def test_join(self):
p1 = Point(1, 1, 4, 0)
p2 = Point(2, 1, 5, 0)
p3 = Point(3, 4, 6, 0)
p4 = Point(0, 2, 7, 0)
p5 = Point(1, 5, 8, 0)
# 4 points
assert join(p1, p2, p3, p4).contains(p5)
# 3 points
assert join(p1, p2, p3).contains(p3)
# two lines
l = Line(p1, p2)
m = Line(p3, p4)
assert join(l, m) == Plane(p1, p2, p3, p4)
# coplanar lines
l = Line(p1, p2)
m = Line(p1, p3)
assert join(l, m).contains(p3)
# point and line
p = join(l, p3)
assert p == join(p1, p2, p3)
# 2 points
l = p1.join(p2)
assert l.contains(Point(3, 1, 6, 0))
def test_pappos():
a1 = Point(0, 1)
b1 = Point(1, 2)
c1 = Point(2, 3)
a2 = Point(0, 0)
b2 = Point(1, 0)
c2 = Point(2, 0)
p = a1.join(b2).meet(b1.join(a2))
q = b1.join(c2).meet(c1.join(b2))
r = c1.join(a2).meet(a1.join(c2))
assert is_collinear(p, q, r)
def test_join(self):
p1 = Point(1, 1, 0)
p2 = Point(2, 1, 0)
p3 = Point(3, 4, 0)
p4 = Point(0, 2, 0)
# 3 points
assert join(p1, p2, p3).contains(p4)
# 2 points
l = p1.join(p2)
assert l.contains(Point(3, 1, 0))
# two lines
m = Line(Point(0, 0, 0), Point(1, 2, 0))
assert join(l, m) == Plane(0, 0, 1, 0)
# point and line
p = join(l, p3)
assert p.contains(p4)
def test_join(self):
p = Point(1, 0)
q = Point(0, 1)
assert p.join(q) == Line(-1, -1, 1)
