(89, 106), classes=["given"], label="A")
# Plane CD corners
D1 = model.set_point(sp.Rational(34, 106), sp.Rational(28, 106), label="D1")
D = model.set_point(sp.Rational(166, 106), sp.Rational(28, 106), classes=["given"], label="D")
D3 = model.set_point(sp.Rational(120, 106), sp.Rational(-36, 106), label="D3")
C = model.set_point(sp.Rational(12, 106), sp.Rational(-36, 106), classes=["given"], label="C")
# Segments and sections
model.set_segment(E, F)
model.set_segment(F, K)
model.set_segment(E, K)
model.set_section([E, F, K])
model.set_segment(G, H)
model.set_segment(H, K)
model.set_segment(G, K)
model.set_section([G, H, K])
model.set_segment(E, G)
model.set_segment(F, H)
# Planes
model.set_polygon([B1, B, B3, A])
model.set_polygon([D1, D, D3, C])
model.set_polygon([E, F, H, G])
return model
if __name__ == "__main__":
construct_g1()
