"""Programmatic construction for Book XI, Proposition 11 (XI.11).
From a given elevated point to draw a straight line perpendicular to a given
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 11 using geometor.model."""
model = Model("XI.11")
# Plane of reference boundary corners
P1 = model.set_point(sp.Rational(-46, 92), sp.Rational(42, 92), label="P1")
P2 = model.set_point(sp.Rational(113, 92), sp.Rational(42, 92), label="P2")
P3 = model.set_point(sp.Rational(97, 92), sp.Rational(-57, 92), label="P3")
P4 = model.set_point(sp.Rational(-58, 92), sp.Rational(-57, 92), label="P4")
# 1. Given elevated point A and random straight line BC in the plane of
# reference; AD drawn perpendicular to BC, DE at right angles to BC in
# the plane, AF perpendicular to DE, and GH through F parallel to BC.
F = model.set_point(0, 0, classes=["given"], ID="F")
A = model.set_point(0, 1, classes=["given"], ID="A")
D = model.set_point(sp.Rational(61, 92), sp.Rational(-24, 92), label="D")
E = model.set_point(sp.Rational(-36, 92), sp.Rational(15, 92), label="E")
B = model.set_point(sp.Rational(25, 92), sp.Rational(-43, 92), label="B")
C = model.set_point(sp.Rational(95, 92), sp.Rational(-6, 92), label="C")
G = model.set_point(sp.Rational(-31, 92), sp.Rational(-17, 92), label="G")
H = model.set_point(sp.Rational(60, 92), sp.Rational(32, 92), label="H")
# Collinear lines and sub-segments
model.construct_line(B, C)
model.set_section([B, D, C])
model.set_segment(B, D)
model.set_segment(D, C)
model.set_segment(B, C)
model.construct_line(E, D)
model.set_section([E, F, D])
model.set_segment(E, F)
model.set_segment(F, D)
model.set_segment(D, E)
model.construct_line(G, H)
model.set_section([G, F, H])
model.set_segment(G, F)
model.set_segment(F, H)
model.set_segment(G, H)
# Perpendiculars AD and AF
model.set_segment(A, D)
model.set_segment(A, F)
# Planes
model.set_polygon([P1, P2, P3, P4])
model.set_polygon([A, D, E])
return model
if __name__ == "__main__":
construct_g1()
