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_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_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 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 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)))