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pen_geom_tests.py
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# MIT-licensed; see LICENSE for details
from unittest import TestCase, skip
import pen_geom as g
from fractions import Fraction as Q
from pen_num import Number as Y, phi, inv_phi, sqrt5, alpha
from itertools import zip_longest
class PenGeomSanityCheck(TestCase):
'''Quick way to make sure tests in this module are being run'''
def test_hello_world(self):
self.assertEqual(2+2, 4)
#def test_error(self):
# self.assertTrue(False)
class TestPoint(TestCase):
def test_point_constructor_succeed(self):
cases = [
( (Y(0), Y(0)), Y(0, 0, 0, 0), Y(0, 0, 0, 0) ),
( (Y(1), Y(-4)), Y(1, 0, 0, 0), Y(-4, 0, 0, 0) ),
( (Y(0,2,0,0), Y(0,0,0,1)), Y(0, 2, 0, 0), Y(0, 0, 0, 1) ),
( (Q(-1,3), Q(4, 3)), Y(Q(-1,3), 0, 0, 0), Y(Q(4,3), 0, 0, 0) ),
( (5, 0), Y(5, 0, 0, 0), Y(0, 0, 0, 0) ),
( (g.Point(5, 0),), Y(5, 0, 0, 0), Y(0, 0, 0, 0) ),
( ('1/2', 2), Y(Q(1,2), 0, 0, 0), Y(2, 0, 0, 0) ),
]
for args, x, y in cases:
with self.subTest(args = args):
pt = g.Point(*args)
self.assertEqual(type(pt), g.Point)
self.assertEqual(pt.x, x)
self.assertEqual(pt.y, y)
def test_point_constructor_fail(self):
cases = [
( (), TypeError ),
( ((), ()), TypeError ),
( (Y(42),), TypeError ),
( (Y(14), False), TypeError ),
( (g.Point(1,1), 0), TypeError ),
( (g.Vector(1,1),), TypeError ),
( ('lkaskfdj',), TypeError ),
( ('bleh', True), TypeError ),
( ('xyzzy', 'plugh'), TypeError ),
]
for args, ex in cases:
with self.subTest(args = args):
self.assertRaises(ex, g.Point, *args)
def test_point_equality_and_hash(self):
P = g.Point
cases = [
(0, P(3, 4), P(Y(3,0,0,0), Y(4,0,0,0)), True),
(1, P(Y(0,1), 1), P(Y(0,1,0,0), Y(1,0,0,0)), True),
(2, P(3, 5), P(3, 4), False),
(3, P(Y('-864/227',1),0), P(Y('-863/227',1),0), False),
(4, P(Y('-864/227',1),0), P(0, 0), False),
(5, P(2, 3), P(3, 2), False),
(6, P('32/4', -2), P(8, '-2'), True),
(7, P(1, 1), P(1, 1), True),
(8, P(phi, -phi), P(phi, -phi), True),
(9, P(-phi, phi), P(-phi, phi), True),
(10, P(phi, -phi), P(-phi, phi), False),
(11, P(phi, phi), P(-phi, -phi), False),
(12, P(1, 0), g.Vector(1, 0), False),
]
for i, a, b, result in cases:
with self.subTest(i = i, a = a, b = b):
self.assertEqual(a == b, result)
self.assertEqual(b == a, result)
self.assertEqual(a != b, not result)
self.assertEqual(b != a, not result)
self.assertTrue(a == a)
self.assertTrue(b == b)
if result:
self.assertEqual(hash(a), hash(b))
def test_transform(self):
P, AT, ident = g.Point, g.AffineTransform, g.identity_transform
T, R, S = g.translation, g.rotation, g.scaling
cases = [
(0, P(0, 0), ident, P(0, 0)),
(1, P(phi, 1), ident, P(phi, 1)),
(2, P(2, -3), ident, P(2, -3)),
(3, P(0, 0), AT(0,2,3, 3,0,1), P(3, 1)),
(4, P(1, 0), AT(0,2,3, 3,0,1), P(3, 4)),
(5, P(0, 1), AT(0,2,3, 3,0,1), P(5, 1)),
(6, P(1, 1), R(5), P(-1, 1)),
(7, P(5, 4), R(-5) @ T(1,1), P(5, -6)),
(8, P(-1, -1), S(phi), P(-phi, -phi)),
]
for i, pt, trans, result in cases:
with self.subTest(i = i, pt = pt, trans = trans):
self.assertEqual(pt.transform(trans), result)
self.assertEqual(trans @ pt, result)
def test_subtraction_succeed(self):
P, V = g.Point, g.Vector
cases = [
(0, P(2, 3), P(0, 0), V(2, 3)),
(1, P(25, -9), P(2, -sqrt5), V(23, -9 + sqrt5)),
(2, P(35, 2), P(23, 24), V(12, -22)),
]
for i, a, b, c in cases:
with self.subTest(i = i, a = a, b = b):
self.assertEqual(a - b, c)
self.assertEqual(b - a, -c)
def test_subtraction_fail(self):
P, AT = g.Point, g.AffineTransform
cases = [
(0, P(0, 0), Y(0), TypeError),
(1, P(35, 0), AT(1,1,1,2,2,2), TypeError),
(2, P(25, -24), 'hello, world', TypeError),
(3, Q(25), P(0, 0), TypeError),
]
for i, a, b, ex in cases:
with self.subTest(i = i, a = a, b = b):
self.assertRaises(ex, (lambda x, y: x - y), a, b)
def test_addition_succeed(self):
P, V = g.Point, g.Vector
cases = [
(0, P(0, 0), V(0, 0), P(0, 0)),
(1, P(0, 0), V(254, -3), P(254, -3)),
(2, P(14, phi), V(-14, 0), P(0, phi)),
(3, P(Y(0,1),Q(1,3)), V(2, 3), P(Y(2,1), Y(Q(10,3)))),
]
for i, a, b, c in cases:
with self.subTest(i = i, a = a, b = b):
self.assertEqual(a + b, c)
self.assertEqual(b + a, c)
def test_addition_fail(self):
P = g.Point
cases = [
(0, P(0, 0), P(0, 0), TypeError),
(1, P(15, 2), P(-15, -2), TypeError),
(2, P(20, 2), Y(-23), TypeError),
(3, P(3, -3), False, TypeError),
]
for i, a, b, ex in cases:
with self.subTest(i = i, a = a, b = b):
self.assertRaises(ex, (lambda x, y: x + y), a, b)
self.assertRaises(ex, (lambda x, y: x + y), b, a)
def test_translate(self):
P, V = g.Point, g.Vector
cases = [
(0, P(0, 0), (0, 0), P(0, 0)),
(1, P(0, 0), (phi, -sqrt5), P(phi, -sqrt5)),
(2, P(-4, 2), (1, 1), P(-3, 3)),
(3, P(23, 2), (V(2, 4),), P(25, 6)),
]
for i, pt, args, result in cases:
with self.subTest(i = i, pt = pt, args = args):
self.assertEqual(pt.translate(*args), result)
def test_translate_fail(self):
P, V, R = g.Point, g.Vector, g.rotation
cases = [
(0, P(0, 0), (0,), TypeError),
(1, P(2, 3), (0,), TypeError),
(2, P(-3, 2), (Y(23),), TypeError),
(3, P(1, 1), (R(7), 2), TypeError),
(4, P(5, 6), (V(1,1), V(0,0)), TypeError),
(5, P(2, 43), (4, '1/q'), ValueError),
(6, P(2, 4), (V(2,3), 555), TypeError),
(7, P(23, 4), (), TypeError),
]
for i, pt, args, ex in cases:
with self.subTest(i = i, pt = pt, args = args):
self.assertRaises(ex, (lambda p, a: p.translate(*a)), pt, args)
def test_rotate(self):
P = g.Point
cases = [
(0, P(0, 0), 0, P(0, 0)),
(1, P(0, 0), 4, P(0, 0)),
(2, P(1, 0), 0, P(1, 0)),
(3, P(1, 0), 5, P(0, 1)),
(4, P(1, 0), 10, P(-1, 0)),
(5, P(1, 0), 15, P(0, -1)),
(6, P(1, 0), 20, P(1, 0)),
(7, P(0, 1), 0, P(0, 1)),
(8, P(0, 1), 5, P(-1, 0)),
(9, P(0, 1), 10, P(0, -1)),
(10, P(0, 1), 15, P(1, 0)),
(11, P(0, 1), 20, P(0, 1)),
(12, P(0, 1), 45, P(-1, 0)),
(13, P(0, 1), -15, P(-1, 0)),
(14, P(4, 0), 1, P(Y(0,1), Y(-6,0,Q(1,2)))),
]
for i, pt, theta, result in cases:
with self.subTest(i = i, pt = pt, theta = theta):
self.assertEqual(pt.rotate(theta), result)
def test_bbox(self):
cases = [
(0, 0, 0),
(1, 23, 4),
(2, -23, -234),
(3, phi, -sqrt5),
]
for i, x, y in cases:
with self.subTest(i = i, x = x, y = y):
self.assertEqual(g.Point(x, y).bbox(), g.Rectangle(x, y, x, y))
def test_as_offset_vector(self):
P, V = g.Point, g.Vector
cases = [
(P(0, 0), V(0, 0)),
(P(1, 0), V(1, 0)),
(P(0, 1), V(0, 1)),
(P(31,'1/2'), V(31,Q(1,2))),
(P(-5, phi), V(-5, phi))
]
for pt, vec in cases:
with self.subTest(pt = pt):
self.assertEqual(pt.as_offset_vector(), vec)
class TestVector(TestCase):
def test_vector_constructor_succeed(self):
cases = [
(0, (Y(0), Y(0)), Y(0,0,0,0), Y(0,0,0,0)),
(1, (0, 0), Y(0,0,0,0), Y(0,0,0,0)),
(2, (14, -2), Y(14,0,0,0), Y(-2,0,0,0)),
(3, (Q(1,4),Q(3,7)), Y(Q(1,4),0,0,0), Y(Q(3,7),0,0,0)),
(4, (Y(0,1),3), Y(0,1,0,0), Y(3,0,0,0)),
(5, (g.Vector(14,-2),), Y(14,0,0,0), Y(-2,0,0,0)),
(6, (g.Point(3,5),), Y(3,0,0,0), Y(5,0,0,0)),
]
for i, args, x, y in cases:
with self.subTest(i = i, args = args):
v = g.Vector(*args)
self.assertEqual(type(v), g.Vector)
self.assertEqual(v.x, x)
self.assertEqual(v.y, y)
def test_vector_constructor_fail(self):
V, P = g.Vector, g.Point
cases = [
(0, (), TypeError),
(1, (Y(3),), TypeError),
(2, (V(0,0), V(0,0)), TypeError),
(3, (P(3,1), P(2,-1)), TypeError),
(4, (V(3,2), P(1,1)), TypeError),
(5, (V(21,45), Y(2)), TypeError),
]
for i, args, ex in cases:
with self.subTest(i = i, args = args):
self.assertRaises(ex, g.Vector, *args)
def test_vector_equality_and_hash(self):
V = g.Vector
cases = [
(0, V(0, 0), V(0, 0), True),
(1, V(Y(0,1), Y('1/2')), V(Y(0,1),Q(1,2)), True),
(2, V(2, 3), V(3, 2), False),
(3, V(2, -3), V(2, 3), False),
(4, V(14, 4), g.Point(14, 4), False),
(5, V(Y(Q(-864,227),1),-2), V(0, -2), False),
(6, V(2, 3), V(-2, -3), False),
(7, V(1, phi + 1), V(1, phi + 1), True),
]
for i, a, b, result in cases:
with self.subTest(i = i, a = a, b = b):
self.assertEqual(a == b, result)
self.assertEqual(b == a, result)
self.assertTrue(a == a)
self.assertTrue(b == b)
if result:
self.assertEqual(hash(a), hash(b))
def test_negation(self):
V = g.Vector
cases = [
(0, V(0, 0), V(0, 0)),
(1, V(1, 0), V(-1, 0)),
(2, V(0, 1), V(0, -1)),
(3, V(13, sqrt5+1), V(-13, -1-sqrt5)),
(4, V(5, -2), V(-5, 2)),
(5, V(-1, -1), V(1, 1)),
]
for i, v, r in cases:
with self.subTest(i = i, vec = v):
self.assertEqual(-v, r)
self.assertEqual(v, -r)
def test_addition(self):
V = g.Vector
cases = [
(0, V(0, 0), V(0, 0), V(0, 0)),
(1, V(1, 0), V(0, 1), V(1, 1)),
(2, V(Q(1,2),-4), V(-2, Q(1,3)), V(Q(-3,2), Q(-11,3))),
(3, V(-5, 2), V(5, -2), V(0, 0)),
(4, V(phi, 2), V(-1, -1), V(inv_phi, 1)),
]
zero = g.Vector(0, 0)
for i, a, b, r in cases:
with self.subTest(i = i, a = a, b = b):
self.assertEqual(a + b, r)
self.assertEqual(b + a, r)
self.assertEqual(a + zero, a)
self.assertEqual(b + zero, b)
self.assertEqual(zero + a, a)
self.assertEqual(zero + b, b)
def test_subtraction(self):
V = g.Vector
cases = [
(0, V(5, 3), V(0, 0), V(5, 3)),
(1, V(0, 0), V(0, 0), V(0, 0)),
(2, V(3, 2), V(55, Q(10,3)), V(-52, Q(-4,3))),
(3, V(0, 0), V(1, 0), V(-1, 0)),
(4, V(45, -3), V(45, -3), V(0, 0)),
]
zero = g.Vector(0, 0)
for i, a, b, r in cases:
with self.subTest(i = i, a = a, b = b):
self.assertEqual(a - b, r)
self.assertEqual(b - a, -r)
self.assertEqual(a - zero, a)
self.assertEqual(b - zero, b)
self.assertEqual(zero - a, -a)
self.assertEqual(zero - b, -b)
with self.subTest(i = 999):
self.assertEqual(g.Point(5, 7) - V(2, 2), g.Point(3, 5))
def test_scalar_multiplication(self):
V = g.Vector
cases = [
(0, 1, V(3, -4), V(3, -4)),
(1, phi, V(Q(1,2), -2), V(Q(1,2)*phi, -2*phi)),
(2, Q(3,4), V(4, 15), V(3, Q(45,4))),
(3, 35, V(0, 0), V(0, 0)),
(4, 0, V(5*sqrt5, 33), V(0, 0)),
]
zero = g.Vector(0, 0)
for i, a, b, r in cases:
with self.subTest(i = i, a = a, b = b):
self.assertEqual(a * b, r)
self.assertEqual(b * a, r)
self.assertEqual(0 * b, zero)
self.assertEqual(1 * b, b)
def test_transform(self):
V, AT = g.Vector, g.AffineTransform
T, R, S = g.translation, g.rotation, g.scaling
cases = [
(0, V(35, phi - sqrt5), g.identity_transform, V(35, phi-sqrt5)),
(1, V(0, 0), T(4, Q(1,2)), V(0, 0)),
(2, V(3, 4), T(4, Q(1,2)), V(3, 4)),
(3, V(3, 4), S(3, -5), V(9, -20)),
(4, V(-4, 5), AT(3,8,11, 7,-5,-1000), V(28, -53)),
(5, V(1, 1), R(5), V(-1, 1)),
(6, V(1, 2), R(15), V(2, -1)),
]
for i, vec, trans, r in cases:
with self.subTest(i = i, vec = vec, trans = trans):
self.assertEqual(vec.transform(trans), r)
self.assertEqual(trans @ vec, r)
def test_rotate(self):
V = g.Vector
cases = [
(0, V(0, 0), 3, V(0, 0)),
(1, V(0, 0), -14, V(0, 0)),
(2, V(phi, Q(1,2)), -5, V(Q(1,2), -phi)),
(3, V(1, 0), 10, V(-1, 0)),
(4, V(4, 4), -1, V(Y(-6,1,Q(1,2),0),Y(6,1,Q(-1,2),0))),
]
for i, vec, theta, result in cases:
with self.subTest(i = i, vec = vec, theta = theta):
self.assertEqual(vec.rotate(theta), result)
def test_inner_product(self):
V = g.Vector
cases = [
(0, V(0, 0), V(5, 2), Y(0)),
(1, V(1, 0), V(1, 0), 1),
(2, V(1, 0), V(0, 1), 0),
(3, V(1, 2), V(-2, 3), 4),
(4, V(phi, 0), V(-inv_phi, 0), -1),
(5, V(33, 14), V(1, Q(-1,2)), 26),
]
zero = g.Vector(0, 0)
for i, a, b, r in cases:
with self.subTest(i = i, a = a, b = b):
self.assertEqual(a | b, r)
self.assertEqual(b | a, r)
self.assertEqual((-a) | b, -r)
self.assertEqual(a | (-b), -r)
self.assertEqual((3*a) | b, 3*r)
self.assertEqual(a | zero, 0)
self.assertEqual(b | zero, 0)
def test_cross_product(self):
V = g.Vector
cases = [
(0, V(0, 0), V(0, 0), 0),
(1, V(1, 0), V(0, 1), 1),
(2, V(1, 0), V(0, -1), -1),
(3, V(1, 1), V(0, 1), 1),
(4, V(5, 7), V(5, 7), 0),
(5, V(12, -3), V(-5, 14), 153),
(6, V(phi, 1), V(-1, phi), phi + 2),
]
zero = g.Vector(0, 0)
for i, a, b, r in cases:
with self.subTest(i = i, a = a, b = b):
self.assertEqual(a ^ b, r)
self.assertEqual(b ^ a, -r)
self.assertEqual((-a) ^ b, -r)
self.assertEqual(a ^ (-b), -r)
self.assertEqual((3*a) ^ b, 3*r)
self.assertEqual(a ^ zero, 0)
self.assertEqual(b ^ zero, 0)
self.assertEqual(a ^ a, 0)
self.assertEqual(b ^ b, 0)
class TestAffineTransform(TestCase):
def test_transform_constructor_succeed(self):
AT = g.AffineTransform
cases = [
((1,2,3, 4,5,6),
1, 2, 3, 4, 5, 6),
((phi,Y(1,-1),Q(1,3), 33,Q(-88,3),Y(4)),
phi, Y(1,-1), Q(1,3), 33, Q(-88,3), 4),
((AT(1,2,3, 4,5,6),),
1, 2, 3, 4, 5, 6),
]
for args, a, b, c, d, e, f in cases:
with self.subTest(args = args):
trans = g.AffineTransform(*args)
self.assertEqual(type(trans), g.AffineTransform)
self.assertTrue(all(
type(x) == Y for x in [trans.a,trans.b,trans.c,trans.d,trans.e,trans.f]
))
self.assertEqual(trans.a, a)
self.assertEqual(trans.b, b)
self.assertEqual(trans.c, c)
self.assertEqual(trans.d, d)
self.assertEqual(trans.e, e)
self.assertEqual(trans.f, f)
def test_transform_constructor_fail(self):
AT = g.AffineTransform
cases = [
(0, (1, 2, 3, 4), TypeError),
(1, (1, 2, 3, 4, 5, False), TypeError),
(2, (15,), TypeError),
(3, (), TypeError),
(4, (AT(0,0,0,0,0,0),1), TypeError),
(5, (None, 'hi there!'), TypeError),
]
for i, args, ex in cases:
with self.subTest(i = i, args = args):
self.assertRaises(ex, g.AffineTransform, *args)
def test_equals(self):
AT = g.AffineTransform
cases = [
(0, AT(1,2,3, 4,5,6), AT(1,2,3, 4,5,6), True),
(1, AT(Q(1,2),0,0, 0,Q(1,2),0), AT(Q(1,2),0,0, 0,Q(1,2),0), True),
(2, AT(1,0,0, 0,1,0), AT(1,0,1, 0,1,0), False),
(3, AT(0,0,0, 0,0,0), AT(1,2,3, 4,5,6), False),
(4, AT(3,3,1, 3,3,2), AT(3,3,1, 3,0,2), False),
]
for i, t1, t2, r in cases:
with self.subTest(i = i, t1 = str(t1), t2 = str(t2)):
self.assertEqual(t1 == t2, r)
self.assertEqual(t2 == t1, r)
self.assertTrue(t1 == t1)
self.assertTrue(t2 == t2)
def test_transform(self):
AT, T, R, S = g.AffineTransform, g.translation, g.rotation, g.scaling
cases = [
(0, AT(1,2,3, 4,5,6), AT(3,4,8, -1,2,-12), AT(19,26,41, 7,8,-3)),
(1, AT(1,0,0, 0,1,0), AT(0,0,0, 0,0,0), AT(0,0,0, 0,0,0)),
(2, T(1, 2), T(5, 7), T(6, 9)),
(3, T(-1, 3), S(5), T(-5,15)@S(5)),
(4, R(10), S(-1), g.identity_transform),
(5, S(-2,2), S(Q(-1,3),1), S(Q(2,3),2)),
(6, R(5), R(4), R(9)),
(7, T(1,1), R(5), T(-1,1)@R(5)),
]
for i, t1, t2, t3 in cases:
with self.subTest(i = i, t1 = str(t1), t2 = str(t2)):
self.assertEqual(t1.transform(t2), t3)
self.assertEqual(t2 @ t1, t3)
self.assertEqual(t1.transform(g.identity_transform), t1)
self.assertEqual(t2.transform(g.identity_transform), t2)
self.assertEqual(g.identity_transform.transform(t1), t1)
self.assertEqual(g.identity_transform.transform(t2), t2)
def test_negation(self):
AT, R, S = g.AffineTransform, g.rotation, g.scaling
cases = [
(0, AT(1,0,0, 0,1,0), AT(-1,0,0, 0,-1,0)),
(1, AT(1,0,2, 0,1,1), AT(-1,0,-2, 0,-1,-1)),
(2, AT(3,3,5, 3,7,0), AT(-3,-3,-5, -3,-7,0)),
(3, R(3), R(13)),
(4, S(1,-1), S(-1,1)),
(5, S(Q(1,3)), S(Q(-1,3))),
]
for i, trans, result in cases:
with self.subTest(i = i, trans = str(trans)):
self.assertEqual(-trans, result)
self.assertEqual(trans, -result)
def test_determinant(self):
AT, T, R, S = g.AffineTransform, g.translation, g.rotation, g.scaling
cases = [
(0, AT(3,3,5, 7,-2,188), Y(-27)),
(1, R(3), 1),
(2, R(15), 1),
(3, T(2324, 500*phi), 1),
(4, AT(1,1,2, 0,0,234), 0),
(5, T(-55, 55), 1),
(6, S(-1), 1),
(7, S(-2, 3), -6),
(8, S(14), 196),
]
for i, trans, det in cases:
with self.subTest(i = i, trans = str(trans)):
self.assertEqual(trans.det(), det)
self.assertEqual(trans.det(), det) # sanity check for memoization
self.assertEqual(type(trans.det()), Y)
self.assertEqual((-trans).det(), det)
def test_is_orientation_preserving(self):
AT, T, R, S = g.AffineTransform, g.translation, g.rotation, g.scaling
cases = [
(0, AT(3,0,23, 0,2,-1000), True),
(1, R(14), True),
(2, T(23523, Y(0,-2334)), True),
(3, g.identity_transform, True),
(4, S(100), True),
(5, S(-100), True),
(6, S(-1, 1), False),
(7, S(-5, -7), True),
(8, R(2) @ S(5), True),
]
for i, trans, result in cases:
with self.subTest(i = i, trans = str(trans)):
self.assertEqual(trans.is_orientation_preserving(), result)
self.assertEqual(trans.is_orientation_preserving(), result)
def test_is_conformal(self):
AT, T, R, S = g.AffineTransform, g.translation, g.rotation, g.scaling
cases = [
(0, g.identity_transform, True),
(1, S(-5), True),
(2, S(15), True),
(3, S(-5, 5), True),
(4, S(0), True),
(5, AT(3,3,2, 3,3,18), False),
(6, T(5, phi*3), True),
(7, R(1), True),
(8, AT(0,0,8, 0,1,9), False),
]
for i, trans, result in cases:
with self.subTest(i = i, trans = str(trans)):
self.assertEqual(trans.is_conformal(), result)
self.assertEqual(trans.is_conformal(), result)
class TestTransformFunctions(TestCase):
def test_identity_transform(self):
cases = [
g.Point(25, Q(-5,6)),
g.Vector(4, 6),
g.AffineTransform(1,2,3, 4,5,6),
g.Point(0, 0),
g.Point(1, 0),
g.Point(0, 1),
g.Vector(0, 0),
g.Vector(1, 0),
g.Vector(0, 1),
]
identity = g.identity_transform
for c in cases:
with self.subTest(case = str(c)):
self.assertEqual(c.transform(identity), c)
self.assertEqual(identity @ c, c)
def test_rotation(self):
P, V, AT = g.Point, g.Vector, g.AffineTransform
cases = [
(0, 0, P(1, 0), P(1, 0)),
(1, 5, P(1, 0), P(0, 1)),
(2, -15, P(0, 1), P(-1, 0)),
(3, 0, V(0, 2), V(0, 2)),
(4, 1, V(0, 3), V(Y(Q(9,2),0,Q(-3,8),0), Y(0,Q(3,4)))),
(5, 10, V(3, 55), V(-3, -55)),
(6, 5, AT(3,0,2, 0,3,8), AT(0,-3,-8, 3,0,2)),
]
for i, theta, x, r in cases:
with self.subTest(i = i, x = str(x), theta = theta):
self.assertEqual(x.transform(g.rotation(theta)), r)
self.assertEqual(x, r.transform(g.rotation(-theta)))
def test_scaling(self):
V, P, S = g.Vector, g.Point, g.scaling
cases = [
(0, (1,), V(1, 0), V(1, 0)),
(1, (1,), V(0, 1), V(0, 1)),
(2, (2, 3), V(4, 5), V(8, 15)),
(3, (-2,), P(1, 2), P(-2, -4)),
(4, (1, 4), S(Q(1,2)), S(Q(1,2),2)),
(5, (-2,), P(1, 17), P(-2, -34)),
]
for i, args, x, r in cases:
with self.subTest(i = i, x = str(x), args = args):
trans = g.scaling(*args)
self.assertEqual(x.transform(trans), r)
def test_translation(self):
P, V, AT = g.Point, g.Vector, g.AffineTransform
cases = [
(0, (3,5), P(1, 2), P(4, 7)),
(1, (3,5), V(1, 2), V(1, 2)),
(2, (V(3,5),), P(1, 2), P(4, 7)),
(3, (-8,2), AT(1,2,3, 4,5,6), AT(1,2,-5, 4,5,8)),
(4, (V(-8,2),), AT(1,2,3, 4,5,6), AT(1,2,-5, 4,5,8)),
(5, (4,-10), P(5, -7), P(9, -17)),
(6, (4,-10), V(5, -7), V(5, -7)),
]
for i, args, x, r in cases:
with self.subTest(i = i, x = str(x), args = args):
trans = g.translation(*args)
self.assertEqual(x.transform(trans), r)
class TestLineSegment(TestCase):
def test_constructor_succeed(self):
P, V = g.Point, g.Vector
cases = [
(0, (P(0,0), P(1,0)), P(0,0), P(1,0), V(1,0)),
(1, (P(1,0), P(0,0)), P(1,0), P(0,0), V(-1,0)),
(2, (P(-3,5), V(3,Q(2,3))), P(-3,5), P(0,Q(17,3)), V(3,Q(2,3))),
(3, (P(inv_phi,2), P(phi,-sqrt5)), P(inv_phi,2), P(phi,-sqrt5), V(1,-(2+sqrt5))),
(4, (P(14,2), V(-14,-2)), P(14,2), P(0,0), V(-14,-2)),
]
for i, args, begin, end, d in cases:
with self.subTest(i = i, args = args):
seg = g.LineSegment(*args)
self.assertEqual(type(seg), g.LineSegment)
self.assertEqual(seg.begin, begin)
self.assertEqual(seg.end, end)
self.assertEqual(seg.direction, d)
def test_constructor_fail(self):
P, V = g.Point, g.Vector
cases = [
(0, (P(1,2),), TypeError),
(1, (V(3,2), P(0,1)), TypeError),
(2, (P(3,3), P(3,3)), ValueError),
(3, (V(5,phi),), TypeError),
(4, (), TypeError),
(5, (P(14,6),V(0,0)), ValueError),
(6, (P(0,0),), TypeError),
]
for i, args, ex in cases:
with self.subTest(i = i, args = args):
self.assertRaises(ex, g.LineSegment, *args)
def test_equality(self):
LS = lambda d, e: g.LineSegment(g.Point(*d), g.Point(*e))
cases = [
(0, LS((0,0), (1,0)), LS((0,0), (1,0)), True),
(1, LS((0,0), (1,0)), LS((1,0), (0,0)), False), # order matters!
(2, LS((3,sqrt5), (5,2)), LS((-3,-sqrt5), (-5,-2)), False),
(3, LS((5,3), (2,1)), g.LineSegment(g.Point(5,3), g.Vector(-3,-2)), True),
(4, LS((3,inv_phi), (1,1)), LS((3,phi-1), (1,1)), True),
(5, LS((1,2), (3,4)), LS((1,2), (3,4)), True),
(6, LS((1,2), (3,4)), LS((1,2), (3,5)), False),
(7, LS((1,2), (3,4)), LS((1,2), (4,4)), False),
(8, LS((1,2), (3,4)), LS((1,3), (3,4)), False),
(9, LS((1,2), (3,4)), LS((0,2), (3,4)), False),
(10, LS((1,2), (88,4)), LS((2,3), (89,5)), False), # same direction, but still different
]
for i, a, b, result in cases:
with self.subTest(i = i, a = str(a), b = str(b)):
self.assertEqual(a == b, result)
self.assertEqual(b == a, result)
self.assertEqual(a != b, not result)
self.assertEqual(b != a, not result)
def test_addition(self):
LS = lambda d, e: g.LineSegment(g.Point(*d), g.Point(*e))
V = g.Vector
cases = [
(0, LS((5,7), (3,2)), V(0,0), LS((5,7), (3,2))),
(1, LS((5,7), (3,2)), V(-5,-7), LS((0,0), (-2,-5))),
(2, LS((-phi,0),(0,phi)), V(phi, phi), LS((0,phi), (phi,2*phi))),
(3, LS((0,0), (1,0)), V(0,-1), LS((0,-1), (1,-1))),
]
for i, seg, v, r in cases:
with self.subTest(i = i, seg = str(seg), v = str(v)):
self.assertEqual(seg + v, r)
self.assertEqual(v + seg, r)
def test_transform_succeed(self):
LS = lambda d, e: g.LineSegment(g.Point(*d), g.Point(*e))
AT, I, T, R, S = g.AffineTransform, g.identity_transform, g.translation, g.rotation, g.scaling
cases = [
(0, LS((0,0), (1,0)), I, LS((0,0), (1,0))),
(1, LS((3,5), (18,-7)), I, LS((3,5), (18,-7))),
(2, LS((2,3), (4,5)), R(5), LS((-3,2), (-5,4))),
(3, LS((phi,0), (phi,-phi)), S(inv_phi), LS((1,0), (1,-1))),
]
for i, seg, trans, r in cases:
with self.subTest(i = i, seg = str(seg), trans = str(trans)):
self.assertEqual(seg.transform(trans), r)
self.assertEqual(trans @ seg, r)
def test_transform_fail(self):
LS = lambda d, e: g.LineSegment(g.Point(*d), g.Point(*e))
AT, S = g.AffineTransform, g.scaling
cases = [
(0, LS((15,8), (-20,7)), S(0), ValueError),
(1, LS((15,8), (-20,8)), S(0,1), ValueError),
(2, LS((15,8), (15,7)), S(-1,0), ValueError),
(3, LS((12,8), (1,19)), AT(1,1,4, -1,-1,7), ValueError),
]
for i, seg, trans, ex in cases:
with self.subTest(i = i, seg = str(seg), trans = str(trans)):
self.assertRaises(ex, lambda s, t: s.transform(t), seg, trans)
self.assertRaises(ex, lambda s, t: t @ s, seg, trans)
def test_bbox(self):
LS = lambda d, e: g.LineSegment(g.Point(*d), g.Point(*e))
R = g.Rectangle
cases = [
(0, LS((0,0), (1,0)), R(0,0,1,0)),
(1, LS((3,5), (2,17)), R(2,5,3,17)),
(2, LS((-2,-phi), (-2,1)), R(-2,-phi,-2,1)),
(3, LS((15,9), (3,2)), R(3,2,15,9)),
]
for i, seg, bbox in cases:
with self.subTest(i = i, seg = str(seg)):
self.assertEqual(seg.bbox(), bbox)
class TestRectangle(TestCase):
def test_constructor_succeed(self):
P, V = g.Point, g.Vector
cases = [
(0, (P(1,2), P(3,5)), Y(1), Y(2), Y(3), Y(5)),
(1, (14, 2, -6, 8), Y(-6), Y(2), Y(14), Y(8)),
(2, (P(13,8), V(-4,-5)), 9, 3, 13, 8),
(3, (V(0,0), P(5,2)), 5, 2, 5, 2),
(4, (4, 5, -6, -7), -6, -7, 4, 5),
(5, (P(Q(1,2), Q(3,2)), V(1,1)),
Q(1,2), Q(3,2), Q(3,2), Q(5,2)),
]
for i, args, minx, miny, maxx, maxy in cases:
with self.subTest(i = i, args = args):
r = g.Rectangle(*args)
self.assertEqual(type(r), g.Rectangle)
self.assertTrue(type(x) == Y for x in [r.min_x,r.min_y,r.max_x,r.max_y])
self.assertEqual(r.min_x, minx)
self.assertEqual(r.min_y, miny)
self.assertEqual(r.max_x, maxx)
self.assertEqual(r.max_y, maxy)
def test_constructor_fail(self):
P, V, LS = g.Point, g.Vector, g.LineSegment
cases = [
(0, (), TypeError),
(1, (P(3,5),), TypeError),
(2, (V(1,7),), TypeError),
(3, (V(5,5), V(1,2)), TypeError),
(4, (LS(P(0,0), P(1,2)),), TypeError),
(5, (P(3,4), 45, 2), TypeError),
(6, (3, 4, P(45, 2)), TypeError),
(7, (1, 2, 3, 'hi!'), TypeError),
]
for i, args, ex in cases:
with self.subTest(i = i, args = args):
self.assertRaises(ex, g.Rectangle, ex)
def test_equality(self):
R = g.Rectangle
cases = [
(0, R(0,0,0,0), R(0,0,0,0), True),
(1, R(0,0,0,0), R(0,0,0,1), False),
(2, R(-1,0,0,0), R(0,0,0,0), False),
(3, R(5,phi,8,2), R(8,phi,5,2), True),
(4, R(35,8,90,8), R(90,8,35,8), True),
(5, R(Q(1,1000),2,-5,3),
R(-5,2,0,3), False),
(6, R(1,2,3,4), g.LineSegment(g.Point(1,2), g.Point(3,4)),
False),
(7, R(1,2,1,2), g.Point(1,2), False),
]
for i, a, b, r in cases:
with self.subTest(i = i, a = str(a), b = str(b)):
self.assertEqual(a == b, r)
self.assertEqual(b == a, r)
self.assertEqual(a != b, not r)
self.assertEqual(b != a, not r)
def test_bbox(self):
R = g.Rectangle
cases = [
(0, R(1,2,4,3)),
(1, R(8,2,1,1)),
(2, R(0,0,0,0)),
(3, R(0,0,1,0)),
(4, R(0,0,0,1)),
(5, R(-213,239,Q(2382839,4),-sqrt5)),
]
for i, rect in cases:
with self.subTest(i = i, rect = str(rect)):
self.assertEqual(rect.bbox(), rect)
class TestDoBboxesOverlap(TestCase):
def test_do_bboxes_overlap(self):
R = g.Rectangle
cases = [
(0, R(1,2,3,4), R(-1,-2,-3,-4), False),
(1, R(1,2,3,4), R(1,2,3,4), True),
(2, R(1,2,3,4), R(3,4,5,6), True), # event single-point overlap counts
(3, R(13,4,13,8), R(13,8,13,10), True),
(4, R(13,4,13,8), R(13,21,13,99), False),
(5, R(-13,4,-13,8), R(-13,5,-13,7), True),
(6, R(-13,4,-13,8), R(-13,6,-13,10), True),
(7, R(1,2,3,4), R(3,3,8,5), True),
(8, R(1,2,1,2), R(1,2,1,2), True),
(9, R(1,2,1,2), R(0,0,4,4), True),
(10, R(1,2,1,2), R(-2,-2,-4,-4), False),
]
for i, a, b, r in cases:
with self.subTest(i = i, a = str(a), b = str(b)):
self.assertEqual(g.do_bboxes_overlap(a, b), r)
self.assertEqual(g.do_bboxes_overlap(b, a), r)
class TestPolygon(TestCase):
def test_constructor_succeed(self):
P = g.Point
a2 = ((1,5), (2,6), (-1,7))
cases = [
(0, (P(0,0), P(1,0), P(0,1)), 3),
(1, (P(0,0), P(1,0), P(1,1), P(0,1)), 4),
(2, ([P(0,0), P(2,0), P(2,2)],), 3), # list
(3, ((P(2,0), P(2,2), P(0,0)),), 3), # tuple
(4, ((g.Point(*coords) for coords in a2),), 3), # generator
(5, (P(3,0), P(1,1), P(0,3), P(-1,1), P(-3,0), P(-1,-1), P(0,-3), P(1,-1)), 8),
]
for i, args, n in cases:
with self.subTest(i = i, args = args):
poly = g.Polygon(*args)
self.assertEqual(type(poly), g.Polygon)
self.assertEqual(len(poly._v), n)
e = poly.edges()
self.assertEqual(len(poly._e), n)
def test_constructor_fail(self):
P = g.Point
cases = [
(0, (), ValueError),
(1, ([P(0,0), P(1,0), P(1,1)], P(0,1)), TypeError),
(2, ([P(0,0), P(1,0), P(1,1)], [P(-3,2), P(-4,2), P(-4,1)]), TypeError),
(3, (P(3,2), P(4,1)), ValueError),
(4, (P(4,4),), ValueError),
(5, (P(3,2), P(4,4), P(5,2), 'hi!'), TypeError),
(6, ('hi!'), TypeError),
]
for i, args, ex in cases:
with self.subTest(i = i, args = args):
self.assertRaises(ex, g.Polygon, *args)
_test_polygons = {
}
_test_polygon_data = {
'simple-triangle': ((0,0), (1,0), (0,1)),
'non-convex-quad': ((0,0), (3,0), (1,1), (0,3)),
'unit-pentagon': ((p.x, p.y) for p in (g.Point(1,0).rotate(4*n) for n in range(5))),
'zig-zag': ((0,0), (2,0), (2,2), (4,2), (4,4),
(4,5), (3,5), (3,3), (1,3), (1,1)),
}
_up_pt1 = g.Point(1,0).rotate(4)
_up_pt2 = _up_pt1.rotate(4)
_up_pt3 = _up_pt2.rotate(4)
_up_pt4 = _up_pt3.rotate(4)
@classmethod
def setUpClass(cls):
for k, v in cls._test_polygon_data.items():
cls._test_polygons[k] = g.Polygon(g.Point(*coord) for coord in v)
def test_vertices(self):
cases = [
('simple-triangle', [(0,0), (1,0), (0,1)]),
('non-convex-quad', [(0,0), (3,0), (1,1), (0,3)]),
('unit-pentagon', [(1,0), (self._up_pt1.x,self._up_pt1.y),
(self._up_pt2.x,self._up_pt2.y),
(self._up_pt3.x,self._up_pt3.y),
(self._up_pt4.x,self._up_pt4.y)]),
('zig-zag', [(0,0), (2,0), (2,2), (4,2), (4,4), (4,5), (3,5), (3,3), (1,3), (1,1)]),
]
for i, r in cases:
with self.subTest(polyName = i):
poly = self._test_polygons[i]
self.assertEqual(len(poly.vertices()), len(r))
self.assertTrue(all(
(type(v_poly) == g.Point and v_poly == v_r)
for v_poly, v_r
in zip_longest(poly.vertices(), (g.Point(*c) for c in r))
))
def test_edges(self):
LS = lambda d, e: g.LineSegment(g.Point(*d), g.Point(*e))
LS2 = g.LineSegment
cases = [
('simple-triangle', [LS((0,0), (1,0)), LS((1,0), (0,1)), LS((0,1), (0,0))]),
('non-convex-quad', [LS((0,0), (3,0)), LS((3,0), (1,1)),
LS((1,1), (0,3)), LS((0,3), (0,0))]),
('unit-pentagon', [LS2(g.Point(1,0), self._up_pt1),
LS2(self._up_pt1, self._up_pt2),
LS2(self._up_pt2, self._up_pt3),
LS2(self._up_pt3, self._up_pt4),
LS2(self._up_pt4, g.Point(1,0))]),
('zig-zag', [LS((0,0), (2,0)), LS((2,0), (2,2)),
LS((2,2), (4,2)), LS((4,2), (4,4)),
LS((4,4), (4,5)), LS((4,5), (3,5)),
LS((3,5), (3,3)), LS((3,3), (1,3)),
LS((1,3), (1,1)), LS((1,1), (0,0))]),
]
for i, r in cases:
with self.subTest(polyName = i):
poly = self._test_polygons[i]
self.assertEqual(len(poly.edges()), len(r))
self.assertTrue(all(
(type(e_poly) == g.LineSegment and e_poly == e_r)
for e_poly, e_r
in zip_longest(poly.edges(), r)
))
def test_is_convex(self):
cases = [
('simple-triangle', True),
('non-convex-quad', False),
('unit-pentagon', True),
('zig-zag', False),
]
for i, r in cases:
with self.subTest(polyName = i):
poly = self._test_polygons[i]
self.assertEqual(poly.is_convex(), r)
self.assertEqual(poly.is_convex(), r)
def test_bbox(self):
R = g.Rectangle
cases = [
('simple-triangle', R(0, 0, 1, 1)),
('non-convex-quad', R(0, 0, 3, 3)),
('unit-pentagon', R(self._up_pt2.x, self._up_pt4.y, 1, self._up_pt1.y)),
('zig-zag', R(0, 0, 4, 5)),
]
for i, bbox in cases:
with self.subTest(polyName = i, pb = str(self._test_polygons[i].bbox())):
poly = self._test_polygons[i]
self.assertEqual(poly.bbox(), bbox)
self.assertEqual(poly.bbox(), bbox)
class TestPolygonAlgorithms(TestCase):
_test_polygons = {
'unit-pentagon': g.Polygon(g.rotation(4*n) @ g.Point(1, 0) for n in range(5)),
}