1330 lines
59 KiB
Python
1330 lines
59 KiB
Python
# External dependencies
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from __future__ import division, absolute_import, print_function
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import unittest
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from math import sqrt, pi
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from operator import itemgetter
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from numpy import poly1d, linspace
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# Internal dependencies
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from svgpathtools import *
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# An important note for those doing any debugging:
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# ------------------------------------------------
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# Most of these test points are not calculated separately, as that would
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# take too long and be too error prone. Instead the curves have been verified
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# to be correct visually with the disvg() function.
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class LineTest(unittest.TestCase):
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def test_lines(self):
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# These points are calculated, and not just regression tests.
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line1 = Line(0j, 400 + 0j)
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self.assertAlmostEqual(line1.point(0), 0j)
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self.assertAlmostEqual(line1.point(0.3), (120 + 0j))
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self.assertAlmostEqual(line1.point(0.5), (200 + 0j))
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self.assertAlmostEqual(line1.point(0.9), (360 + 0j))
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self.assertAlmostEqual(line1.point(1), (400 + 0j))
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self.assertAlmostEqual(line1.length(), 400)
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line2 = Line(400 + 0j, 400 + 300j)
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self.assertAlmostEqual(line2.point(0), (400 + 0j))
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self.assertAlmostEqual(line2.point(0.3), (400 + 90j))
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self.assertAlmostEqual(line2.point(0.5), (400 + 150j))
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self.assertAlmostEqual(line2.point(0.9), (400 + 270j))
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self.assertAlmostEqual(line2.point(1), (400 + 300j))
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self.assertAlmostEqual(line2.length(), 300)
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line3 = Line(400 + 300j, 0j)
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self.assertAlmostEqual(line3.point(0), (400 + 300j))
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self.assertAlmostEqual(line3.point(0.3), (280 + 210j))
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self.assertAlmostEqual(line3.point(0.5), (200 + 150j))
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self.assertAlmostEqual(line3.point(0.9), (40 + 30j))
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self.assertAlmostEqual(line3.point(1), 0j)
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self.assertAlmostEqual(line3.length(), 500)
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def test_equality(self):
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# This is to test the __eq__ and __ne__ methods, so we can't use
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# assertEqual and assertNotEqual
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line = Line(0j, 400 + 0j)
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cubic = CubicBezier(600 + 500j, 600 + 350j, 900 + 650j, 900 + 500j)
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self.assertTrue(line == Line(0, 400))
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self.assertTrue(line != Line(100, 400))
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self.assertFalse(line == str(line))
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self.assertTrue(line != str(line))
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self.assertFalse(cubic == line)
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class CubicBezierTest(unittest.TestCase):
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def test_approx_circle(self):
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"""This is a approximate circle drawn in Inkscape"""
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cub1 = CubicBezier(
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complex(0, 0),
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complex(0, 109.66797),
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complex(-88.90345, 198.57142),
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complex(-198.57142, 198.57142)
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)
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self.assertAlmostEqual(cub1.point(0), 0j)
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self.assertAlmostEqual(cub1.point(0.1), (-2.59896457 + 32.20931647j))
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self.assertAlmostEqual(cub1.point(0.2), (-10.12330256 + 62.76392816j))
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self.assertAlmostEqual(cub1.point(0.3), (-22.16418039 + 91.25500149j))
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self.assertAlmostEqual(cub1.point(0.4), (-38.31276448 + 117.27370288j))
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self.assertAlmostEqual(cub1.point(0.5), (-58.16022125 + 140.41119875j))
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self.assertAlmostEqual(cub1.point(0.6), (-81.29771712 + 160.25865552j))
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self.assertAlmostEqual(cub1.point(0.7), (-107.31641851 + 176.40723961j))
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self.assertAlmostEqual(cub1.point(0.8), (-135.80749184 + 188.44811744j))
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self.assertAlmostEqual(cub1.point(0.9), (-166.36210353 + 195.97245543j))
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self.assertAlmostEqual(cub1.point(1), (-198.57142 + 198.57142j))
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cub2 = CubicBezier(
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complex(-198.57142, 198.57142),
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complex(-109.66797 - 198.57142, 0 + 198.57142),
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complex(-198.57143 - 198.57142, -88.90345 + 198.57142),
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complex(-198.57143 - 198.57142, 0),
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)
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self.assertAlmostEqual(cub2.point(0), (-198.57142 + 198.57142j))
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self.assertAlmostEqual(cub2.point(0.1), (-230.78073675 + 195.97245543j))
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self.assertAlmostEqual(cub2.point(0.2), (-261.3353492 + 188.44811744j))
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self.assertAlmostEqual(cub2.point(0.3), (-289.82642365 + 176.40723961j))
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self.assertAlmostEqual(cub2.point(0.4), (-315.8451264 + 160.25865552j))
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self.assertAlmostEqual(cub2.point(0.5), (-338.98262375 + 140.41119875j))
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self.assertAlmostEqual(cub2.point(0.6), (-358.830082 + 117.27370288j))
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self.assertAlmostEqual(cub2.point(0.7), (-374.97866745 + 91.25500149j))
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self.assertAlmostEqual(cub2.point(0.8), (-387.0195464 + 62.76392816j))
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self.assertAlmostEqual(cub2.point(0.9), (-394.54388515 + 32.20931647j))
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self.assertAlmostEqual(cub2.point(1), (-397.14285 + 0j))
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cub3 = CubicBezier(
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complex(-198.57143 - 198.57142, 0),
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complex(0 - 198.57143 - 198.57142, -109.66797),
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complex(88.90346 - 198.57143 - 198.57142, -198.57143),
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complex(-198.57142, -198.57143)
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)
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self.assertAlmostEqual(cub3.point(0), (-397.14285 + 0j))
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self.assertAlmostEqual(cub3.point(0.1), (-394.54388515 - 32.20931675j))
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self.assertAlmostEqual(cub3.point(0.2), (-387.0195464 - 62.7639292j))
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self.assertAlmostEqual(cub3.point(0.3), (-374.97866745 - 91.25500365j))
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self.assertAlmostEqual(cub3.point(0.4), (-358.830082 - 117.2737064j))
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self.assertAlmostEqual(cub3.point(0.5), (-338.98262375 - 140.41120375j))
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self.assertAlmostEqual(cub3.point(0.6), (-315.8451264 - 160.258662j))
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self.assertAlmostEqual(cub3.point(0.7), (-289.82642365 - 176.40724745j))
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self.assertAlmostEqual(cub3.point(0.8), (-261.3353492 - 188.4481264j))
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self.assertAlmostEqual(cub3.point(0.9), (-230.78073675 - 195.97246515j))
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self.assertAlmostEqual(cub3.point(1), (-198.57142 - 198.57143j))
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cub4 = CubicBezier(
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complex(-198.57142, -198.57143),
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complex(109.66797 - 198.57142, 0 - 198.57143),
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complex(0, 88.90346 - 198.57143),
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complex(0, 0),
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)
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self.assertAlmostEqual(cub4.point(0), (-198.57142 - 198.57143j))
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self.assertAlmostEqual(cub4.point(0.1), (-166.36210353 - 195.97246515j))
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self.assertAlmostEqual(cub4.point(0.2), (-135.80749184 - 188.4481264j))
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self.assertAlmostEqual(cub4.point(0.3), (-107.31641851 - 176.40724745j))
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self.assertAlmostEqual(cub4.point(0.4), (-81.29771712 - 160.258662j))
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self.assertAlmostEqual(cub4.point(0.5), (-58.16022125 - 140.41120375j))
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self.assertAlmostEqual(cub4.point(0.6), (-38.31276448 - 117.2737064j))
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self.assertAlmostEqual(cub4.point(0.7), (-22.16418039 - 91.25500365j))
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self.assertAlmostEqual(cub4.point(0.8), (-10.12330256 - 62.7639292j))
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self.assertAlmostEqual(cub4.point(0.9), (-2.59896457 - 32.20931675j))
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self.assertAlmostEqual(cub4.point(1), 0j)
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def test_svg_examples(self):
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# M100,200 C100,100 250,100 250,200
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path1 = CubicBezier(100 + 200j, 100 + 100j, 250 + 100j, 250 + 200j)
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self.assertAlmostEqual(path1.point(0), (100 + 200j))
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self.assertAlmostEqual(path1.point(0.3), (132.4 + 137j))
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self.assertAlmostEqual(path1.point(0.5), (175 + 125j))
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self.assertAlmostEqual(path1.point(0.9), (245.8 + 173j))
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self.assertAlmostEqual(path1.point(1), (250 + 200j))
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# S400,300 400,200
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path2 = CubicBezier(250 + 200j, 250 + 300j, 400 + 300j, 400 + 200j)
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self.assertAlmostEqual(path2.point(0), (250 + 200j))
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self.assertAlmostEqual(path2.point(0.3), (282.4 + 263j))
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self.assertAlmostEqual(path2.point(0.5), (325 + 275j))
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self.assertAlmostEqual(path2.point(0.9), (395.8 + 227j))
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self.assertAlmostEqual(path2.point(1), (400 + 200j))
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# M100,200 C100,100 400,100 400,200
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path3 = CubicBezier(100 + 200j, 100 + 100j, 400 + 100j, 400 + 200j)
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self.assertAlmostEqual(path3.point(0), (100 + 200j))
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self.assertAlmostEqual(path3.point(0.3), (164.8 + 137j))
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self.assertAlmostEqual(path3.point(0.5), (250 + 125j))
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self.assertAlmostEqual(path3.point(0.9), (391.6 + 173j))
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self.assertAlmostEqual(path3.point(1), (400 + 200j))
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# M100,500 C25,400 475,400 400,500
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path4 = CubicBezier(100 + 500j, 25 + 400j, 475 + 400j, 400 + 500j)
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self.assertAlmostEqual(path4.point(0), (100 + 500j))
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self.assertAlmostEqual(path4.point(0.3), (145.9 + 437j))
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self.assertAlmostEqual(path4.point(0.5), (250 + 425j))
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self.assertAlmostEqual(path4.point(0.9), (407.8 + 473j))
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self.assertAlmostEqual(path4.point(1), (400 + 500j))
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# M100,800 C175,700 325,700 400,800
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path5 = CubicBezier(100 + 800j, 175 + 700j, 325 + 700j, 400 + 800j)
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self.assertAlmostEqual(path5.point(0), (100 + 800j))
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self.assertAlmostEqual(path5.point(0.3), (183.7 + 737j))
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self.assertAlmostEqual(path5.point(0.5), (250 + 725j))
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self.assertAlmostEqual(path5.point(0.9), (375.4 + 773j))
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self.assertAlmostEqual(path5.point(1), (400 + 800j))
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# M600,200 C675,100 975,100 900,200
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path6 = CubicBezier(600 + 200j, 675 + 100j, 975 + 100j, 900 + 200j)
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self.assertAlmostEqual(path6.point(0), (600 + 200j))
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self.assertAlmostEqual(path6.point(0.3), (712.05 + 137j))
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self.assertAlmostEqual(path6.point(0.5), (806.25 + 125j))
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self.assertAlmostEqual(path6.point(0.9), (911.85 + 173j))
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self.assertAlmostEqual(path6.point(1), (900 + 200j))
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# M600,500 C600,350 900,650 900,500
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path7 = CubicBezier(600 + 500j, 600 + 350j, 900 + 650j, 900 + 500j)
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self.assertAlmostEqual(path7.point(0), (600 + 500j))
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self.assertAlmostEqual(path7.point(0.3), (664.8 + 462.2j))
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self.assertAlmostEqual(path7.point(0.5), (750 + 500j))
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self.assertAlmostEqual(path7.point(0.9), (891.6 + 532.4j))
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self.assertAlmostEqual(path7.point(1), (900 + 500j))
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# M600,800 C625,700 725,700 750,800
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path8 = CubicBezier(600 + 800j, 625 + 700j, 725 + 700j, 750 + 800j)
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self.assertAlmostEqual(path8.point(0), (600 + 800j))
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self.assertAlmostEqual(path8.point(0.3), (638.7 + 737j))
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self.assertAlmostEqual(path8.point(0.5), (675 + 725j))
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self.assertAlmostEqual(path8.point(0.9), (740.4 + 773j))
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self.assertAlmostEqual(path8.point(1), (750 + 800j))
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# S875,900 900,800
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inversion = (750 + 800j) + (750 + 800j) - (725 + 700j)
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path9 = CubicBezier(750 + 800j, inversion, 875 + 900j, 900 + 800j)
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self.assertAlmostEqual(path9.point(0), (750 + 800j))
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self.assertAlmostEqual(path9.point(0.3), (788.7 + 863j))
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self.assertAlmostEqual(path9.point(0.5), (825 + 875j))
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self.assertAlmostEqual(path9.point(0.9), (890.4 + 827j))
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self.assertAlmostEqual(path9.point(1), (900 + 800j))
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def test_length(self):
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# A straight line:
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cub = CubicBezier(
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complex(0, 0),
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complex(0, 0),
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complex(0, 100),
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complex(0, 100)
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)
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self.assertAlmostEqual(cub.length(), 100)
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# A diagonal line:
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cub = CubicBezier(
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complex(0, 0),
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complex(0, 0),
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complex(100, 100),
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complex(100, 100)
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)
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self.assertAlmostEqual(cub.length(), sqrt(2 * 100 * 100))
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# A quarter circle large_arc with radius 100
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# http://www.whizkidtech.redprince.net/bezier/circle/
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kappa = 4 * (sqrt(2) - 1) / 3
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cub = CubicBezier(
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complex(0, 0),
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complex(0, kappa * 100),
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complex(100 - kappa * 100, 100),
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complex(100, 100)
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)
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# We can't compare with pi*50 here, because this is just an
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# approximation of a circle large_arc. pi*50 is 157.079632679
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# So this is just yet another "warn if this changes" test.
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# This value is not verified to be correct.
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self.assertAlmostEqual(cub.length(), 157.1016698)
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# A recursive solution has also been suggested, but for CubicBezier
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# curves it could get a false solution on curves where the midpoint is
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# on a straight line between the start and end. For example, the
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# following curve would get solved as a straight line and get the
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# length 300.
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# Make sure this is not the case.
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cub = CubicBezier(
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complex(600, 500),
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complex(600, 350),
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complex(900, 650),
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complex(900, 500)
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)
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self.assertTrue(cub.length() > 300.0)
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def test_equality(self):
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# This is to test the __eq__ and __ne__ methods, so we can't use
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# assertEqual and assertNotEqual
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segment = CubicBezier(complex(600, 500), complex(600, 350),
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complex(900, 650), complex(900, 500))
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self.assertTrue(segment ==
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CubicBezier(600 + 500j, 600 + 350j, 900 + 650j, 900 + 500j))
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self.assertTrue(segment !=
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CubicBezier(600 + 501j, 600 + 350j, 900 + 650j, 900 + 500j))
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self.assertTrue(segment != Line(0, 400))
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class QuadraticBezierTest(unittest.TestCase):
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def test_svg_examples(self):
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"""These is the path in the SVG specs"""
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# M200,300 Q400,50 600,300 T1000,300
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path1 = QuadraticBezier(200 + 300j, 400 + 50j, 600 + 300j)
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self.assertAlmostEqual(path1.point(0), (200 + 300j))
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self.assertAlmostEqual(path1.point(0.3), (320 + 195j))
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self.assertAlmostEqual(path1.point(0.5), (400 + 175j))
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self.assertAlmostEqual(path1.point(0.9), (560 + 255j))
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self.assertAlmostEqual(path1.point(1), (600 + 300j))
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# T1000, 300
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inversion = (600 + 300j) + (600 + 300j) - (400 + 50j)
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path2 = QuadraticBezier(600 + 300j, inversion, 1000 + 300j)
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self.assertAlmostEqual(path2.point(0), (600 + 300j))
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self.assertAlmostEqual(path2.point(0.3), (720 + 405j))
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self.assertAlmostEqual(path2.point(0.5), (800 + 425j))
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self.assertAlmostEqual(path2.point(0.9), (960 + 345j))
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self.assertAlmostEqual(path2.point(1), (1000 + 300j))
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def test_length(self):
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# expected results calculated with
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# svg.path.segment_length(q, 0, 1, q.start, q.end, 1e-14, 20, 0)
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q1 = QuadraticBezier(200 + 300j, 400 + 50j, 600 + 300j)
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q2 = QuadraticBezier(200 + 300j, 400 + 50j, 500 + 200j)
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closedq = QuadraticBezier(6+2j, 5-1j, 6+2j)
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linq1 = QuadraticBezier(1, 2, 3)
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linq2 = QuadraticBezier(1+3j, 2+5j, -9 - 17j)
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nodalq = QuadraticBezier(1, 1, 1)
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tests = [(q1, 487.77109389525975),
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(q2, 379.90458193489155),
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(closedq, 3.1622776601683795),
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(linq1, 2),
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(linq2, 22.73335777124786),
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(nodalq, 0)]
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for q, exp_res in tests:
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self.assertAlmostEqual(q.length(), exp_res)
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# partial length tests
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tests = [(q1, 212.34775387566032),
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(q2, 166.22170622052397),
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(closedq, 0.7905694150420949),
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(linq1, 1.0),
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(nodalq, 0.0)]
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t0 = 0.25
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t1 = 0.75
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for q, exp_res in tests:
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self.assertAlmostEqual(q.length(t0=t0, t1=t1), exp_res)
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# linear partial cases
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linq2 = QuadraticBezier(1+3j, 2+5j, -9 - 17j)
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tests = [(0, 1/24, 0.13975424859373725),
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(0, 1/12, 0.1863389981249823),
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(0, 0.5, 4.844813951249543),
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(0, 1, 22.73335777124786),
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(1/24, 1/12, 0.04658474953124506),
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(1/24, 0.5, 4.705059702655722),
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(1/24, 1, 22.59360352265412),
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(1/12, 0.5, 4.658474953124562),
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(1/12, 1, 22.54701877312288),
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(0.5, 1, 17.88854381999832)]
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for t0, t1, exp_s in tests:
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self.assertAlmostEqual(linq2.length(t0=t0, t1=t1), exp_s)
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def test_equality(self):
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# This is to test the __eq__ and __ne__ methods, so we can't use
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# assertEqual and assertNotEqual
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segment = QuadraticBezier(200 + 300j, 400 + 50j, 600 + 300j)
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self.assertTrue(segment ==
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QuadraticBezier(200 + 300j, 400 + 50j, 600 + 300j))
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self.assertTrue(segment !=
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QuadraticBezier(200 + 301j, 400 + 50j, 600 + 300j))
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self.assertFalse(segment == Arc(0j, 100 + 50j, 0, 0, 0, 100 + 50j))
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self.assertTrue(Arc(0j, 100 + 50j, 0, 0, 0, 100 + 50j) != segment)
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class ArcTest(unittest.TestCase):
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def test_trusting_acos(self):
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"""`u1.real` is > 1 in this arc due to numerical error."""
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try:
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a1 = Arc(start=(160.197+102.925j),
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radius=(0.025+0.025j),
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rotation=0.0,
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large_arc=False,
|
|
sweep=True,
|
|
end=(160.172+102.95j))
|
|
except ValueError:
|
|
self.fail("Arc() raised ValueError unexpectedly!")
|
|
|
|
def test_points(self):
|
|
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, -90.0)
|
|
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, -90.0)
|
|
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))
|
|
|
|
arc5 = Arc((725.307482225571-915.5548199281527j),
|
|
(202.79421639137703+148.77294617167183j),
|
|
225.6910319606926, 1, 1,
|
|
(-624.6375539637027+896.5483089399895j))
|
|
self.assertAlmostEqual(arc5.point(0.0), (725.307482226-915.554819928j))
|
|
self.assertAlmostEqual(arc5.point(0.0909090909091),
|
|
(1023.47397369-597.730444283j))
|
|
self.assertAlmostEqual(arc5.point(0.181818181818),
|
|
(1242.80253007-232.251400124j))
|
|
self.assertAlmostEqual(arc5.point(0.272727272727),
|
|
(1365.52445614+151.273373978j))
|
|
self.assertAlmostEqual(arc5.point(0.363636363636),
|
|
(1381.69755131+521.772981736j))
|
|
self.assertAlmostEqual(arc5.point(0.454545454545),
|
|
(1290.01156757+849.231748376j))
|
|
self.assertAlmostEqual(arc5.point(0.545454545455),
|
|
(1097.89435807+1107.12091209j))
|
|
self.assertAlmostEqual(arc5.point(0.636363636364),
|
|
(820.910116547+1274.54782658j))
|
|
self.assertAlmostEqual(arc5.point(0.727272727273),
|
|
(481.49845896+1337.94855893j))
|
|
self.assertAlmostEqual(arc5.point(0.818181818182),
|
|
(107.156499251+1292.18675889j))
|
|
self.assertAlmostEqual(arc5.point(0.909090909091),
|
|
(-271.788803303+1140.96977533j))
|
|
|
|
def test_length(self):
|
|
# 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_equality(self):
|
|
# 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))
|
|
|
|
|
|
class TestPath(unittest.TestCase):
|
|
|
|
def test_circle(self):
|
|
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):
|
|
"""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
|
|
|
|
# Commented out because by Andy cause I was skeptical of path.point
|
|
# ground truth values
|
|
# 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), (600+350j))
|
|
# self.assertAlmostEqual(path.point(0.3), (755.239799276+212.182020958j))
|
|
# self.assertAlmostEqual(path.point(0.5), (827.730749264+147.824157418j))
|
|
# self.assertAlmostEqual(path.point(0.9), (971.284357806+106.302352605j))
|
|
# self.assertAlmostEqual(path.point(1), (1050+125j))
|
|
# # The errors seem to accumulate. Still 6 decimal places is more
|
|
# # than good enough.
|
|
# self.assertAlmostEqual(path.length(), 928.3886394081095)
|
|
|
|
def test_repr(self):
|
|
path = Path(
|
|
Line(start=600 + 350j, end=650 + 325j),
|
|
Arc(start=650 + 325j, radius=25 + 25j, rotation=-30,
|
|
large_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_equality(self):
|
|
# 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,
|
|
large_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,
|
|
large_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's not equal to a list of it's segments
|
|
self.assertTrue(path1 != path1[:])
|
|
self.assertFalse(path1 == path1[:])
|
|
|
|
def test_continuous_subpaths(self):
|
|
"""Test the Path.continuous_subpaths() method."""
|
|
|
|
# Continuous and open example
|
|
q = Path(Line(1, 2))
|
|
a = [Path(Line(1, 2))]
|
|
subpaths = q.continuous_subpaths()
|
|
chk1 = all(subpath.iscontinuous() for subpath in subpaths)
|
|
chk2 = (q == Path(*[seg for subpath in subpaths for seg in subpath]))
|
|
self.assertTrue(subpaths == a)
|
|
self.assertTrue(chk1)
|
|
self.assertTrue(chk2)
|
|
|
|
# # Continuous and closed example
|
|
q = Path(Line(1, 2), Line(2, 1))
|
|
a = [Path(Line(1, 2), Line(2, 1))]
|
|
subpaths = q.continuous_subpaths()
|
|
chk1 = all(subpath.iscontinuous() for subpath in subpaths)
|
|
chk2 = q == Path(*[seg for subpath in subpaths for seg in subpath])
|
|
self.assertTrue(subpaths == a)
|
|
self.assertTrue(chk1)
|
|
self.assertTrue(chk2)
|
|
|
|
# Continuous and open example
|
|
q = Path(Line(1, 2), Line(2, 3), Line(3, 4))
|
|
a = [Path(Line(1, 2), Line(2, 3), Line(3, 4))]
|
|
subpaths = q.continuous_subpaths()
|
|
chk1 = all(subpath.iscontinuous() for subpath in subpaths)
|
|
chk2 = (q == Path(*[seg for subpath in subpaths for seg in subpath]))
|
|
self.assertTrue(subpaths == a)
|
|
self.assertTrue(chk1)
|
|
self.assertTrue(chk2)
|
|
|
|
# Continuous and closed example
|
|
q = Path(Line(1, 2), Line(2, 3), Line(3, 4), Line(4, 1))
|
|
a = [Path(Line(1, 2), Line(2, 3), Line(3, 4), Line(4, 1))]
|
|
subpaths = q.continuous_subpaths()
|
|
chk1 = all(subpath.iscontinuous() for subpath in subpaths)
|
|
chk2 = (q == Path(*[seg for subpath in subpaths for seg in subpath]))
|
|
self.assertTrue(subpaths == a)
|
|
self.assertTrue(chk1)
|
|
self.assertTrue(chk2)
|
|
|
|
# Discontinuous example
|
|
q = Path(Line(1, 2), Line(2, 3), Line(3, 4),
|
|
Line(10, 11))
|
|
a = [Path(Line(1, 2), Line(2, 3), Line(3, 4)),
|
|
Path(Line(10, 11))]
|
|
subpaths = q.continuous_subpaths()
|
|
chk1 = all(subpath.iscontinuous() for subpath in subpaths)
|
|
chk2 = (q == Path(*[seg for subpath in subpaths for seg in subpath]))
|
|
self.assertTrue(subpaths == a)
|
|
self.assertTrue(chk1)
|
|
self.assertTrue(chk2)
|
|
|
|
# Discontinuous closed example
|
|
q = Path(Line(1, 2), Line(2, 3), Line(3, 4), Line(4, 1),
|
|
Line(10, 11), Line(11, 12))
|
|
a = [Path(Line(1, 2), Line(2, 3), Line(3, 4), Line(4, 1)),
|
|
Path(Line(10, 11), Line(11, 12))]
|
|
subpaths = q.continuous_subpaths()
|
|
chk1 = all(subpath.iscontinuous() for subpath in subpaths)
|
|
chk2 = (q == Path(*[seg for subpath in subpaths for seg in subpath]))
|
|
self.assertTrue(subpaths == a)
|
|
self.assertTrue(chk1)
|
|
self.assertTrue(chk2)
|
|
|
|
# Discontinuous example
|
|
q = Path(Line(1, 2),
|
|
Line(1, 2), Line(2, 3),
|
|
Line(10, 11), Line(11, 12), Line(12, 13),
|
|
Line(10, 11), Line(11, 12), Line(12, 13), Line(13, 14))
|
|
a = [Path(Line(1, 2)),
|
|
Path(Line(1, 2), Line(2, 3)),
|
|
Path(Line(10, 11), Line(11, 12), Line(12, 13)),
|
|
Path(Line(10, 11), Line(11, 12), Line(12, 13), Line(13, 14))]
|
|
subpaths = q.continuous_subpaths()
|
|
chk1 = all(subpath.iscontinuous() for subpath in subpaths)
|
|
chk2 = (q == Path(*[seg for subpath in subpaths for seg in subpath]))
|
|
self.assertTrue(subpaths == a)
|
|
self.assertTrue(chk1)
|
|
self.assertTrue(chk2)
|
|
|
|
# Discontinuous example with overlapping end
|
|
q = Path(Line(1, 2),
|
|
Line(5, 6), Line(6, 7),
|
|
Line(10, 11), Line(11, 12), Line(12, 13),
|
|
Line(10, 11), Line(11, 12), Line(12, 13), Line(13, 1))
|
|
a = [Path(Line(1, 2)),
|
|
Path(Line(5, 6), Line(6, 7)),
|
|
Path(Line(10, 11), Line(11, 12), Line(12, 13)),
|
|
Path(Line(10, 11), Line(11, 12), Line(12, 13), Line(13, 1))]
|
|
subpaths = q.continuous_subpaths()
|
|
chk1 = all(subpath.iscontinuous() for subpath in subpaths)
|
|
chk2 = (q == Path(*[seg for subpath in subpaths for seg in subpath]))
|
|
self.assertTrue(subpaths == a)
|
|
self.assertTrue(chk1)
|
|
self.assertTrue(chk2)
|
|
|
|
def test_cropped(self):
|
|
p_closed = Path(Line(0, 1), Line(1, 1 + 1j), Line(1 + 1j, 1j),
|
|
Line(1j, 0))
|
|
first_half = Path(Line(0, 1), Line(1, 1 + 1j))
|
|
second_half = Path(Line(1 + 1j, 1j), Line(1j, 0))
|
|
middle_half = Path(Line(1, 1 + 1j), Line(1 + 1j, 1j))
|
|
other_middle_half = Path(Line(1j, 0), Line(0, 1))
|
|
self.assertTrue(p_closed.cropped(0, 0.5) == first_half)
|
|
self.assertTrue(p_closed.cropped(1, 0.5) == first_half)
|
|
self.assertTrue(p_closed.cropped(.5, 1) == second_half)
|
|
self.assertTrue(p_closed.cropped(0.25, 0.75) == middle_half)
|
|
self.assertTrue(p_closed.cropped(0.75, 0.25) == other_middle_half)
|
|
with self.assertRaises(AssertionError):
|
|
p_closed.cropped(1, 0)
|
|
with self.assertRaises(AssertionError):
|
|
p_closed.cropped(.5, 1.1)
|
|
with self.assertRaises(AssertionError):
|
|
p_closed.cropped(-0.1, 0.1)
|
|
|
|
p_open = Path(Line(0, 1), Line(1, 1 + 1j), Line(1 + 1j, 1j),
|
|
Line(1j, 2j))
|
|
self.assertTrue(p_open.cropped(0, 0.5) == first_half)
|
|
with self.assertRaises(ValueError):
|
|
p_open.cropped(.75, .25)
|
|
with self.assertRaises(ValueError):
|
|
p_open.cropped(1, .25)
|
|
with self.assertRaises(AssertionError):
|
|
p_open.cropped(1, 0)
|
|
|
|
def test_transform_scale(self):
|
|
line1 = Line(600.5 + 350.5j, 650.5 + 325.5j)
|
|
arc1 = Arc(650 + 325j, 25 + 25j, -30, 0, 1, 700 + 300j)
|
|
arc2 = Arc(650 + 325j, 30 + 25j, -30, 0, 0, 700 + 300j)
|
|
cub1 = CubicBezier(650 + 325j, 25 + 25j, -30, 700 + 300j)
|
|
cub2 = CubicBezier(700 + 300j, 800 + 400j, 750 + 200j, 600 + 100j)
|
|
quad3 = QuadraticBezier(600 + 100j, 600, 600 + 300j)
|
|
linez = Line(600 + 300j, 600 + 350j)
|
|
|
|
bezpath = Path(line1, cub1, cub2, quad3)
|
|
bezpathz = Path(line1, cub1, cub2, quad3, linez)
|
|
path = Path(line1, arc1, cub2, quad3)
|
|
pathz = Path(line1, arc1, cub2, quad3, linez)
|
|
lpath = Path(linez)
|
|
qpath = Path(quad3)
|
|
cpath = Path(cub1)
|
|
apath = Path(arc1, arc2)
|
|
|
|
test_curves = ([bezpath, bezpathz, path, pathz, lpath, qpath, cpath, apath] +
|
|
[line1, arc1, arc2, cub1, cub2, quad3, linez])
|
|
|
|
for path_orig in test_curves:
|
|
|
|
# scale by 2 around (100, 100)
|
|
path_trns = path_orig.scaled(2.0, complex(100, 100))
|
|
|
|
# expected length
|
|
len_orig = path_orig.length()
|
|
len_trns = path_trns.length()
|
|
self.assertAlmostEqual(len_orig * 2.0, len_trns)
|
|
|
|
# expected positions
|
|
for T in linspace(0.0, 1.0, num=100):
|
|
pt_orig = path_orig.point(T)
|
|
pt_trns = path_trns.point(T)
|
|
pt_xpct = (pt_orig - complex(100, 100)) * 2.0 + complex(100, 100)
|
|
self.assertAlmostEqual(pt_xpct, pt_trns)
|
|
|
|
for path_orig in test_curves:
|
|
|
|
# scale by 0.3 around (0, -100)
|
|
# the 'almost equal' test fails at the 7th decimal place for
|
|
# some length and position tests here.
|
|
path_trns = path_orig.scaled(0.3, complex(0, -100))
|
|
|
|
# expected length
|
|
len_orig = path_orig.length()
|
|
len_trns = path_trns.length()
|
|
self.assertAlmostEqual(len_orig * 0.3, len_trns, delta = 0.000001)
|
|
|
|
# expected positions
|
|
for T in linspace(0.0, 1.0, num=100):
|
|
pt_orig = path_orig.point(T)
|
|
pt_trns = path_trns.point(T)
|
|
pt_xpct = (pt_orig - complex(0, -100)) * 0.3 + complex(0, -100)
|
|
self.assertAlmostEqual(pt_xpct, pt_trns, delta = 0.000001)
|
|
|
|
|
|
class Test_ilength(unittest.TestCase):
|
|
# See svgpathtools.notes.inv_arclength.py for information on how these
|
|
# test values were generated (using the .length() method).
|
|
##############################################################
|
|
|
|
def test_ilength_lines(self):
|
|
l = Line(1, 3-1j)
|
|
nodall = Line(1+1j, 1+1j)
|
|
|
|
tests = [(l, 0.01, 0.022360679774997897),
|
|
(l, 0.1, 0.223606797749979),
|
|
(l, 0.5, 1.118033988749895),
|
|
(l, 0.9, 2.012461179749811),
|
|
(l, 0.99, 2.213707297724792)]
|
|
|
|
for (l, t, s) in tests:
|
|
self.assertAlmostEqual(l.ilength(s), t)
|
|
|
|
def test_ilength_quadratics(self):
|
|
q1 = QuadraticBezier(200 + 300j, 400 + 50j, 600 + 300j)
|
|
q2 = QuadraticBezier(200 + 300j, 400 + 50j, 500 + 200j)
|
|
closedq = QuadraticBezier(6 + 2j, 5 - 1j, 6 + 2j)
|
|
linq = QuadraticBezier(1+3j, 2+5j, -9 - 17j)
|
|
nodalq = QuadraticBezier(1, 1, 1)
|
|
|
|
tests = [(q1, 0.01, 6.364183310105577),
|
|
(q1, 0.1, 60.23857499635088),
|
|
(q1, 0.5, 243.8855469477619),
|
|
(q1, 0.9, 427.53251889917294),
|
|
(q1, 0.99, 481.40691058541813),
|
|
(q2, 0.01, 6.365673533661836),
|
|
(q2, 0.1, 60.31675895732397),
|
|
(q2, 0.5, 233.24592830045907),
|
|
(q2, 0.9, 346.42891253298706),
|
|
(q2, 0.99, 376.32659156736844),
|
|
(closedq, 0.01, 0.06261309767133393),
|
|
(closedq, 0.1, 0.5692099788303084),
|
|
(closedq, 0.5, 1.5811388300841898),
|
|
(closedq, 0.9, 2.5930676813380713),
|
|
(closedq, 0.99, 3.0996645624970456),
|
|
(linq, 0.01, 0.04203807797699605),
|
|
(linq, 0.1, 0.19379255804998186),
|
|
(linq, 0.5, 4.844813951249544),
|
|
(linq, 0.9, 18.0823363780483),
|
|
(linq, 0.99, 22.24410609777091)]
|
|
|
|
for q, t, s in tests:
|
|
try:
|
|
self.assertAlmostEqual(q.ilength(s), t)
|
|
except:
|
|
print(q)
|
|
print(s)
|
|
print(t)
|
|
raise
|
|
|
|
def test_ilength_cubics(self):
|
|
c1 = CubicBezier(200 + 300j, 400 + 50j, 600+100j, -200)
|
|
symc = CubicBezier(1-2j, 10-1j, 10+1j, 1+2j)
|
|
closedc = CubicBezier(1-2j, 10-1j, 10+1j, 1-2j)
|
|
|
|
tests = [(c1, 0.01, 9.53434737943073),
|
|
(c1, 0.1, 88.89941848775852),
|
|
(c1, 0.5, 278.5750942713189),
|
|
(c1, 0.9, 651.4957786584646),
|
|
(c1, 0.99, 840.2010603832538),
|
|
(symc, 0.01, 0.2690118556702902),
|
|
(symc, 0.1, 2.45230693868727),
|
|
(symc, 0.5, 7.256147083644424),
|
|
(symc, 0.9, 12.059987228602886),
|
|
(symc, 0.99, 14.243282311619401),
|
|
(closedc, 0.01, 0.26901140075538765),
|
|
(closedc, 0.1, 2.451722765460998),
|
|
(closedc, 0.5, 6.974058969750422),
|
|
(closedc, 0.9, 11.41781741489913),
|
|
(closedc, 0.99, 13.681324783697782)]
|
|
|
|
for (c, t, s) in tests:
|
|
self.assertAlmostEqual(c.ilength(s), t)
|
|
|
|
def test_ilength_arcs(self):
|
|
arc1 = Arc(0j, 100 + 50j, 0, 0, 0, 100 + 50j)
|
|
arc2 = Arc(0j, 100 + 50j, 0, 1, 0, 100 + 50j)
|
|
arc3 = Arc(0j, 100 + 50j, 0, 0, 1, 100 + 50j)
|
|
arc4 = Arc(0j, 100 + 50j, 0, 1, 1, 100 + 50j)
|
|
arc5 = Arc(0j, 100 + 100j, 0, 0, 0, 200 + 0j)
|
|
arc6 = Arc(200 + 0j, 100 + 100j, 0, 0, 0, 0j)
|
|
arc7 = Arc(0j, 100 + 50j, 0, 0, 0, 100 + 50j)
|
|
|
|
tests = [(arc1, 0.01, 0.785495042476231),
|
|
(arc1, 0.1, 7.949362877455911),
|
|
(arc1, 0.5, 48.28318721111137),
|
|
(arc1, 0.9, 105.44598206942156),
|
|
(arc1, 0.99, 119.53485487631241),
|
|
(arc2, 0.01, 4.71108115728524),
|
|
(arc2, 0.1, 45.84152747676626),
|
|
(arc2, 0.5, 169.38878996795734),
|
|
(arc2, 0.9, 337.44707303579696),
|
|
(arc2, 0.99, 360.95800139278765),
|
|
(arc3, 0.01, 1.5707478805335624),
|
|
(arc3, 0.1, 15.659620687424416),
|
|
(arc3, 0.5, 72.82241554573457),
|
|
(arc3, 0.9, 113.15623987939003),
|
|
(arc3, 0.99, 120.3201077143697),
|
|
(arc4, 0.01, 2.3588068777503897),
|
|
(arc4, 0.1, 25.869735234740887),
|
|
(arc4, 0.5, 193.9280183025816),
|
|
(arc4, 0.9, 317.4752807937718),
|
|
(arc4, 0.99, 358.6057271132536),
|
|
(arc5, 0.01, 3.141592653589793),
|
|
(arc5, 0.1, 31.415926535897935),
|
|
(arc5, 0.5, 157.07963267948966),
|
|
(arc5, 0.9, 282.7433388230814),
|
|
(arc5, 0.99, 311.01767270538954),
|
|
(arc6, 0.01, 3.141592653589793),
|
|
(arc6, 0.1, 31.415926535897928),
|
|
(arc6, 0.5, 157.07963267948966),
|
|
(arc6, 0.9, 282.7433388230814),
|
|
(arc6, 0.99, 311.01767270538954),
|
|
(arc7, 0.01, 0.785495042476231),
|
|
(arc7, 0.1, 7.949362877455911),
|
|
(arc7, 0.5, 48.28318721111137),
|
|
(arc7, 0.9, 105.44598206942156),
|
|
(arc7, 0.99, 119.53485487631241)]
|
|
|
|
for (c, t, s) in tests:
|
|
self.assertAlmostEqual(c.ilength(s), t)
|
|
|
|
def test_ilength_paths(self):
|
|
line1 = Line(600 + 350j, 650 + 325j)
|
|
arc1 = Arc(650 + 325j, 25 + 25j, -30, 0, 1, 700 + 300j)
|
|
cub1 = CubicBezier(650 + 325j, 25 + 25j, -30, 700 + 300j)
|
|
cub2 = CubicBezier(700 + 300j, 800 + 400j, 750 + 200j, 600 + 100j)
|
|
quad3 = QuadraticBezier(600 + 100j, 600, 600 + 300j)
|
|
linez = Line(600 + 300j, 600 + 350j)
|
|
|
|
bezpath = Path(line1, cub1, cub2, quad3)
|
|
bezpathz = Path(line1, cub1, cub2, quad3, linez)
|
|
path = Path(line1, arc1, cub2, quad3)
|
|
pathz = Path(line1, arc1, cub2, quad3, linez)
|
|
lpath = Path(linez)
|
|
qpath = Path(quad3)
|
|
cpath = Path(cub1)
|
|
apath = Path(arc1)
|
|
|
|
tests = [(bezpath, 0.0, 0.0),
|
|
(bezpath, 0.1111111111111111, 286.2533595149515),
|
|
(bezpath, 0.2222222222222222, 503.8620222915423),
|
|
(bezpath, 0.3333333333333333, 592.6337135346268),
|
|
(bezpath, 0.4444444444444444, 644.3880677233315),
|
|
(bezpath, 0.5555555555555556, 835.0384185011363),
|
|
(bezpath, 0.6666666666666666, 1172.8729938994575),
|
|
(bezpath, 0.7777777777777778, 1308.6205983178952),
|
|
(bezpath, 0.8888888888888888, 1532.8473168900994),
|
|
(bezpath, 1.0, 1758.2427369258733),
|
|
(bezpathz, 0.0, 0.0),
|
|
(bezpathz, 0.1111111111111111, 294.15942308605435),
|
|
(bezpathz, 0.2222222222222222, 512.4295461513882),
|
|
(bezpathz, 0.3333333333333333, 594.0779370040138),
|
|
(bezpathz, 0.4444444444444444, 658.7361976564598),
|
|
(bezpathz, 0.5555555555555556, 874.1674336581542),
|
|
(bezpathz, 0.6666666666666666, 1204.2371344392693),
|
|
(bezpathz, 0.7777777777777778, 1356.773042865213),
|
|
(bezpathz, 0.8888888888888888, 1541.808492602876),
|
|
(bezpathz, 1.0, 1808.2427369258733),
|
|
(path, 0.0, 0.0),
|
|
(path, 0.1111111111111111, 81.44016397108298),
|
|
(path, 0.2222222222222222, 164.72556816469307),
|
|
(path, 0.3333333333333333, 206.71343564679154),
|
|
(path, 0.4444444444444444, 265.4898349999353),
|
|
(path, 0.5555555555555556, 367.5420981413199),
|
|
(path, 0.6666666666666666, 487.29863861165995),
|
|
(path, 0.7777777777777778, 511.84069655405284),
|
|
(path, 0.8888888888888888, 579.9530841780238),
|
|
(path, 1.0, 732.9614757397469),
|
|
(pathz, 0.0, 0.0),
|
|
(pathz, 0.1111111111111111, 86.99571952663854),
|
|
(pathz, 0.2222222222222222, 174.33662608180325),
|
|
(pathz, 0.3333333333333333, 214.42194393858466),
|
|
(pathz, 0.4444444444444444, 289.94661033436205),
|
|
(pathz, 0.5555555555555556, 408.38391100702125),
|
|
(pathz, 0.6666666666666666, 504.4309373835351),
|
|
(pathz, 0.7777777777777778, 533.774834546298),
|
|
(pathz, 0.8888888888888888, 652.931321760894),
|
|
(pathz, 1.0, 782.9614757397469),
|
|
(lpath, 0.0, 0.0),
|
|
(lpath, 0.1111111111111111, 5.555555555555555),
|
|
(lpath, 0.2222222222222222, 11.11111111111111),
|
|
(lpath, 0.3333333333333333, 16.666666666666664),
|
|
(lpath, 0.4444444444444444, 22.22222222222222),
|
|
(lpath, 0.5555555555555556, 27.77777777777778),
|
|
(lpath, 0.6666666666666666, 33.33333333333333),
|
|
(lpath, 0.7777777777777778, 38.88888888888889),
|
|
(lpath, 0.8888888888888888, 44.44444444444444),
|
|
(lpath, 1.0, 50.0),
|
|
(qpath, 0.0, 0.0),
|
|
(qpath, 0.1111111111111111, 17.28395061728395),
|
|
(qpath, 0.2222222222222222, 24.69135802469136),
|
|
(qpath, 0.3333333333333333, 27.777777777777786),
|
|
(qpath, 0.4444444444444444, 40.12345679012344),
|
|
(qpath, 0.5555555555555556, 62.3456790123457),
|
|
(qpath, 0.6666666666666666, 94.44444444444446),
|
|
(qpath, 0.7777777777777778, 136.41975308641975),
|
|
(qpath, 0.8888888888888888, 188.27160493827154),
|
|
(qpath, 1.0, 250.0),
|
|
(cpath, 0.0, 0.0),
|
|
(cpath, 0.1111111111111111, 207.35525375551356),
|
|
(cpath, 0.2222222222222222, 366.0583590267552),
|
|
(cpath, 0.3333333333333333, 474.34064293812787),
|
|
(cpath, 0.4444444444444444, 530.467036317684),
|
|
(cpath, 0.5555555555555556, 545.0444351253911),
|
|
(cpath, 0.6666666666666666, 598.9767847757622),
|
|
(cpath, 0.7777777777777778, 710.4080903390646),
|
|
(cpath, 0.8888888888888888, 881.1796899225557),
|
|
(cpath, 1.0, 1113.0914444911352),
|
|
(apath, 0.0, 0.0),
|
|
(apath, 0.1111111111111111, 9.756687033889872),
|
|
(apath, 0.2222222222222222, 19.51337406777974),
|
|
(apath, 0.3333333333333333, 29.27006110166961),
|
|
(apath, 0.4444444444444444, 39.02674813555948),
|
|
(apath, 0.5555555555555556, 48.783435169449355),
|
|
(apath, 0.6666666666666666, 58.54012220333922),
|
|
(apath, 0.7777777777777778, 68.2968092372291),
|
|
(apath, 0.8888888888888888, 78.05349627111896),
|
|
(apath, 1.0, 87.81018330500885)]
|
|
|
|
for (c, t, s) in tests:
|
|
self.assertAlmostEqual(c.ilength(s), t, msg=str((c, t, s)))
|
|
|
|
# Exceptional Cases
|
|
def test_ilength_exceptions(self):
|
|
nodalq = QuadraticBezier(1, 1, 1)
|
|
with self.assertRaises(AssertionError):
|
|
nodalq.ilength(1)
|
|
|
|
lin = Line(0, 0.5j)
|
|
with self.assertRaises(ValueError):
|
|
lin.ilength(1)
|
|
|
|
|
|
class Test_intersect(unittest.TestCase):
|
|
def test_intersect(self):
|
|
|
|
###################################################################
|
|
# test that `some_seg.intersect(another_seg)` will produce properly
|
|
# ordered tuples, i.e. the first element in each tuple refers to
|
|
# `some_seg` and the second element refers to `another_seg`.
|
|
# Also tests that the correct number of intersections is found.
|
|
a = Line(0 + 200j, 300 + 200j)
|
|
b = QuadraticBezier(40 + 150j, 70 + 200j, 210 + 300j)
|
|
c = CubicBezier(60 + 150j, 40 + 200j, 120 + 250j, 200 + 160j)
|
|
d = Arc(70 + 150j, 50 + 100j, 0, 0, 0, 200 + 100j)
|
|
segdict = {'line': a, "quadratic": b, 'cubic': c, 'arc': d}
|
|
|
|
# test each segment type against each other type
|
|
for x, y in [(x, y) for x in segdict for y in segdict]:
|
|
if x == y:
|
|
continue
|
|
x = segdict[x]
|
|
y = segdict[y]
|
|
xiy = sorted(x.intersect(y, tol=1e-15))
|
|
yix = sorted(y.intersect(x, tol=1e-15), key=itemgetter(1))
|
|
for xy, yx in zip(xiy, yix):
|
|
self.assertAlmostEqual(xy[0], yx[1])
|
|
self.assertAlmostEqual(xy[1], yx[0])
|
|
self.assertAlmostEqual(x.point(xy[0]), y.point(yx[0]))
|
|
self.assertTrue(len(xiy), len(yix))
|
|
self.assertTrue(len(xiy), 2)
|
|
self.assertTrue(len(yix), 2)
|
|
|
|
# test each segment against another segment of same type
|
|
for x in segdict:
|
|
if x == 'arc':
|
|
# this is an example of the Arc.intersect method not working
|
|
# in call cases. See docstring for a note on its
|
|
# incomplete implementation.
|
|
continue
|
|
x = segdict[x]
|
|
y = x.rotated(90).translated(5)
|
|
xiy = sorted(x.intersect(y, tol=1e-15))
|
|
yix = sorted(y.intersect(x, tol=1e-15), key=itemgetter(1))
|
|
for xy, yx in zip(xiy, yix):
|
|
self.assertAlmostEqual(xy[0], yx[1])
|
|
self.assertAlmostEqual(xy[1], yx[0])
|
|
self.assertAlmostEqual(x.point(xy[0]), y.point(yx[0]))
|
|
self.assertTrue(len(xiy), len(yix))
|
|
self.assertTrue(len(xiy), 1)
|
|
self.assertTrue(len(yix), 1)
|
|
###################################################################
|
|
|
|
def test_line_line_0(self):
|
|
l0 = Line(start=(25.389999999999997+99.989999999999995j),
|
|
end=(25.389999999999997+90.484999999999999j))
|
|
l1 = Line(start=(25.390000000000001+84.114999999999995j),
|
|
end=(25.389999999999997+74.604202137430320j))
|
|
i = l0.intersect(l1)
|
|
assert(len(i)) == 0
|
|
|
|
def test_line_line_1(self):
|
|
l0 = Line(start=(-124.705378549+327.696674827j),
|
|
end=(12.4926214511+121.261674827j))
|
|
l1 = Line(start=(-12.4926214511+121.261674827j),
|
|
end=(124.705378549+327.696674827j))
|
|
i = l0.intersect(l1)
|
|
assert(len(i)) == 1
|
|
assert(abs(l0.point(i[0][0])-l1.point(i[0][1])) < 1e-9)
|
|
|
|
|
|
class TestPathTools(unittest.TestCase):
|
|
# moved from test_pathtools.py
|
|
|
|
def setUp(self):
|
|
self.arc1 = Arc(650+325j, 25+25j, -30.0, False, True, 700+300j)
|
|
self.line1 = Line(0, 100+100j)
|
|
self.quadratic1 = QuadraticBezier(100+100j, 150+150j, 300+200j)
|
|
self.cubic1 = CubicBezier(300+200j, 350+400j, 400+425j, 650+325j)
|
|
self.path_of_all_seg_types = Path(self.line1, self.quadratic1,
|
|
self.cubic1, self.arc1)
|
|
self.path_of_bezier_seg_types = Path(self.line1, self.quadratic1,
|
|
self.cubic1)
|
|
|
|
def test_is_bezier_segment(self):
|
|
|
|
# False
|
|
self.assertFalse(is_bezier_segment(self.arc1))
|
|
self.assertFalse(is_bezier_segment(self.path_of_bezier_seg_types))
|
|
|
|
# True
|
|
self.assertTrue(is_bezier_segment(self.line1))
|
|
self.assertTrue(is_bezier_segment(self.quadratic1))
|
|
self.assertTrue(is_bezier_segment(self.cubic1))
|
|
|
|
def test_is_bezier_path(self):
|
|
|
|
# False
|
|
self.assertFalse(is_bezier_path(self.path_of_all_seg_types))
|
|
self.assertFalse(is_bezier_path(self.line1))
|
|
self.assertFalse(is_bezier_path(self.quadratic1))
|
|
self.assertFalse(is_bezier_path(self.cubic1))
|
|
self.assertFalse(is_bezier_path(self.arc1))
|
|
|
|
# True
|
|
self.assertTrue(is_bezier_path(self.path_of_bezier_seg_types))
|
|
self.assertTrue(is_bezier_path(Path()))
|
|
|
|
def test_polynomial2bezier(self):
|
|
|
|
def distfcn(tup1, tup2):
|
|
assert len(tup1) == len(tup2)
|
|
return sum((tup1[i]-tup2[i])**2 for i in range(len(tup1)))**0.5
|
|
|
|
# Case: Line
|
|
pcoeffs = [(-1.7-2j), (6+2j)]
|
|
p = poly1d(pcoeffs)
|
|
correct_bpoints = [(6+2j), (4.3+0j)]
|
|
|
|
# Input poly1d object
|
|
bez = poly2bez(p)
|
|
bpoints = bez.bpoints()
|
|
self.assertAlmostEqual(distfcn(bpoints, correct_bpoints), 0)
|
|
|
|
# Input list of coefficients
|
|
bpoints = poly2bez(pcoeffs, return_bpoints=True)
|
|
self.assertAlmostEqual(distfcn(bpoints, correct_bpoints), 0)
|
|
|
|
# Case: Quadratic
|
|
pcoeffs = [(29.5+15.5j), (-31-19j), (7.5+5.5j)]
|
|
p = poly1d(pcoeffs)
|
|
correct_bpoints = [(7.5+5.5j), (-8-4j), (6+2j)]
|
|
|
|
# Input poly1d object
|
|
bez = poly2bez(p)
|
|
bpoints = bez.bpoints()
|
|
self.assertAlmostEqual(distfcn(bpoints, correct_bpoints), 0)
|
|
|
|
# Input list of coefficients
|
|
bpoints = poly2bez(pcoeffs, return_bpoints=True)
|
|
self.assertAlmostEqual(distfcn(bpoints, correct_bpoints), 0)
|
|
|
|
# Case: Cubic
|
|
pcoeffs = [(-18.5-12.5j), (34.5+16.5j), (-18-6j), (6+2j)]
|
|
p = poly1d(pcoeffs)
|
|
correct_bpoints = [(6+2j), 0j, (5.5+3.5j), (4+0j)]
|
|
|
|
# Input poly1d object
|
|
bez = poly2bez(p)
|
|
bpoints = bez.bpoints()
|
|
self.assertAlmostEqual(distfcn(bpoints, correct_bpoints), 0)
|
|
|
|
# Input list of coefficients object
|
|
bpoints = poly2bez(pcoeffs, return_bpoints=True)
|
|
self.assertAlmostEqual(distfcn(bpoints, correct_bpoints), 0)
|
|
|
|
def test_bpoints2bezier(self):
|
|
cubic_bpoints = [(6+2j), 0, (5.5+3.5j), (4+0j)]
|
|
quadratic_bpoints = [(6+2j), 0, (5.5+3.5j)]
|
|
line_bpoints = [(6+2j), 0]
|
|
self.assertTrue(isinstance(bpoints2bezier(cubic_bpoints), CubicBezier))
|
|
self.assertTrue(isinstance(bpoints2bezier(quadratic_bpoints),
|
|
QuadraticBezier))
|
|
self.assertTrue(isinstance(bpoints2bezier(line_bpoints), Line))
|
|
self.assertSequenceEqual(bpoints2bezier(cubic_bpoints).bpoints(),
|
|
cubic_bpoints)
|
|
self.assertSequenceEqual(bpoints2bezier(quadratic_bpoints).bpoints(),
|
|
quadratic_bpoints)
|
|
self.assertSequenceEqual(bpoints2bezier(line_bpoints).bpoints(),
|
|
line_bpoints)
|
|
|
|
# def test_line2pathd(self):
|
|
# bpoints = (0+1.5j, 100+10j)
|
|
# line = Line(*bpoints)
|
|
#
|
|
# # from Line object
|
|
# pathd = line2pathd(line)
|
|
# path = parse_path(pathd)
|
|
# self.assertTrue(path[0] == line)
|
|
#
|
|
# # from list of bpoints
|
|
# pathd = line2pathd(bpoints)
|
|
# path = parse_path(pathd)
|
|
# self.assertTrue(path[0] == line)
|
|
#
|
|
# def test_cubic2pathd(self):
|
|
# bpoints = (0+1.5j, 100+10j, 150-155.3j, 0)
|
|
# cubic = CubicBezier(*bpoints)
|
|
#
|
|
# # from Line object
|
|
# pathd = cubic2pathd(cubic)
|
|
# path = parse_path(pathd)
|
|
# self.assertTrue(path[0] == cubic)
|
|
#
|
|
# # from list of bpoints
|
|
# pathd = cubic2pathd(bpoints)
|
|
# path = parse_path(pathd)
|
|
# self.assertTrue(path[0] == cubic)
|
|
|
|
def test_closest_point_in_path(self):
|
|
def distfcn(tup1, tup2):
|
|
assert len(tup1) == len(tup2)
|
|
return sum((tup1[i]-tup2[i])**2 for i in range(len(tup1)))**0.5
|
|
|
|
# Note: currently the radiialrange method is not implemented for Arc
|
|
# objects
|
|
# test_path = self.path_of_all_seg_types
|
|
# origin = -123 - 123j
|
|
# expected_result = ???
|
|
# self.assertAlmostEqual(min_radius(origin, test_path),
|
|
# expected_result)
|
|
|
|
# generic case (where is_bezier_path(test_path) == True)
|
|
test_path = self.path_of_bezier_seg_types
|
|
pt = 300+300j
|
|
expected_result = (29.382522853493143, 0.17477067969145446, 2)
|
|
result = closest_point_in_path(pt, test_path)
|
|
err = distfcn(expected_result, result)
|
|
self.assertAlmostEqual(err, 0)
|
|
|
|
# cubic test with multiple valid solutions
|
|
test_path = Path(CubicBezier(1-2j, 10-1j, 10+1j, 1+2j))
|
|
pt = 3
|
|
expected_results = [(1.7191878932122302, 0.90731678233211366, 0),
|
|
(1.7191878932122304, 0.092683217667886342, 0)]
|
|
result = closest_point_in_path(pt, test_path)
|
|
err = min(distfcn(e_res, result) for e_res in expected_results)
|
|
self.assertAlmostEqual(err, 0)
|
|
|
|
def test_farthest_point_in_path(self):
|
|
def distfcn(tup1, tup2):
|
|
assert len(tup1) == len(tup2)
|
|
return sum((tup1[i]-tup2[i])**2 for i in range(len(tup1)))**0.5
|
|
|
|
# Note: currently the radiialrange method is not implemented for Arc
|
|
# objects
|
|
# test_path = self.path_of_all_seg_types
|
|
# origin = -123 - 123j
|
|
# expected_result = ???
|
|
# self.assertAlmostEqual(min_radius(origin, test_path),
|
|
# expected_result)
|
|
|
|
# boundary test
|
|
test_path = self.path_of_bezier_seg_types
|
|
pt = 300+300j
|
|
expected_result = (424.26406871192853, 0, 0)
|
|
result = farthest_point_in_path(pt, test_path)
|
|
err = distfcn(expected_result, result)
|
|
self.assertAlmostEqual(err, 0)
|
|
|
|
# non-boundary test
|
|
test_path = Path(CubicBezier(1-2j, 10-1j, 10+1j, 1+2j))
|
|
pt = 3
|
|
expected_result = (4.75, 0.5, 0)
|
|
result = farthest_point_in_path(pt, test_path)
|
|
err = distfcn(expected_result, result)
|
|
self.assertAlmostEqual(err, 0)
|
|
|
|
def test_path_encloses_pt(self):
|
|
|
|
line1 = Line(0, 100+100j)
|
|
quadratic1 = QuadraticBezier(100+100j, 150+150j, 300+200j)
|
|
cubic1 = CubicBezier(300+200j, 350+400j, 400+425j, 650+325j)
|
|
line2 = Line(650+325j, 650+10j)
|
|
line3 = Line(650+10j, 0)
|
|
open_bez_path = Path(line1, quadratic1, cubic1)
|
|
closed_bez_path = Path(line1, quadratic1, cubic1, line2, line3)
|
|
|
|
inside_pt = 200+20j
|
|
outside_pt1 = 1000+1000j
|
|
outside_pt2 = 800+800j
|
|
boundary_pt = 50+50j
|
|
|
|
# Note: currently the intersect() method is not implemented for Arc
|
|
# objects
|
|
# arc1 = Arc(650+325j, 25+25j, -30.0, False, True, 700+300j)
|
|
# closed_path_with_arc = Path(line1, quadratic1, cubic1, arc1)
|
|
# self.assertTrue(
|
|
# path_encloses_pt(inside_pt, outside_pt2, closed_path_with_arc))
|
|
|
|
# True cases
|
|
self.assertTrue(
|
|
path_encloses_pt(inside_pt, outside_pt2, closed_bez_path))
|
|
self.assertTrue(
|
|
path_encloses_pt(boundary_pt, outside_pt2, closed_bez_path))
|
|
|
|
# False cases
|
|
self.assertFalse(
|
|
path_encloses_pt(outside_pt1, outside_pt2, closed_bez_path))
|
|
|
|
# Exception Cases
|
|
with self.assertRaises(AssertionError):
|
|
path_encloses_pt(inside_pt, outside_pt2, open_bez_path)
|
|
|
|
# Display test paths and points
|
|
# ns2d = [inside_pt, outside_pt1, outside_pt2, boundary_pt]
|
|
# ncolors = ['green', 'red', 'orange', 'purple']
|
|
# disvg(closed_path_with_arc, nodes=ns2d, node_colors=ncolors,
|
|
# openinbrowser=True)
|
|
# disvg(open_bez_path, nodes=ns2d, node_colors=ncolors,
|
|
# openinbrowser=True)
|
|
# disvg(closed_bez_path, nodes=ns2d, node_colors=ncolors,
|
|
# openinbrowser=True)
|
|
|
|
|
|
if __name__ == '__main__':
|
|
unittest.main()
|