import unittest import pytest from math import sqrt, pi from svg.path import ( CubicBezier, QuadraticBezier, Line, Arc, Move, Close, Path, PathSegment, ) from svg.path import parse_path class PathTest(unittest.TestCase): def test_path_class(self) -> None: path = parse_path("M 0 0 L 50 20 M 100 100 L 300 100 L 200 300 z") self.assertTrue(isinstance(path, Path)) # Paths are MutableSequences (ie lists). self.assertEqual(len(path), 6) # So we can take items: self.assertTrue(isinstance(path[0], PathSegment)) # We can slice it: self.assertTrue(isinstance(path[0:3], Path)) self.assertEqual(path[0:3].d(), "M 0,0 L 50,20 M 100,100") # And replace bits in the middle path[1] = QuadraticBezier( start=(0 + 0j), control=(20 + 20j), end=(100 + 100j), smooth=False ) self.assertEqual(len(path), 6) self.assertEqual( path.d(), "M 0,0 Q 20,20 100,100 M 100,100 L 300,100 L 200,300 z" ) # Even multiples can be replaced path[1:2] = [ Line(start=0j, end=(20 + 20j)), QuadraticBezier( start=(20 + 20j), control=(30 + 30j), end=(100 + 100j), smooth=False ), ] # We replaced one with two, it should be longer self.assertEqual(len(path), 7) # And we can delete slices del path[1:3] self.assertEqual(len(path), 5) self.assertEqual(path.d(), "M 0,0 M 100,100 L 300,100 L 200,300 z") # These are type errors, and MyPy will complain about it without # the type: ignore statement, but we want to check that they raise # type errors: with pytest.raises(TypeError): path[1:2] = Line(start=0j, end=(20 + 20j)) # type: ignore with pytest.raises(TypeError): path[1] = [Line(start=0j, end=(20 + 20j))] # type: ignore # Most of these test points are not calculated separately, as that would # take too long and be too error prone. Instead the curves have been verified # to be correct visually, by drawing them with the turtle module, with code # like this: # # import turtle # t = turtle.Turtle() # t.penup() # # for arc in (path1, path2): # p = arc.point(0) # t.goto(p.real - 500, -p.imag + 300) # t.dot(3, 'black') # t.pendown() # for x in range(1, 101): # p = arc.point(x * 0.01) # t.goto(p.real - 500, -p.imag + 300) # t.penup() # t.dot(3, 'black') # # raw_input() # # After the paths have been verified to be correct this way, the testing of # points along the paths has been added as regression tests, to make sure # nobody changes the way curves are drawn by mistake. Therefore, do not take # these points religiously. They might be subtly wrong, unless otherwise # noted. class LineTest(unittest.TestCase): def test_lines(self) -> None: # These points are calculated, and not just regression tests. line1 = Line(0j, 400 + 0j) self.assertAlmostEqual(line1.point(0), (0j)) self.assertAlmostEqual(line1.point(0.3), (120 + 0j)) self.assertAlmostEqual(line1.point(0.5), (200 + 0j)) self.assertAlmostEqual(line1.point(0.9), (360 + 0j)) self.assertAlmostEqual(line1.point(1), (400 + 0j)) self.assertAlmostEqual(line1.length(), 400) line2 = Line(400 + 0j, 400 + 300j) self.assertAlmostEqual(line2.point(0), (400 + 0j)) self.assertAlmostEqual(line2.point(0.3), (400 + 90j)) self.assertAlmostEqual(line2.point(0.5), (400 + 150j)) self.assertAlmostEqual(line2.point(0.9), (400 + 270j)) self.assertAlmostEqual(line2.point(1), (400 + 300j)) self.assertAlmostEqual(line2.length(), 300) line3 = Line(400 + 300j, 0j) self.assertAlmostEqual(line3.point(0), (400 + 300j)) self.assertAlmostEqual(line3.point(0.3), (280 + 210j)) self.assertAlmostEqual(line3.point(0.5), (200 + 150j)) self.assertAlmostEqual(line3.point(0.9), (40 + 30j)) self.assertAlmostEqual(line3.point(1), (0j)) self.assertAlmostEqual(line3.length(), 500) def test_equality(self) -> None: # This is to test the __eq__ and __ne__ methods, so we can't use # assertEqual and assertNotEqual line = Line(0j, 400 + 0j) self.assertTrue(line == Line(0, 400)) self.assertTrue(line != Line(100, 400)) self.assertFalse(line == str(line)) self.assertTrue(line != str(line)) self.assertFalse( CubicBezier(600 + 500j, 600 + 350j, 900 + 650j, 900 + 500j) == line ) class CubicBezierTest(unittest.TestCase): def test_approx_circle(self) -> None: """This is a approximate circle drawn in Inkscape""" arc1 = CubicBezier( complex(0, 0), complex(0, 109.66797), complex(-88.90345, 198.57142), complex(-198.57142, 198.57142), ) self.assertAlmostEqual(arc1.point(0), (0j)) self.assertAlmostEqual(arc1.point(0.1), (-2.59896457 + 32.20931647j)) self.assertAlmostEqual(arc1.point(0.2), (-10.12330256 + 62.76392816j)) self.assertAlmostEqual(arc1.point(0.3), (-22.16418039 + 91.25500149j)) self.assertAlmostEqual(arc1.point(0.4), (-38.31276448 + 117.27370288j)) self.assertAlmostEqual(arc1.point(0.5), (-58.16022125 + 140.41119875j)) self.assertAlmostEqual(arc1.point(0.6), (-81.29771712 + 160.25865552j)) self.assertAlmostEqual(arc1.point(0.7), (-107.31641851 + 176.40723961j)) self.assertAlmostEqual(arc1.point(0.8), (-135.80749184 + 188.44811744j)) self.assertAlmostEqual(arc1.point(0.9), (-166.36210353 + 195.97245543j)) self.assertAlmostEqual(arc1.point(1), (-198.57142 + 198.57142j)) arc2 = CubicBezier( complex(-198.57142, 198.57142), complex(-109.66797 - 198.57142, 0 + 198.57142), complex(-198.57143 - 198.57142, -88.90345 + 198.57142), complex(-198.57143 - 198.57142, 0), ) self.assertAlmostEqual(arc2.point(0), (-198.57142 + 198.57142j)) self.assertAlmostEqual(arc2.point(0.1), (-230.78073675 + 195.97245543j)) self.assertAlmostEqual(arc2.point(0.2), (-261.3353492 + 188.44811744j)) self.assertAlmostEqual(arc2.point(0.3), (-289.82642365 + 176.40723961j)) self.assertAlmostEqual(arc2.point(0.4), (-315.8451264 + 160.25865552j)) self.assertAlmostEqual(arc2.point(0.5), (-338.98262375 + 140.41119875j)) self.assertAlmostEqual(arc2.point(0.6), (-358.830082 + 117.27370288j)) self.assertAlmostEqual(arc2.point(0.7), (-374.97866745 + 91.25500149j)) self.assertAlmostEqual(arc2.point(0.8), (-387.0195464 + 62.76392816j)) self.assertAlmostEqual(arc2.point(0.9), (-394.54388515 + 32.20931647j)) self.assertAlmostEqual(arc2.point(1), (-397.14285 + 0j)) arc3 = CubicBezier( complex(-198.57143 - 198.57142, 0), complex(0 - 198.57143 - 198.57142, -109.66797), complex(88.90346 - 198.57143 - 198.57142, -198.57143), complex(-198.57142, -198.57143), ) self.assertAlmostEqual(arc3.point(0), (-397.14285 + 0j)) self.assertAlmostEqual(arc3.point(0.1), (-394.54388515 - 32.20931675j)) self.assertAlmostEqual(arc3.point(0.2), (-387.0195464 - 62.7639292j)) self.assertAlmostEqual(arc3.point(0.3), (-374.97866745 - 91.25500365j)) self.assertAlmostEqual(arc3.point(0.4), (-358.830082 - 117.2737064j)) self.assertAlmostEqual(arc3.point(0.5), (-338.98262375 - 140.41120375j)) self.assertAlmostEqual(arc3.point(0.6), (-315.8451264 - 160.258662j)) self.assertAlmostEqual(arc3.point(0.7), (-289.82642365 - 176.40724745j)) self.assertAlmostEqual(arc3.point(0.8), (-261.3353492 - 188.4481264j)) self.assertAlmostEqual(arc3.point(0.9), (-230.78073675 - 195.97246515j)) self.assertAlmostEqual(arc3.point(1), (-198.57142 - 198.57143j)) arc4 = CubicBezier( complex(-198.57142, -198.57143), complex(109.66797 - 198.57142, 0 - 198.57143), complex(0, 88.90346 - 198.57143), complex(0, 0), ) self.assertAlmostEqual(arc4.point(0), (-198.57142 - 198.57143j)) self.assertAlmostEqual(arc4.point(0.1), (-166.36210353 - 195.97246515j)) self.assertAlmostEqual(arc4.point(0.2), (-135.80749184 - 188.4481264j)) self.assertAlmostEqual(arc4.point(0.3), (-107.31641851 - 176.40724745j)) self.assertAlmostEqual(arc4.point(0.4), (-81.29771712 - 160.258662j)) self.assertAlmostEqual(arc4.point(0.5), (-58.16022125 - 140.41120375j)) self.assertAlmostEqual(arc4.point(0.6), (-38.31276448 - 117.2737064j)) self.assertAlmostEqual(arc4.point(0.7), (-22.16418039 - 91.25500365j)) self.assertAlmostEqual(arc4.point(0.8), (-10.12330256 - 62.7639292j)) self.assertAlmostEqual(arc4.point(0.9), (-2.59896457 - 32.20931675j)) self.assertAlmostEqual(arc4.point(1), (0j)) def test_svg_examples(self) -> None: # M100,200 C100,100 250,100 250,200 path1 = CubicBezier(100 + 200j, 100 + 100j, 250 + 100j, 250 + 200j) self.assertAlmostEqual(path1.point(0), (100 + 200j)) self.assertAlmostEqual(path1.point(0.3), (132.4 + 137j)) self.assertAlmostEqual(path1.point(0.5), (175 + 125j)) self.assertAlmostEqual(path1.point(0.9), (245.8 + 173j)) self.assertAlmostEqual(path1.point(1), (250 + 200j)) # S400,300 400,200 path2 = CubicBezier(250 + 200j, 250 + 300j, 400 + 300j, 400 + 200j) self.assertAlmostEqual(path2.point(0), (250 + 200j)) self.assertAlmostEqual(path2.point(0.3), (282.4 + 263j)) self.assertAlmostEqual(path2.point(0.5), (325 + 275j)) self.assertAlmostEqual(path2.point(0.9), (395.8 + 227j)) self.assertAlmostEqual(path2.point(1), (400 + 200j)) # M100,200 C100,100 400,100 400,200 path3 = CubicBezier(100 + 200j, 100 + 100j, 400 + 100j, 400 + 200j) self.assertAlmostEqual(path3.point(0), (100 + 200j)) self.assertAlmostEqual(path3.point(0.3), (164.8 + 137j)) self.assertAlmostEqual(path3.point(0.5), (250 + 125j)) self.assertAlmostEqual(path3.point(0.9), (391.6 + 173j)) self.assertAlmostEqual(path3.point(1), (400 + 200j)) # M100,500 C25,400 475,400 400,500 path4 = CubicBezier(100 + 500j, 25 + 400j, 475 + 400j, 400 + 500j) self.assertAlmostEqual(path4.point(0), (100 + 500j)) self.assertAlmostEqual(path4.point(0.3), (145.9 + 437j)) self.assertAlmostEqual(path4.point(0.5), (250 + 425j)) self.assertAlmostEqual(path4.point(0.9), (407.8 + 473j)) self.assertAlmostEqual(path4.point(1), (400 + 500j)) # M100,800 C175,700 325,700 400,800 path5 = CubicBezier(100 + 800j, 175 + 700j, 325 + 700j, 400 + 800j) self.assertAlmostEqual(path5.point(0), (100 + 800j)) self.assertAlmostEqual(path5.point(0.3), (183.7 + 737j)) self.assertAlmostEqual(path5.point(0.5), (250 + 725j)) self.assertAlmostEqual(path5.point(0.9), (375.4 + 773j)) self.assertAlmostEqual(path5.point(1), (400 + 800j)) # M600,200 C675,100 975,100 900,200 path6 = CubicBezier(600 + 200j, 675 + 100j, 975 + 100j, 900 + 200j) self.assertAlmostEqual(path6.point(0), (600 + 200j)) self.assertAlmostEqual(path6.point(0.3), (712.05 + 137j)) self.assertAlmostEqual(path6.point(0.5), (806.25 + 125j)) self.assertAlmostEqual(path6.point(0.9), (911.85 + 173j)) self.assertAlmostEqual(path6.point(1), (900 + 200j)) # M600,500 C600,350 900,650 900,500 path7 = CubicBezier(600 + 500j, 600 + 350j, 900 + 650j, 900 + 500j) self.assertAlmostEqual(path7.point(0), (600 + 500j)) self.assertAlmostEqual(path7.point(0.3), (664.8 + 462.2j)) self.assertAlmostEqual(path7.point(0.5), (750 + 500j)) self.assertAlmostEqual(path7.point(0.9), (891.6 + 532.4j)) self.assertAlmostEqual(path7.point(1), (900 + 500j)) # M600,800 C625,700 725,700 750,800 path8 = CubicBezier(600 + 800j, 625 + 700j, 725 + 700j, 750 + 800j) self.assertAlmostEqual(path8.point(0), (600 + 800j)) self.assertAlmostEqual(path8.point(0.3), (638.7 + 737j)) self.assertAlmostEqual(path8.point(0.5), (675 + 725j)) self.assertAlmostEqual(path8.point(0.9), (740.4 + 773j)) self.assertAlmostEqual(path8.point(1), (750 + 800j)) # S875,900 900,800 inversion = (750 + 800j) + (750 + 800j) - (725 + 700j) path9 = CubicBezier(750 + 800j, inversion, 875 + 900j, 900 + 800j) self.assertAlmostEqual(path9.point(0), (750 + 800j)) self.assertAlmostEqual(path9.point(0.3), (788.7 + 863j)) self.assertAlmostEqual(path9.point(0.5), (825 + 875j)) self.assertAlmostEqual(path9.point(0.9), (890.4 + 827j)) self.assertAlmostEqual(path9.point(1), (900 + 800j)) def test_length(self) -> None: # A straight line: arc = CubicBezier( complex(0, 0), complex(0, 0), complex(0, 100), complex(0, 100) ) self.assertAlmostEqual(arc.length(), 100) # A diagonal line: arc = CubicBezier( complex(0, 0), complex(0, 0), complex(100, 100), complex(100, 100) ) self.assertAlmostEqual(arc.length(), sqrt(2 * 100 * 100)) # A quarter circle arc with radius 100: kappa = ( 4 * (sqrt(2) - 1) / 3 ) # http://www.whizkidtech.redprince.net/bezier/circle/ arc = CubicBezier( complex(0, 0), complex(0, kappa * 100), complex(100 - kappa * 100, 100), complex(100, 100), ) # We can't compare with pi*50 here, because this is just an # approximation of a circle arc. pi*50 is 157.079632679 # So this is just yet another "warn if this changes" test. # This value is not verified to be correct. self.assertAlmostEqual(arc.length(), 157.1016698) # A recursive solution has also been suggested, but for CubicBezier # curves it could get a false solution on curves where the midpoint is on a # straight line between the start and end. For example, the following # curve would get solved as a straight line and get the length 300. # Make sure this is not the case. arc = CubicBezier( complex(600, 500), complex(600, 350), complex(900, 650), complex(900, 500) ) self.assertTrue(arc.length() > 300.0) def test_equality(self) -> None: # This is to test the __eq__ and __ne__ methods, so we can't use # assertEqual and assertNotEqual segment = CubicBezier( complex(600, 500), complex(600, 350), complex(900, 650), complex(900, 500) ) self.assertTrue( segment == CubicBezier(600 + 500j, 600 + 350j, 900 + 650j, 900 + 500j) ) self.assertTrue( segment != CubicBezier(600 + 501j, 600 + 350j, 900 + 650j, 900 + 500j) ) self.assertTrue(segment != Line(0, 400)) def test_smooth(self) -> None: cb1 = CubicBezier(0, 0, 100 + 100j, 100 + 100j) cb2 = CubicBezier(600 + 500j, 600 + 350j, 900 + 650j, 900 + 500j) self.assertFalse(cb2.is_smooth_from(cb1)) cb2.set_smooth_from(cb1) self.assertTrue(cb2.is_smooth_from(cb1)) class QuadraticBezierTest(unittest.TestCase): def test_svg_examples(self) -> None: """These is the path in the SVG specs""" # M200,300 Q400,50 600,300 T1000,300 path1 = QuadraticBezier(200 + 300j, 400 + 50j, 600 + 300j) self.assertAlmostEqual(path1.point(0), (200 + 300j)) self.assertAlmostEqual(path1.point(0.3), (320 + 195j)) self.assertAlmostEqual(path1.point(0.5), (400 + 175j)) self.assertAlmostEqual(path1.point(0.9), (560 + 255j)) self.assertAlmostEqual(path1.point(1), (600 + 300j)) # T1000, 300 inversion = (600 + 300j) + (600 + 300j) - (400 + 50j) path2 = QuadraticBezier(600 + 300j, inversion, 1000 + 300j) self.assertAlmostEqual(path2.point(0), (600 + 300j)) self.assertAlmostEqual(path2.point(0.3), (720 + 405j)) self.assertAlmostEqual(path2.point(0.5), (800 + 425j)) self.assertAlmostEqual(path2.point(0.9), (960 + 345j)) self.assertAlmostEqual(path2.point(1), (1000 + 300j)) def test_length(self) -> None: # expected results calculated with # svg.path.segment_length(q, 0, 1, q.start, q.end, 1e-14, 20, 0) q1 = QuadraticBezier(200 + 300j, 400 + 50j, 600 + 300j) q2 = QuadraticBezier(200 + 300j, 400 + 50j, 500 + 200j) closedq = QuadraticBezier(6 + 2j, 5 - 1j, 6 + 2j) linq1 = QuadraticBezier(1, 2, 3) linq2 = QuadraticBezier(1 + 3j, 2 + 5j, -9 - 17j) nodalq = QuadraticBezier(1, 1, 1) tests = [ (q1, 487.77109389525975), (q2, 379.90458193489155), (closedq, 3.1622776601683795), (linq1, 2), (linq2, 22.73335777124786), (nodalq, 0), ] for q, exp_res in tests: self.assertAlmostEqual(q.length(), exp_res) def test_equality(self) -> None: # This is to test the __eq__ and __ne__ methods, so we can't use # assertEqual and assertNotEqual segment = QuadraticBezier(200 + 300j, 400 + 50j, 600 + 300j) self.assertTrue(segment == QuadraticBezier(200 + 300j, 400 + 50j, 600 + 300j)) self.assertTrue(segment != QuadraticBezier(200 + 301j, 400 + 50j, 600 + 300j)) self.assertFalse(segment == Arc(0j, 100 + 50j, 0, 0, 0, 100 + 50j)) self.assertTrue(Arc(0j, 100 + 50j, 0, 0, 0, 100 + 50j) != segment) def test_linear_arcs_issue_61(self) -> None: p = parse_path("M 206.5,525 Q 162.5,583 162.5,583") self.assertAlmostEqual(p.length(), 72.80109889280519) p = parse_path("M 425.781 446.289 Q 410.40000000000003 373.047 410.4 373.047") self.assertAlmostEqual(p.length(), 74.83959997888816) p = parse_path("M 639.648 568.115 Q 606.6890000000001 507.568 606.689 507.568") self.assertAlmostEqual(p.length(), 68.93645544992873) p = parse_path("M 288.818 616.699 Q 301.025 547.3629999999999 301.025 547.363") self.assertAlmostEqual(p.length(), 70.40235610403947) p = parse_path("M 339.927 706.25 Q 243.92700000000002 806.25 243.927 806.25") self.assertAlmostEqual(p.length(), 138.6217876093077) p = parse_path( "M 539.795 702.637 Q 548.0959999999999 803.4669999999999 548.096 803.467" ) self.assertAlmostEqual(p.length(), 101.17111989594662) p = parse_path( "M 537.815 555.042 Q 570.1680000000001 499.1600000000001 570.168 499.16" ) self.assertAlmostEqual(p.length(), 64.57177814649368) p = parse_path("M 615.297 470.503 Q 538.797 694.5029999999999 538.797 694.503") self.assertAlmostEqual(p.length(), 236.70287281737836) def test_smooth(self) -> None: cb1 = QuadraticBezier(200 + 300j, 400 + 50j, 600 + 300j) cb2 = QuadraticBezier(600 + 300j, 400 + 50j, 1000 + 300j) self.assertFalse(cb2.is_smooth_from(cb1)) cb2.set_smooth_from(cb1) self.assertTrue(cb2.is_smooth_from(cb1)) class ArcTest(unittest.TestCase): def test_points(self) -> None: arc1 = Arc(0j, 100 + 50j, 0, 0, 0, 100 + 50j) self.assertAlmostEqual(arc1.center, 100 + 0j) self.assertAlmostEqual(arc1.theta, 180.0) self.assertAlmostEqual(arc1.delta, -90.0) self.assertAlmostEqual(arc1.point(0.0), (0j)) self.assertAlmostEqual(arc1.point(0.1), (1.23116594049 + 7.82172325201j)) self.assertAlmostEqual(arc1.point(0.2), (4.89434837048 + 15.4508497187j)) self.assertAlmostEqual(arc1.point(0.3), (10.8993475812 + 22.699524987j)) self.assertAlmostEqual(arc1.point(0.4), (19.0983005625 + 29.3892626146j)) self.assertAlmostEqual(arc1.point(0.5), (29.2893218813 + 35.3553390593j)) self.assertAlmostEqual(arc1.point(0.6), (41.2214747708 + 40.4508497187j)) self.assertAlmostEqual(arc1.point(0.7), (54.6009500260 + 44.5503262094j)) self.assertAlmostEqual(arc1.point(0.8), (69.0983005625 + 47.5528258148j)) self.assertAlmostEqual(arc1.point(0.9), (84.3565534960 + 49.3844170298j)) self.assertAlmostEqual(arc1.point(1.0), (100 + 50j)) arc2 = Arc(0j, 100 + 50j, 0, 1, 0, 100 + 50j) self.assertAlmostEqual(arc2.center, 50j) self.assertAlmostEqual(arc2.theta, 270.0) self.assertAlmostEqual(arc2.delta, -270.0) self.assertAlmostEqual(arc2.point(0.0), (0j)) self.assertAlmostEqual(arc2.point(0.1), (-45.399049974 + 5.44967379058j)) self.assertAlmostEqual(arc2.point(0.2), (-80.9016994375 + 20.6107373854j)) self.assertAlmostEqual(arc2.point(0.3), (-98.7688340595 + 42.178276748j)) self.assertAlmostEqual(arc2.point(0.4), (-95.1056516295 + 65.4508497187j)) self.assertAlmostEqual(arc2.point(0.5), (-70.7106781187 + 85.3553390593j)) self.assertAlmostEqual(arc2.point(0.6), (-30.9016994375 + 97.5528258148j)) self.assertAlmostEqual(arc2.point(0.7), (15.643446504 + 99.3844170298j)) self.assertAlmostEqual(arc2.point(0.8), (58.7785252292 + 90.4508497187j)) self.assertAlmostEqual(arc2.point(0.9), (89.1006524188 + 72.699524987j)) self.assertAlmostEqual(arc2.point(1.0), (100 + 50j)) arc3 = Arc(0j, 100 + 50j, 0, 0, 1, 100 + 50j) self.assertAlmostEqual(arc3.center, 50j) self.assertAlmostEqual(arc3.theta, 270.0) self.assertAlmostEqual(arc3.delta, 90.0) self.assertAlmostEqual(arc3.point(0.0), (0j)) self.assertAlmostEqual(arc3.point(0.1), (15.643446504 + 0.615582970243j)) self.assertAlmostEqual(arc3.point(0.2), (30.9016994375 + 2.44717418524j)) self.assertAlmostEqual(arc3.point(0.3), (45.399049974 + 5.44967379058j)) self.assertAlmostEqual(arc3.point(0.4), (58.7785252292 + 9.54915028125j)) self.assertAlmostEqual(arc3.point(0.5), (70.7106781187 + 14.6446609407j)) self.assertAlmostEqual(arc3.point(0.6), (80.9016994375 + 20.6107373854j)) self.assertAlmostEqual(arc3.point(0.7), (89.1006524188 + 27.300475013j)) self.assertAlmostEqual(arc3.point(0.8), (95.1056516295 + 34.5491502813j)) self.assertAlmostEqual(arc3.point(0.9), (98.7688340595 + 42.178276748j)) self.assertAlmostEqual(arc3.point(1.0), (100 + 50j)) arc4 = Arc(0j, 100 + 50j, 0, 1, 1, 100 + 50j) self.assertAlmostEqual(arc4.center, 100 + 0j) self.assertAlmostEqual(arc4.theta, 180.0) self.assertAlmostEqual(arc4.delta, 270.0) self.assertAlmostEqual(arc4.point(0.0), (0j)) self.assertAlmostEqual(arc4.point(0.1), (10.8993475812 - 22.699524987j)) self.assertAlmostEqual(arc4.point(0.2), (41.2214747708 - 40.4508497187j)) self.assertAlmostEqual(arc4.point(0.3), (84.3565534960 - 49.3844170298j)) self.assertAlmostEqual(arc4.point(0.4), (130.901699437 - 47.5528258148j)) self.assertAlmostEqual(arc4.point(0.5), (170.710678119 - 35.3553390593j)) self.assertAlmostEqual(arc4.point(0.6), (195.105651630 - 15.4508497187j)) self.assertAlmostEqual(arc4.point(0.7), (198.768834060 + 7.82172325201j)) self.assertAlmostEqual(arc4.point(0.8), (180.901699437 + 29.3892626146j)) self.assertAlmostEqual(arc4.point(0.9), (145.399049974 + 44.5503262094j)) self.assertAlmostEqual(arc4.point(1.0), (100 + 50j)) def test_length(self) -> None: # I'll test the length calculations by making a circle, in two parts. arc1 = Arc(0j, 100 + 100j, 0, 0, 0, 200 + 0j) arc2 = Arc(200 + 0j, 100 + 100j, 0, 0, 0, 0j) self.assertAlmostEqual(arc1.length(), pi * 100) self.assertAlmostEqual(arc2.length(), pi * 100) def test_length_out_of_range(self) -> None: # See F.6.2 Out-of-range parameters # If the endpoints (x1, y1) and (x2, y2) are identical, then this is # equivalent to omitting the elliptical arc segment entirely. arc = Arc(0j, 100 + 100j, 0, 0, 0, 0j) self.assertAlmostEqual(arc.length(), 0) # If rx = 0 or ry = 0 then this arc is treated as a straight # line segment (a "lineto") joining the endpoints. arc = Arc(0j, 0j, 0, 0, 0, 200 + 0j) self.assertAlmostEqual(arc.length(), 200) # If rx or ry have negative signs, these are dropped; # the absolute value is used instead. arc = Arc(200 + 0j, -100 - 100j, 0, 0, 0, 0j) self.assertAlmostEqual(arc.length(), pi * 100) # If rx, ry and φ are such that there is no solution (basically, # the ellipse is not big enough to reach from (x1, y1) to (x2, y2)) # then the ellipse is scaled up uniformly until there is exactly # one solution (until the ellipse is just big enough). arc = Arc(0j, 1 + 1j, 0, 0, 0, 200 + 0j) self.assertAlmostEqual(arc.length(), pi * 100) # φ is taken mod 360 degrees. arc = Arc(200 + 0j, -100 - 100j, 720, 0, 0, 0j) self.assertAlmostEqual(arc.length(), pi * 100) def test_equality(self) -> None: # This is to test the __eq__ and __ne__ methods, so we can't use # assertEqual and assertNotEqual segment = Arc(0j, 100 + 50j, 0, 0, 0, 100 + 50j) self.assertTrue(segment == Arc(0j, 100 + 50j, 0, 0, 0, 100 + 50j)) self.assertTrue(segment != Arc(0j, 100 + 50j, 0, 1, 0, 100 + 50j)) def test_issue25(self) -> None: # This raised a math domain error Arc( (725.307482225571 - 915.5548199281527j), (202.79421639137703 + 148.77294617167183j), 225.6910319606926, 1, 1, (-624.6375539637027 + 896.5483089399895j), ) class TestPath(unittest.TestCase): def test_circle(self) -> None: arc1 = Arc(0j, 100 + 100j, 0, 0, 0, 200 + 0j) arc2 = Arc(200 + 0j, 100 + 100j, 0, 0, 0, 0j) path = Path(arc1, arc2) self.assertAlmostEqual(path.point(0.0), (0j)) self.assertAlmostEqual(path.point(0.25), (100 + 100j)) self.assertAlmostEqual(path.point(0.5), (200 + 0j)) self.assertAlmostEqual(path.point(0.75), (100 - 100j)) self.assertAlmostEqual(path.point(1.0), (0j)) self.assertAlmostEqual(path.length(), pi * 200) def test_svg_specs(self) -> None: """The paths that are in the SVG specs""" # Big pie: M300,200 h-150 a150,150 0 1,0 150,-150 z path = Path( Line(300 + 200j, 150 + 200j), Arc(150 + 200j, 150 + 150j, 0, 1, 0, 300 + 50j), Line(300 + 50j, 300 + 200j), ) # The points and length for this path are calculated and not regression tests. self.assertAlmostEqual(path.point(0.0), (300 + 200j)) self.assertAlmostEqual(path.point(0.14897825542), (150 + 200j)) self.assertAlmostEqual(path.point(0.5), (406.066017177 + 306.066017177j)) self.assertAlmostEqual(path.point(1 - 0.14897825542), (300 + 50j)) self.assertAlmostEqual(path.point(1.0), (300 + 200j)) # The errors seem to accumulate. Still 6 decimal places is more than good enough. self.assertAlmostEqual(path.length(), pi * 225 + 300, places=6) # Little pie: M275,175 v-150 a150,150 0 0,0 -150,150 z path = Path( Line(275 + 175j, 275 + 25j), Arc(275 + 25j, 150 + 150j, 0, 0, 0, 125 + 175j), Line(125 + 175j, 275 + 175j), ) # The points and length for this path are calculated and not regression tests. self.assertAlmostEqual(path.point(0.0), (275 + 175j)) self.assertAlmostEqual(path.point(0.2800495767557787), (275 + 25j)) self.assertAlmostEqual( path.point(0.5), (168.93398282201787 + 68.93398282201787j) ) self.assertAlmostEqual(path.point(1 - 0.2800495767557787), (125 + 175j)) self.assertAlmostEqual(path.point(1.0), (275 + 175j)) # The errors seem to accumulate. Still 6 decimal places is more than good enough. self.assertAlmostEqual(path.length(), pi * 75 + 300, places=6) # Bumpy path: M600,350 l 50,-25 # a25,25 -30 0,1 50,-25 l 50,-25 # a25,50 -30 0,1 50,-25 l 50,-25 # a25,75 -30 0,1 50,-25 l 50,-25 # a25,100 -30 0,1 50,-25 l 50,-25 path = Path( Line(600 + 350j, 650 + 325j), Arc(650 + 325j, 25 + 25j, -30, 0, 1, 700 + 300j), Line(700 + 300j, 750 + 275j), Arc(750 + 275j, 25 + 50j, -30, 0, 1, 800 + 250j), Line(800 + 250j, 850 + 225j), Arc(850 + 225j, 25 + 75j, -30, 0, 1, 900 + 200j), Line(900 + 200j, 950 + 175j), Arc(950 + 175j, 25 + 100j, -30, 0, 1, 1000 + 150j), Line(1000 + 150j, 1050 + 125j), ) # These are *not* calculated, but just regression tests. Be skeptical. self.assertAlmostEqual(path.point(0.0), (600 + 350j)) self.assertAlmostEqual(path.point(0.3), (755.23979927 + 212.1820209585j)) self.assertAlmostEqual(path.point(0.5), (827.73074926 + 147.8241574162j)) self.assertAlmostEqual(path.point(0.9), (971.28435780 + 106.3023526073j)) self.assertAlmostEqual(path.point(1.0), (1050 + 125j)) self.assertAlmostEqual(path.length(), 928.388639381) def test_repr(self) -> None: path = Path( Line(start=600 + 350j, end=650 + 325j), Arc( start=650 + 325j, radius=25 + 25j, rotation=-30, arc=0, sweep=1, end=700 + 300j, ), CubicBezier( start=700 + 300j, control1=800 + 400j, control2=750 + 200j, end=600 + 100j, ), QuadraticBezier(start=600 + 100j, control=600, end=600 + 300j), ) self.assertEqual(eval(repr(path)), path) def test_reverse(self) -> None: # Currently you can't reverse paths. self.assertRaises(NotImplementedError, Path().reverse) def test_equality(self) -> None: # This is to test the __eq__ and __ne__ methods, so we can't use # assertEqual and assertNotEqual path1 = Path( Line(start=600 + 350j, end=650 + 325j), Arc( start=650 + 325j, radius=25 + 25j, rotation=-30, arc=0, sweep=1, end=700 + 300j, ), CubicBezier( start=700 + 300j, control1=800 + 400j, control2=750 + 200j, end=600 + 100j, ), QuadraticBezier(start=600 + 100j, control=600, end=600 + 300j), ) path2 = Path( Line(start=600 + 350j, end=650 + 325j), Arc( start=650 + 325j, radius=25 + 25j, rotation=-30, arc=0, sweep=1, end=700 + 300j, ), CubicBezier( start=700 + 300j, control1=800 + 400j, control2=750 + 200j, end=600 + 100j, ), QuadraticBezier(start=600 + 100j, control=600, end=600 + 300j), ) self.assertTrue(path1 == path2) # Modify path2: path2[0].start = 601 + 350j self.assertTrue(path1 != path2) # Modify back: path2[0].start = 600 + 350j self.assertFalse(path1 != path2) # Get rid of the last segment: del path2[-1] self.assertFalse(path1 == path2) # It is equal to a list of it's segments self.assertEqual(path1, path1[:]) def test_non_arc(self) -> None: # And arc with the same start and end is a noop. segment = Arc(0j + 70j, 35 + 35j, 0, 1, 0, 0 + 70j) self.assertEqual(segment.length(), 0) self.assertEqual(segment.point(0.5), segment.start) def test_zero_paths(self) -> None: move_only = Path(Move(0)) self.assertEqual(move_only.point(0), 0 + 0j) self.assertEqual(move_only.point(0.5), 0 + 0j) self.assertEqual(move_only.point(1), 0 + 0j) self.assertEqual(move_only.length(), 0) move_onlyz = Path(Move(0), Close(0, 0)) self.assertEqual(move_onlyz.point(0), 0 + 0j) self.assertEqual(move_onlyz.point(0.5), 0 + 0j) self.assertEqual(move_onlyz.point(1), 0 + 0j) self.assertEqual(move_onlyz.length(), 0) zero_line = Path(Move(0), Line(0, 0)) self.assertEqual(zero_line.point(0), 0 + 0j) self.assertEqual(zero_line.point(0.5), 0 + 0j) self.assertEqual(zero_line.point(1), 0 + 0j) self.assertEqual(zero_line.length(), 0) only_line = Path(Line(1 + 1j, 1 + 1j)) self.assertEqual(only_line.point(0), 1 + 1j) self.assertEqual(only_line.point(0.5), 1 + 1j) self.assertEqual(only_line.point(1), 1 + 1j) self.assertEqual(only_line.length(), 0) def test_tangent(self) -> None: path = Path( Line(start=600 + 350j, end=650 + 325j), Arc( start=650 + 325j, radius=25 + 25j, rotation=-30, arc=0, sweep=1, end=700 + 300j, ), CubicBezier( start=700 + 300j, control1=800 + 400j, control2=750 + 200j, end=600 + 100j, ), QuadraticBezier(start=600 + 100j, control=600, end=600 + 300j), ) self.assertEqual(path.tangent(0), 50 - 25j) # These are *not* calculated, but just regression tests. Be skeptical. self.assertAlmostEqual( path.tangent(0.25), 197.17077123205894 + 106.56022001841387j ) self.assertAlmostEqual( path.tangent(0.5), -226.30788045372367 - 364.5433357646594j ) self.assertAlmostEqual(path.tangent(0.75), 13.630819414210208j) self.assertAlmostEqual(path.tangent(1), 600j) def test_tangent_magnitude(self) -> None: line1 = Line(start=6 + 3.5j, end=6.5 + 3.25j) line2 = Line(start=6 + 3.5j, end=7 + 3j) # line2 is twice as long as line1, the tangent should have twice the magnitude: self.assertAlmostEqual(line2.tangent(0.5) / line1.tangent(0.5), 2) arc1 = Arc( start=0 - 2.5j, radius=2.5 + 2.5j, rotation=0, arc=0, sweep=1, end=0 + 2.5j ) arc2 = Arc(start=0 - 5j, radius=5 + 5j, rotation=0, arc=0, sweep=1, end=0 + 5j) # The radius is twice as large, so the magnitude is twice as large self.assertAlmostEqual(arc2.tangent(0.5) / arc1.tangent(0.5), 2) bez1 = CubicBezier(start=0, control1=1 + 1j, control2=2 - 1j, end=3) bez2 = CubicBezier(start=0, control1=2 + 2j, control2=4 - 2j, end=6) # Length should be double, tangent is double. self.assertAlmostEqual(bez2.tangent(0.5) / bez1.tangent(0.5), 2) qb1 = QuadraticBezier(start=0, control=1 + 1j, end=2) qb2 = QuadraticBezier(start=0, control=2 + 2j, end=4) # Length should be double, tangent is double. self.assertAlmostEqual(qb2.tangent(0.5) / qb1.tangent(0.5), 2) # Code for visually verifying these tangents. I should make a test of this. # import turtle # t = turtle.Turtle() # t.penup() # for arc in (line1, line2, arc1, arc2, bez1, bez2): # p = arc.point(0) # t.goto(p.real*20, -p.imag*20) # t.dot(3, 'black') # t.pendown() # for x in range(1, 101): # p = arc.point(x * 0.01) # t.goto(p.real*20,-p.imag*20) # t.penup() # t.dot(3, 'black') # p = arc.point(0.5) # t.goto(p.real*20,-p.imag*20) # t.dot(3, 'red') # t.pendown() # p += arc.tangent(0.5) # t.goto(p.real*20,-p.imag*20) # t.penup()