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()