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_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 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_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 path(self, P): for curve in P: self.assertIsInstance(curve, Curve) self.assertAlmostEqual(P(0), P.front()(0)) self.curves_equal(P.front(), P[0]) self.curves_equal(P.back_default(), P[P.size_default() - 1]) self.curves_equal(P.back_open(), P.back()) self.assertEqual(P.size_open(), P.size()) self.assertFalse(P.empty() ^ (P.size() == 0)) exact = P.bounds_exact().Rect exact.expand_by(1e-5) fast = P.bounds_fast().Rect fast.expand_by(1e-5) A1 = Affine(3, 1, 8, 3, 9, 9) A2 = Rotate(0.231) for i in range(100 * P.size_open() + 1): t = i / 100.0 self.assertTrue(exact.contains(P(t))) self.assertTrue(fast.contains(P(t))) self.assertAlmostEqual((P * A1)(t), P(t) * A1) self.assertAlmostEqual((P * A2)(t), P(t) * A2) self.assertAlmostEqual(P(t), P.point_at(t)) self.assertAlmostEqual(P(t).x, P.value_at(t, 0)) self.assertAlmostEqual(P(t).y, P.value_at(t, 1)) if P.closed(): self.curves_equal(P.back_default(), P.back_closed()) self.assertEqual(P.size_default(), P.size_closed()) else: self.curves_equal(P.back_default(), P.back_open()) self.assertEqual(P.size_default(), P.size_open()) for i in range(10): for root in P.roots(i, 0): if root < P.size_default(): self.assertAlmostEqual(P.value_at(root, 0), i) for root in P.roots(i, 1): if root < P.size_default(): self.assertAlmostEqual(P.value_at(root, 1), i) for t in P.all_nearest_times(P(0)): self.assertAlmostEqual(P(t), P(0)) self.assertAlmostEqual(min(P.all_nearest_times(P(0))), 0) self.assertAlmostEqual(P.nearest_time(P(0), 0, 0.2), 0) self.assertEqual(len(P.nearest_time_per_curve(Point())), P.size_default()) t, distSq = P.nearest_time_and_dist_sq(Point(-1, -1), 0, P.size()) self.assertAlmostEqual(distSq**0.5, abs(P(t) - Point(-1, -1))) self.assertAlmostEqual(P.portion(0.3, 0.4)(0), P(0.3)) self.assertAlmostEqual( P.portion(interval=Interval(P.size(), P.size() * 2) / 3)(0), P(P.size() / 3.0)) self.assertAlmostEqual(P(0.23), P.reverse()(P.size() - 0.23)) self.assertAlmostEqual(P.initial_point(), P(0)) self.assertAlmostEqual(P.final_point(), P(P.size()))
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 curve(self, C): self.assertAlmostEqual(C.initial_point(), C(0)) self.assertAlmostEqual(C.final_point(), C.point_at(1)) #Doesn't have to be true #~ if C.length() > 0.01: #~ self.assertFalse(C.is_degenerate()) if C.is_degenerate(): #trivial special case return for i in range(11): t = i/10.0 self.assertAlmostEqual(C(t).x, C.point_at(t).x) self.assertAlmostEqual(C(t).y, C.value_at(t, 1)) self.assertEqual( C(t), C.point_and_derivatives(t, 1)[0] ) self.assertTrue( C.bounds_exact().contains(C(t)) ) self.assertTrue( C.bounds_fast().contains(C(t)) ) #TODO why this works only with degree = 0? if C.bounds_local(OptInterval(t-0.05, t+0.05), 0 ) and ( C.bounds_local(OptInterval(t-0.05, t+0.05), 0).Rect.area() > 1e-10): #ruling out too small rectangles, they have problems with precision self.assertTrue( C.bounds_local( OptInterval(t-0.05, t+0.05), 0 ).Rect.contains(C(t))) D = C.duplicate() D.set_initial(Point()) self.assertAlmostEqual(D.initial_point(), Point()) D.set_final(Point(1, 1)) self.assertAlmostEqual(D.final_point(), Point(1, 1)) A = Affine( uniform(-10, 10), uniform(-10, 10), uniform(-10, 10), uniform(-10, 10), uniform(-10, 10), uniform(-10, 10)) E = C.transformed(A) for i in range(11): t = i/10.0 # self.assertAlmostEqual( E(t), C(t)*A ) G1 = C.portion(0.2, 0.8) G2 = C.portion( interval=Interval(2, 8)/10 ) self.assertAlmostEqual( G1(0), C(0.2) ) self.assertAlmostEqual( G2(0.5), C( lerp(0.5, 0.2, 0.8) )) self.assertAlmostEqual( G1(1), G2(1) ) for i in range(11): t = i/10.0 self.assertAlmostEqual( C.reverse()(t), C(1-t) ) self.assertAlmostEqual( C.point_and_derivatives(0.3, 1)[1], C.derivative()(0.3) ) self.assertAlmostEqual( C.nearest_time(C(0)), 0 ) self.assertAlmostEqual( C( C.nearest_time(C(0.5), interval=Interval(0.2, 0.5)) ), C(0.5) ) self.assertAlmostEqual( C( C.nearest_time(C(0.5), 0.2, 0.5) ), C(0.5) ) for p in C.all_nearest_times( C(0), 0, 1): self.assertEqual(C(p), C(0)) for p in C.all_nearest_times( C(1), interval=Interval(0, 1)): self.assertEqual(C(p), C(1)) for r in C.roots(0, 0): self.assertAlmostEqual(C.value_at(r, 0), 0) self.assertGreaterEqual(C.length(), abs(C(1) - C(0))) self.assertEqual(C.winding(Point()), int(C.winding(Point())) ) self.assertAlmostEqual( C.unit_tangent_at(0.5), Point.unit_vector(C.derivative()(0.5)) ) self.assertTrue(isinstance(C.to_SBasis()[0], SBasis))
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_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))