def test_approx_circle(self):
"""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):
# 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))
