"""Programmatic construction for Book XI, Proposition 12 (XI.12).
To set up a straight line at right angles to a given plane from a given point
in it.
"""
from __future__ import annotations
import sympy as sp
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure for Book XI, Proposition 12 using geometor.model."""
model = Model("XI.12")
# Plane of reference boundary corners
P1 = model.set_point(sp.Rational(-23, 107), sp.Rational(55, 107), label="P1")
P2 = model.set_point(sp.Rational(112, 107), sp.Rational(56, 107), label="P2")
P3 = model.set_point(sp.Rational(77, 107), sp.Rational(-27, 107), label="P3")
P4 = model.set_point(sp.Rational(-42, 107), sp.Rational(-28, 107), label="P4")
# 1. Given point A in the plane of reference, and elevated point B;
# BC drawn perpendicular to the plane, and AD drawn parallel to BC.
A = model.set_point(0, 0, classes=["given"], ID="A")
D = model.set_point(0, 1, ID="D")
C = model.set_point(sp.Rational(76, 107), sp.Rational(28, 107), label="C")
B = model.set_point(sp.Rational(75, 107), sp.Rational(112, 107), classes=["given"], label="B")
model.set_segment(A, D)
model.set_segment(B, C)
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])
return model
if __name__ == "__main__":
construct_g1()
