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import unittest
from math import pi, sqrt, sin, cos
from random import randint, uniform
import cy2geom
from cy2geom import Point, IntPoint
from cy2geom import Line, Ray, Rect
from cy2geom import Rect
from cy2geom import Affine
from cy2geom import Translate, Scale, Rotate, VShear, HShear, Zoom
from cy2geom import Eigen
class TestPrimitives(unittest.TestCase):
def affine(self, A, B):
c0, c1, c2, c3, c4, c5 = A[0], A[1], A[2], A[3], A[4], A[5]
C = Affine(c0, c1, c2, c3, c4, c5)
self.assertEqual(C, A)
E = Affine.identity()
self.assertEqual(C, C*E)
self.assertEqual(E*B, B)
self.assertEqual(E.det(), 1)
self.assertAlmostEqual(A.det(), c0*c3-c1*c2)
self.assertAlmostEqual(abs(A.det()), A.descrim2())
self.assertAlmostEqual(abs(A.det())**0.5, A.descrim())
#xor
self.assertFalse( A.flips() ^ (A.det() < 0) )
if A.is_singular():
self.assertAlmostEqual(A.det(), 0)
else:
self.assertTrue( Affine.are_near (A*A.inverse(), E) )
self.assertAlmostEqual(A.det(), 1/A.inverse().det())
self.assertEqual( A.x_axis(), Point(c0, c1) )
self.assertEqual( A.y_axis(), Point(c2, c3) )
self.assertEqual( A.translation(), Point(c4, c5) )
self.assertAlmostEqual(A.expansion_X(), A.x_axis().length())
self.assertAlmostEqual(A.expansion_Y(), A.y_axis().length())
if abs(A.expansion_X()) > 1e-7 and abs(A.expansion_Y()) > 1e-7:
A.set_expansion_X(2)
A.set_expansion_Y(3)
self.assertAlmostEqual(A.expansion_X(), 2)
self.assertAlmostEqual(A.expansion_Y(), 3)
A.set_identity()
self.assertTrue(A.is_identity())
self.assertTrue(A.is_translation())
self.assertFalse(A.is_nonzero_translation())
self.assertTrue(A.is_scale())
self.assertTrue(A.is_uniform_scale())
self.assertFalse(A.is_nonzero_scale())
self.assertFalse(A.is_nonzero_uniform_scale())
self.assertTrue(A.is_rotation())
self.assertFalse(A.is_nonzero_rotation())
self.assertTrue(A.is_HShear())
self.assertTrue(A.is_VShear())
self.assertFalse(A.is_nonzero_HShear())
self.assertFalse(A.is_nonzero_VShear())
self.assertTrue(A.is_zoom())
self.assertTrue(A.preserves_area() and A.preserves_angles() and A.preserves_distances())
self.assertFalse( A.flips() )
self.assertFalse( A.is_singular() )
A.set_X_axis(Point(c0, c1))
A.set_Y_axis(Point(c2, c3))
self.assertEqual(A.without_translation(), A)
A.set_translation(Point(c4, c5))
self.assertEqual(C, A)
self.assertAlmostEqual( (A*B).det(), A.det()*B.det() )
self.assertEqual( A.translation(), Point()*A )
self.assertEqual( Point(1, 1)*A, Point( c0+c2+c4, c1+c3+c5 ))
l = Line(Point(1, 1), 2)
self.assertEqual( (l.transformed(A)).origin(), l.origin()*A )
self.assertTrue( Line.are_near( l.point_at(3)*A, l.transformed(A) ) )
r = Ray(Point(2, 3), 4)
self.assertEqual( (r.transformed(A)).origin(), r.origin()*A )
self.assertTrue( Ray.are_near( r.point_at(3)*A, r.transformed(A) ) )
def test_affine(self):
al = []
for i in range(10):
al.append(Affine( uniform(-10, 10),
uniform(-10, 10),
uniform(-10, 10),
uniform(-10, 10),
uniform(-10, 10),
uniform(-10, 10)))
for A in al:
for B in al:
self.affine(A, B)
o = Point(2, 4)
v = Point(-1, 1)/sqrt(2)
l = Line.from_origin_and_versor(o, v)
R = Affine.reflection(v, o)
for i in range(100):
p = Point(randint(0, 100), randint(0, 100))
self.assertAlmostEqual(Line.distance(p, l), Line.distance(p*R, l))
self.assertTrue( Affine.are_near( R, R.inverse() ) )
self.affine(R, R.inverse())
def test_translate(self):
T = Translate()
U = Translate(Point(2, 4))
V = Translate(1, -9)
self.assertTrue(Affine(T).is_translation())
self.assertTrue(Affine(U).is_nonzero_translation())
self.assertEqual( (U*V).vector(), U.vector()+V.vector() )
self.assertEqual( U.inverse().vector(), -U.vector() )
self.assertEqual(T, Translate.identity())
self.assertEqual( U.vector(), Point(U[0], U[1]) )
self.affine(Affine(V), Affine(U))
self.affine(Affine(U), Affine(V))
r = Rect.from_points( Point(0, 2), Point(4, 8) )
self.assertEqual( ( r*(U*V) ).min(), r.min()+U.vector()+V.vector())
def test_scale(self):
S = Scale()
T = Scale( Point (3, 8) )
U = Scale( -3, 1)
V = Scale(sqrt(2))
self.assertTrue( Affine(T).is_scale() )
self.assertTrue( Affine(T).is_nonzero_scale() )
self.assertTrue( Affine(V).is_nonzero_uniform_scale())
self.assertEqual( (T*V).vector(), T.vector()*sqrt(2) )
self.assertEqual( (T*U)[0], T[0]*U[0] )
self.assertAlmostEqual( 1/U.inverse()[1], U[1] )
r = Rect.from_points( Point(0, 2), Point(4, 8) )
self.assertAlmostEqual((r*V).area(), 2*r.area())
self.assertFalse(Affine(U).preserves_area())
self.assertTrue(Affine(V).preserves_angles())
self.affine(Affine(T), Affine(U))
self.affine(Affine(U), Affine(V))
self.affine(Affine(V), Affine(T))
def test_rotate(self):
R = Rotate()
S = Rotate(pi/3)
T = Rotate(Point( 1, 1 ))
U = Rotate( -1, 1 )
self.assertTrue(S.vector(), Point(cos(pi/3), sin(pi/3)) )
self.assertEqual( Point(T[0], T[1]), T.vector() )
self.assertTrue( Affine.are_near( Rotate.from_degrees(60), S ) )
self.assertEqual(R, Rotate.identity())
self.assertTrue( Point.are_near( ( S * T ).vector(),
Point( cos( pi/3 + pi/4 ), sin( pi/3 + pi/4 ) ) ) )
self.affine( Affine(R), Affine(S))
self.affine( Affine(S), Affine(T))
self.affine( Affine(T), Affine(U))
self.affine( Affine(U), Affine(R))
def test_shear(self):
H = HShear(2.98)
V = VShear(-sqrt(2))
self.assertAlmostEqual(H.factor(), 2.98)
self.assertAlmostEqual(V.inverse().factor(), sqrt(2))
G = HShear.identity()
H.set_factor(0)
self.assertEqual(G, H)
G.set_factor(2)
H.set_factor(4)
self.assertAlmostEqual((G*H).factor(), G.factor()+H.factor())
W = VShear.identity()
V.set_factor(0)
self.assertEqual(W, V)
W.set_factor(-2)
V.set_factor(3)
self.assertAlmostEqual((W*V).factor(), W.factor()+V.factor())
def test_zoom(self):
Z = Zoom(3)
Y = Zoom(translate=Translate(3,2))
X = Zoom(sqrt(3), Translate(-1, 3))
self.assertEqual(
Zoom(Z.scale(), Translate(Y.translation())),
Y*Z )
Z.set_translation(Y.translation())
Y.set_scale(Z.scale())
self.assertEqual(Z, Y)
self.assertEqual(Y.inverse().scale(), 1/Y.scale())
r = Rect.from_xywh( 1, 1, 3, 6)
q = Rect.from_xywh( 0, -1, 1, 2)
W = Zoom.map_rect(r, q)
self.assertAlmostEqual(W.scale()*r.width(), q.width())
self.assertTrue(Point.are_near(
r.min()+W.translation(),
q.min()))
def test_eigen(self):
#TODO looks like bug in eigen - (1, 0) should be eigenvector too
#~ S = Scale(1, 2)
#~ E_S = Eigen(S)
#~ print E_S.vectors, E_S.values
#~ print Affine(S)
#~ for i in E_S.vectors:
#~ print i, i*S, Point(1, 0) * S
B = Affine(-2, 2, 2, 1, 0, 0)
G1 = Eigen(B)
G2 = Eigen( [[-2, 2], [2, 1]] )
self.assertAlmostEqual(min(G1.values), min(G2.values))
self.assertAlmostEqual(max(G1.values), max(G2.values))
if Point.are_near( G1.vectors[0]*G1.values[0], G1.vectors[0]*B ):
self.assertTrue( Point.are_near( G1.vectors[1]*G1.values[1], G1.vectors[1]*B ) )
else:
self.assertTrue( Point.are_near( G1.vectors[1]*G1.values[0], G1.vectors[1]*B ) )
self.assertTrue( Point.are_near( G1.vectors[0]*G1.values[1], G1.vectors[0]*B ) )
unittest.main()
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