"""Programmatic construction for Book XI, Proposition 6 (XI.6).
If two straight lines be at right angles to the same plane, the straight lines
will be 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 6 using geometor.model."""
model = Model("XI.6")
# Perspective plane of reference corners
P1 = model.set_point(sp.Rational(-112, 77), sp.Rational(34, 77), label="P1")
P2 = model.set_point(sp.Rational(47, 77), sp.Rational(35, 77), label="P2")
P3 = model.set_point(sp.Rational(6, 77), sp.Rational(-53, 77), label="P3")
P4 = model.set_point(sp.Rational(-129, 77), sp.Rational(-53, 77), label="P4")
# 1. Let the two straight lines AB, CD be at right angles to the plane of
# reference, meeting it at the points B, D.
B = model.set_point(0, 0, classes=["given"], ID="B")
A = model.set_point(0, 1, classes=["given"], ID="A")
D = model.set_point(sp.Rational(-85, 77), sp.Rational(-14, 77), classes=["given"], label="D")
C = model.set_point(sp.Rational(-86, 77), sp.Rational(75, 77), classes=["given"], label="C")
# 2. Let BD be joined, and let DE be drawn in the plane of reference at
# right angles to BD, with DE made equal to AB.
E = model.set_point(sp.Rational(-70, 77), sp.Rational(-42, 77), label="E")
# 3. Join BE, AE, AD.
model.set_segment(A, B)
model.set_segment(C, D)
model.set_segment(B, D)
model.set_segment(D, E)
model.set_segment(B, E)
model.set_segment(A, E)
model.set_segment(A, D)
# Plane of reference boundary
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])
# Triangles and planes compared in the proof
model.set_polygon([A, B, D])
model.set_polygon([E, D, B])
model.set_polygon([A, B, E])
model.set_polygon([E, D, A])
model.set_polygon([B, D, A, C])
return model
if __name__ == "__main__":
construct_g1()
