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))
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 ) )
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_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_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_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_point(self):
p = Point(3, 4)
q = Point(8, 16)
p_inf = Point(float('inf'), 1)
#y axis points downwards
p_ccw = Point(4, -3)
self.assertAlmostEqual(p.length(), 5)
self.assertAlmostEqual(p.ccw(), p_ccw)
self.assertAlmostEqual(p_ccw.cw(), p)
self.assertAlmostEqual(p[0], 3)
self.assertAlmostEqual(p[1], 4)
self.assertFalse(p_inf.isFinite())
self.assertTrue(p.isFinite())
self.assertFalse(p.isNormalized())
self.assertTrue((p / p.length()).isNormalized())
self.assertFalse(p.isZero())
self.assertTrue((p * 0).isZero())
self.assertTrue((p + p.ccw().ccw()).isZero)
self.assertAlmostEqual((q - p).length(), 13)
self.assertGreater(q, p)
self.assertGreaterEqual(q, p)
self.assertEqual(p, p)
self.assertNotEqual(p, q)
self.assertLess(Point(1, 1), Point(1, 2))
self.assertLessEqual(p, p)
self.assertTrue(
Point.are_near(Point.polar(pi / 4, sqrt(2)), Point(1, 1)))
self.assertAlmostEqual(sqrt(2), Point.L2(Point(1, 1)))
self.assertAlmostEqual(2, Point.L2sq(Point(1, 1)))
self.assertAlmostEqual(Point.middle_point(Point(), q), q / 2)
self.assertAlmostEqual(Point.rot90(p), p.cw())
self.assertAlmostEqual(
Point.lerp(0.2, Point(), Point(3, 4)).length(), 1)
self.assertAlmostEqual(Point.dot(p, p_ccw), 0)
self.assertAlmostEqual(Point.dot(p, p_inf), float('inf'))
self.assertAlmostEqual(Point.dot(p, q), 88)
#TODO this might be implemented incorrectly in lib2geom!
self.assertAlmostEqual(Point.cross(p, q), -16)
self.assertAlmostEqual(Point.distance(p, q), 13)
self.assertAlmostEqual(Point.distanceSq(p, p_ccw), 50)
self.assertAlmostEqual(Point.unit_vector(p), p / 5)
self.assertAlmostEqual(Point.L1(p), 7)
self.assertAlmostEqual(Point.L1(p_inf), float('inf'))
self.assertAlmostEqual(Point.LInfty(q), 16)
self.assertAlmostEqual(Point.LInfty(p_inf), float('inf'))
self.assertTrue(Point.is_zero(Point()))
self.assertFalse(Point.is_zero(p))
self.assertTrue(Point.is_unit_vector(p / 5))
self.assertFalse(Point.is_unit_vector(q))
self.assertAlmostEqual(Point.atan2(Point(1, 1)), pi / 4)
self.assertAlmostEqual(Point.angle_between(p, p_ccw), -pi / 2)
self.assertAlmostEqual(Point.abs(-p), p)
def test_point(self):
p = Point(3, 4)
q = Point(8, 16)
p_inf = Point(float('inf'), 1)
#y axis points downwards
p_ccw = Point(4, -3)
self.assertAlmostEqual(p.length(), 5)
self.assertAlmostEqual(p.ccw(), p_ccw)
self.assertAlmostEqual(p_ccw.cw(), p)
self.assertAlmostEqual(p[0], 3)
self.assertAlmostEqual(p[1], 4)
self.assertFalse(p_inf.isFinite())
self.assertTrue(p.isFinite())
self.assertFalse(p.isNormalized())
self.assertTrue((p/p.length()).isNormalized())
self.assertFalse(p.isZero())
self.assertTrue((p*0).isZero())
self.assertTrue( (p + p.ccw().ccw()).isZero)
self.assertAlmostEqual( (q-p).length(), 13)
self.assertGreater(q, p)
self.assertGreaterEqual(q, p)
self.assertEqual(p, p)
self.assertNotEqual(p, q)
self.assertLess( Point(1, 1), Point(1, 2) )
self.assertLessEqual(p, p)
self.assertTrue( Point.are_near(
Point.polar(pi/4, sqrt(2)),
Point(1, 1) ))
self.assertAlmostEqual(sqrt(2), Point.L2(Point(1, 1)))
self.assertAlmostEqual(2, Point.L2sq(Point(1, 1)))
self.assertAlmostEqual( Point.middle_point(Point(), q), q/2 )
self.assertAlmostEqual( Point.rot90(p), p.cw() )
self.assertAlmostEqual(
Point.lerp(0.2, Point(), Point(3,4)).length(),
1)
self.assertAlmostEqual(Point.dot(p, p_ccw), 0)
self.assertAlmostEqual(Point.dot(p, p_inf), float('inf'))
self.assertAlmostEqual(Point.dot(p, q), 88)
#TODO this might be implemented incorrectly in lib2geom!
self.assertAlmostEqual(Point.cross(p, q), -16)
self.assertAlmostEqual(Point.distance(p, q), 13)
self.assertAlmostEqual(Point.distanceSq(p, p_ccw), 50)
self.assertAlmostEqual(Point.unit_vector(p), p/5)
self.assertAlmostEqual(Point.L1(p), 7)
self.assertAlmostEqual(Point.L1(p_inf), float('inf'))
self.assertAlmostEqual(Point.LInfty(q), 16)
self.assertAlmostEqual(Point.LInfty(p_inf), float('inf'))
self.assertTrue(Point.is_zero(Point()))
self.assertFalse(Point.is_zero(p))
self.assertTrue(Point.is_unit_vector(p/5))
self.assertFalse(Point.is_unit_vector(q))
self.assertAlmostEqual(Point.atan2(Point(1, 1)), pi/4)
self.assertAlmostEqual(Point.angle_between(p, p_ccw), -pi/2)
self.assertAlmostEqual(Point.abs(-p), p)
