# External dependencies from __future__ import division, absolute_import, print_function import sys import unittest from math import sqrt, pi from operator import itemgetter import numpy as np import random import warnings # Internal dependencies from svgpathtools import * from svgpathtools.path import _NotImplemented4ArcException, bezier_radialrange # An important note for those doing any debugging: # ------------------------------------------------ # 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 with the disvg() function. RUN_SLOW_TESTS = False TOL = 1e-4 # default for tests that don't specify a `delta` or `places` def random_line(): x = (random.random() - 0.5) * 2000 y = (random.random() - 0.5) * 2000 start = complex(x, y) x = (random.random() - 0.5) * 2000 y = (random.random() - 0.5) * 2000 end = complex(x, y) return Line(start, end) def random_arc(): x = (random.random() - 0.5) * 2000 y = (random.random() - 0.5) * 2000 start = complex(x, y) x = (random.random() - 0.5) * 2000 y = (random.random() - 0.5) * 2000 end = complex(x, y) x = (random.random() - 0.5) * 2000 y = (random.random() - 0.5) * 2000 radius = complex(x, y) large_arc = random.choice([True, False]) sweep = random.choice([True, False]) return Arc(start=start, radius=radius, rotation=0.0, large_arc=large_arc, sweep=sweep, end=end) def assert_intersections(test_case, a_seg, b_seg, intersections, count, msg=None, tol=1e-4): if count is not None: test_case.assertTrue(len(intersections) == count, msg=msg) for i in intersections: test_case.assertTrue(i[0] >= 0.0, msg=msg) test_case.assertTrue(i[0] <= 1.0, msg=msg) test_case.assertTrue(i[1] >= 0.0, msg=msg) test_case.assertTrue(i[1] <= 1.0, msg=msg) test_case.assertAlmostEqual(a_seg.point(i[0]), b_seg.point(i[1]), msg=msg, delta=tol) class LineTest(unittest.TestCase): def test_lines(self): # These points are calculated, and not just regression tests. line1 = Line(0j, 400 + 0j) self.assertAlmostEqual(line1.point(0), 0j, delta=TOL) self.assertAlmostEqual(line1.point(0.3), (120 + 0j), delta=TOL) self.assertAlmostEqual(line1.point(0.5), (200 + 0j), delta=TOL) self.assertAlmostEqual(line1.point(0.9), (360 + 0j), delta=TOL) self.assertAlmostEqual(line1.point(1), (400 + 0j), delta=TOL) self.assertAlmostEqual(line1.length(), 400, delta=TOL) line2 = Line(400 + 0j, 400 + 300j) self.assertAlmostEqual(line2.point(0), (400 + 0j), delta=TOL) self.assertAlmostEqual(line2.point(0.3), (400 + 90j), delta=TOL) self.assertAlmostEqual(line2.point(0.5), (400 + 150j), delta=TOL) self.assertAlmostEqual(line2.point(0.9), (400 + 270j), delta=TOL) self.assertAlmostEqual(line2.point(1), (400 + 300j), delta=TOL) self.assertAlmostEqual(line2.length(), 300, delta=TOL) line3 = Line(400 + 300j, 0j) self.assertAlmostEqual(line3.point(0), (400 + 300j), delta=TOL) self.assertAlmostEqual(line3.point(0.3), (280 + 210j), delta=TOL) self.assertAlmostEqual(line3.point(0.5), (200 + 150j), delta=TOL) self.assertAlmostEqual(line3.point(0.9), (40 + 30j), delta=TOL) self.assertAlmostEqual(line3.point(1), 0j, delta=TOL) self.assertAlmostEqual(line3.length(), 500, delta=TOL) def test_equality(self): # This is to test the __eq__ and __ne__ methods, so we can't use # assertEqual and assertNotEqual line = Line(0j, 400 + 0j) cubic = CubicBezier(600 + 500j, 600 + 350j, 900 + 650j, 900 + 500j) self.assertTrue(line == Line(0, 400)) self.assertTrue(line != Line(100, 400)) self.assertFalse(line == str(line)) self.assertTrue(line != str(line)) self.assertFalse(cubic == line) def test_point_to_t(self): l = Line(start=(0+0j), end=(0+10j)) self.assertEqual(l.point_to_t(0+0j), 0.0) self.assertAlmostEqual(l.point_to_t(0+5j), 0.5, delta=TOL) self.assertEqual(l.point_to_t(0+10j), 1.0) self.assertIsNone(l.point_to_t(1+0j)) self.assertIsNone(l.point_to_t(0-1j)) self.assertIsNone(l.point_to_t(0+11j)) l = Line(start=(0+0j), end=(10+10j)) self.assertEqual(l.point_to_t(0+0j), 0.0) self.assertAlmostEqual(l.point_to_t(5+5j), 0.5, delta=TOL) self.assertEqual(l.point_to_t(10+10j), 1.0) self.assertIsNone(l.point_to_t(1+0j)) self.assertIsNone(l.point_to_t(0-1j)) self.assertIsNone(l.point_to_t(0+11j)) self.assertIsNone(l.point_to_t(10.001+10.001j)) self.assertIsNone(l.point_to_t(-0.001-0.001j)) l = Line(start=(0+0j), end=(10+0j)) self.assertEqual(l.point_to_t(0+0j), 0.0) self.assertAlmostEqual(l.point_to_t(5+0j), 0.5, delta=TOL) self.assertEqual(l.point_to_t(10+0j), 1.0) self.assertIsNone(l.point_to_t(0+1j)) self.assertIsNone(l.point_to_t(0-1j)) self.assertIsNone(l.point_to_t(0+11j)) self.assertIsNone(l.point_to_t(10.001+0j)) self.assertIsNone(l.point_to_t(-0.001-0j)) l = Line(start=(-2-1j), end=(11-20j)) self.assertEqual(l.point_to_t(-2-1j), 0.0) self.assertAlmostEqual(l.point_to_t(4.5-10.5j), 0.5, delta=TOL) self.assertEqual(l.point_to_t(11-20j), 1.0) self.assertIsNone(l.point_to_t(0+1j)) self.assertIsNone(l.point_to_t(0-1j)) self.assertIsNone(l.point_to_t(0+11j)) self.assertIsNone(l.point_to_t(10.001+0j)) self.assertIsNone(l.point_to_t(-0.001-0j)) l = Line(start=(40.234-32.613j), end=(12.7-32.613j)) self.assertEqual(l.point_to_t(40.234-32.613j), 0.0) self.assertAlmostEqual(l.point_to_t(33.3505-32.613j), 0.25, delta=TOL) self.assertAlmostEqual(l.point_to_t(26.467-32.613j), 0.50, delta=TOL) self.assertAlmostEqual(l.point_to_t(19.5835-32.613j), 0.75, delta=TOL) self.assertEqual(l.point_to_t(12.7-32.613j), 1.0) self.assertIsNone(l.point_to_t(40.25-32.613j)) self.assertIsNone(l.point_to_t(12.65-32.613j)) self.assertIsNone(l.point_to_t(11-20j)) self.assertIsNone(l.point_to_t(0+1j)) self.assertIsNone(l.point_to_t(0-1j)) self.assertIsNone(l.point_to_t(0+11j)) self.assertIsNone(l.point_to_t(10.001+0j)) self.assertIsNone(l.point_to_t(-0.001-0j)) random.seed() for line_index in range(100): l = random_line() for t_index in range(100): orig_t = random.random() p = l.point(orig_t) computed_t = l.point_to_t(p) self.assertAlmostEqual(orig_t, computed_t, delta=TOL) def test_radialrange(self): def crand(): return 100*(np.random.rand() + np.random.rand()*1j) for _ in range(100): z = crand() l = Line(crand(), crand()) (min_da, min_ta), (max_da, max_ta) = l.radialrange(z) (min_db, min_tb), (max_db, max_tb) = bezier_radialrange(l, z) self.assertAlmostEqual(min_da, min_db, delta=TOL) self.assertAlmostEqual(min_ta, min_tb, delta=TOL) self.assertAlmostEqual(max_da, max_db, delta=TOL) self.assertAlmostEqual(max_ta, max_tb, delta=TOL) class CubicBezierTest(unittest.TestCase): def test_approx_circle(self): """This is a approximate circle drawn in Inkscape""" cub1 = CubicBezier( complex(0, 0), complex(0, 109.66797), complex(-88.90345, 198.57142), complex(-198.57142, 198.57142) ) cub1_tests = [ (0, 0j), (0.1, (-2.59896457 + 32.20931647j)), (0.2, (-10.12330256 + 62.76392816j)), (0.3, (-22.16418039 + 91.25500149j)), (0.4, (-38.31276448 + 117.27370288j)), (0.5, (-58.16022125 + 140.41119875j)), (0.6, (-81.29771712 + 160.25865552j)), (0.7, (-107.31641851 + 176.40723961j)), (0.8, (-135.80749184 + 188.44811744j)), (0.9, (-166.36210353 + 195.97245543j)), (1, (-198.57142 + 198.57142j)), ] cub2 = 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), ) cub2_tests = [ (0, (-198.57142 + 198.57142j)), (0.1, (-230.78073675 + 195.97245543j)), (0.2, (-261.3353492 + 188.44811744j)), (0.3, (-289.82642365 + 176.40723961j)), (0.4, (-315.8451264 + 160.25865552j)), (0.5, (-338.98262375 + 140.41119875j)), (0.6, (-358.830082 + 117.27370288j)), (0.7, (-374.97866745 + 91.25500149j)), (0.8, (-387.0195464 + 62.76392816j)), (0.9, (-394.54388515 + 32.20931647j)), (1, (-397.14285 + 0j)), ] cub3 = 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) ) cub3_tests = [ (0, (-397.14285 + 0j)), (0.1, (-394.54388515 - 32.20931675j)), (0.2, (-387.0195464 - 62.7639292j)), (0.3, (-374.97866745 - 91.25500365j)), (0.4, (-358.830082 - 117.2737064j)), (0.5, (-338.98262375 - 140.41120375j)), (0.6, (-315.8451264 - 160.258662j)), (0.7, (-289.82642365 - 176.40724745j)), (0.8, (-261.3353492 - 188.4481264j)), (0.9, (-230.78073675 - 195.97246515j)), (1, (-198.57142 - 198.57143j)), ] cub4 = CubicBezier( complex(-198.57142, -198.57143), complex(109.66797 - 198.57142, 0 - 198.57143), complex(0, 88.90346 - 198.57143), complex(0, 0), ) cub4_tests = [ (0, (-198.57142 - 198.57143j)), (0.1, (-166.36210353 - 195.97246515j)), (0.2, (-135.80749184 - 188.4481264j)), (0.3, (-107.31641851 - 176.40724745j)), (0.4, (-81.29771712 - 160.258662j)), (0.5, (-58.16022125 - 140.41120375j)), (0.6, (-38.31276448 - 117.2737064j)), (0.7, (-22.16418039 - 91.25500365j)), (0.8, (-10.12330256 - 62.7639292j)), (0.9, (-2.59896457 - 32.20931675j)), (1, 0j), ] test_sets = [ ('cub1', cub1, cub1_tests), ('cub2', cub2, cub2_tests), ('cub3', cub3, cub3_tests), ('cub4', cub4, cub4_tests), ] tol = 1e-4 for set_name, path_segment, test_set in test_sets: for t, expected_result in test_set: result = path_segment.point(t) msg = '{}.point({}) = {} | expected_result = {}' \ ''.format(set_name, t, result, expected_result) self.assertAlmostEqual(result, expected_result, msg=msg, delta=tol) 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), delta=TOL) self.assertAlmostEqual(path1.point(0.3), (132.4 + 137j), delta=TOL) self.assertAlmostEqual(path1.point(0.5), (175 + 125j), delta=TOL) self.assertAlmostEqual(path1.point(0.9), (245.8 + 173j), delta=TOL) self.assertAlmostEqual(path1.point(1), (250 + 200j), delta=TOL) # S400,300 400,200 path2 = CubicBezier(250 + 200j, 250 + 300j, 400 + 300j, 400 + 200j) self.assertAlmostEqual(path2.point(0), (250 + 200j), delta=TOL) self.assertAlmostEqual(path2.point(0.3), (282.4 + 263j), delta=TOL) self.assertAlmostEqual(path2.point(0.5), (325 + 275j), delta=TOL) self.assertAlmostEqual(path2.point(0.9), (395.8 + 227j), delta=TOL) self.assertAlmostEqual(path2.point(1), (400 + 200j), delta=TOL) # 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), delta=TOL) self.assertAlmostEqual(path3.point(0.3), (164.8 + 137j), delta=TOL) self.assertAlmostEqual(path3.point(0.5), (250 + 125j), delta=TOL) self.assertAlmostEqual(path3.point(0.9), (391.6 + 173j), delta=TOL) self.assertAlmostEqual(path3.point(1), (400 + 200j), delta=TOL) # 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), delta=TOL) self.assertAlmostEqual(path4.point(0.3), (145.9 + 437j), delta=TOL) self.assertAlmostEqual(path4.point(0.5), (250 + 425j), delta=TOL) self.assertAlmostEqual(path4.point(0.9), (407.8 + 473j), delta=TOL) self.assertAlmostEqual(path4.point(1), (400 + 500j), delta=TOL) # 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), delta=TOL) self.assertAlmostEqual(path5.point(0.3), (183.7 + 737j), delta=TOL) self.assertAlmostEqual(path5.point(0.5), (250 + 725j), delta=TOL) self.assertAlmostEqual(path5.point(0.9), (375.4 + 773j), delta=TOL) self.assertAlmostEqual(path5.point(1), (400 + 800j), delta=TOL) # 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), delta=TOL) self.assertAlmostEqual(path6.point(0.3), (712.05 + 137j), delta=TOL) self.assertAlmostEqual(path6.point(0.5), (806.25 + 125j), delta=TOL) self.assertAlmostEqual(path6.point(0.9), (911.85 + 173j), delta=TOL) self.assertAlmostEqual(path6.point(1), (900 + 200j), delta=TOL) # 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), delta=TOL) self.assertAlmostEqual(path7.point(0.3), (664.8 + 462.2j), delta=TOL) self.assertAlmostEqual(path7.point(0.5), (750 + 500j), delta=TOL) self.assertAlmostEqual(path7.point(0.9), (891.6 + 532.4j), delta=TOL) self.assertAlmostEqual(path7.point(1), (900 + 500j), delta=TOL) # 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), delta=TOL) self.assertAlmostEqual(path8.point(0.3), (638.7 + 737j), delta=TOL) self.assertAlmostEqual(path8.point(0.5), (675 + 725j), delta=TOL) self.assertAlmostEqual(path8.point(0.9), (740.4 + 773j), delta=TOL) self.assertAlmostEqual(path8.point(1), (750 + 800j), delta=TOL) # 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), delta=TOL) self.assertAlmostEqual(path9.point(0.3), (788.7 + 863j), delta=TOL) self.assertAlmostEqual(path9.point(0.5), (825 + 875j), delta=TOL) self.assertAlmostEqual(path9.point(0.9), (890.4 + 827j), delta=TOL) self.assertAlmostEqual(path9.point(1), (900 + 800j), delta=TOL) def test_length(self): # A straight line: cub = CubicBezier( complex(0, 0), complex(0, 0), complex(0, 100), complex(0, 100) ) self.assertAlmostEqual(cub.length(), 100, delta=TOL) # A diagonal line: cub = CubicBezier( complex(0, 0), complex(0, 0), complex(100, 100), complex(100, 100) ) self.assertAlmostEqual(cub.length(), sqrt(2 * 100 * 100), delta=TOL) # A quarter circle large_arc with radius 100 # http://www.whizkidtech.redprince.net/bezier/circle/ kappa = 4 * (sqrt(2) - 1) / 3 cub = 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 large_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(cub.length(), 157.1016698, delta=TOL) # 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. cub = CubicBezier( complex(600, 500), complex(600, 350), complex(900, 650), complex(900, 500) ) self.assertTrue(cub.length() > 300.0) def test_equality(self): # 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)) class QuadraticBezierTest(unittest.TestCase): def test_svg_examples(self): """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), delta=TOL) self.assertAlmostEqual(path1.point(0.3), (320 + 195j), delta=TOL) self.assertAlmostEqual(path1.point(0.5), (400 + 175j), delta=TOL) self.assertAlmostEqual(path1.point(0.9), (560 + 255j), delta=TOL) self.assertAlmostEqual(path1.point(1), (600 + 300j), delta=TOL) # T1000, 300 inversion = (600 + 300j) + (600 + 300j) - (400 + 50j) path2 = QuadraticBezier(600 + 300j, inversion, 1000 + 300j) self.assertAlmostEqual(path2.point(0), (600 + 300j), delta=TOL) self.assertAlmostEqual(path2.point(0.3), (720 + 405j), delta=TOL) self.assertAlmostEqual(path2.point(0.5), (800 + 425j), delta=TOL) self.assertAlmostEqual(path2.point(0.9), (960 + 345j), delta=TOL) self.assertAlmostEqual(path2.point(1), (1000 + 300j), delta=TOL) def test_length(self): # 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, delta=TOL) # partial length tests tests = [(q1, 212.34775387566032), (q2, 166.22170622052397), (closedq, 0.7905694150420949), (linq1, 1.0), (nodalq, 0.0)] t0 = 0.25 t1 = 0.75 for q, exp_res in tests: self.assertAlmostEqual(q.length(t0=t0, t1=t1), exp_res, delta=TOL) # linear partial cases linq2 = QuadraticBezier(1+3j, 2+5j, -9 - 17j) tests = [(0, 1/24, 0.13975424859373725), (0, 1/12, 0.1863389981249823), (0, 0.5, 4.844813951249543), (0, 1, 22.73335777124786), (1/24, 1/12, 0.04658474953124506), (1/24, 0.5, 4.705059702655722), (1/24, 1, 22.59360352265412), (1/12, 0.5, 4.658474953124562), (1/12, 1, 22.54701877312288), (0.5, 1, 17.88854381999832)] for t0, t1, exp_s in tests: self.assertAlmostEqual(linq2.length(t0=t0, t1=t1), exp_s, delta=TOL) def test_equality(self): # 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) class ArcTest(unittest.TestCase): def test_trusting_acos(self): """`u1.real` is > 1 in this arc due to numerical error.""" try: a1 = Arc(start=(160.197+102.925j), radius=(0.025+0.025j), rotation=0.0, 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, delta=TOL) self.assertAlmostEqual(arc1.theta, 180.0, delta=TOL) self.assertAlmostEqual(arc1.delta, -90.0, delta=TOL) self.assertAlmostEqual(arc1.point(0.0), 0j, delta=TOL) self.assertAlmostEqual(arc1.point(0.1), (1.23116594049 + 7.82172325201j), delta=TOL) self.assertAlmostEqual(arc1.point(0.2), (4.89434837048 + 15.4508497187j), delta=TOL) self.assertAlmostEqual(arc1.point(0.3), (10.8993475812 + 22.699524987j), delta=TOL) self.assertAlmostEqual(arc1.point(0.4), (19.0983005625 + 29.3892626146j), delta=TOL) self.assertAlmostEqual(arc1.point(0.5), (29.2893218813 + 35.3553390593j), delta=TOL) self.assertAlmostEqual(arc1.point(0.6), (41.2214747708 + 40.4508497187j), delta=TOL) self.assertAlmostEqual(arc1.point(0.7), (54.6009500260 + 44.5503262094j), delta=TOL) self.assertAlmostEqual(arc1.point(0.8), (69.0983005625 + 47.5528258148j), delta=TOL) self.assertAlmostEqual(arc1.point(0.9), (84.3565534960 + 49.3844170298j), delta=TOL) self.assertAlmostEqual(arc1.point(1.0), (100 + 50j), delta=TOL) arc2 = Arc(0j, 100 + 50j, 0, 1, 0, 100 + 50j) self.assertAlmostEqual(arc2.center, 50j, delta=TOL) self.assertAlmostEqual(arc2.theta, -90.0, delta=TOL) self.assertAlmostEqual(arc2.delta, -270.0, delta=TOL) self.assertAlmostEqual(arc2.point(0.0), 0j, delta=TOL) self.assertAlmostEqual(arc2.point(0.1), (-45.399049974 + 5.44967379058j), delta=TOL) self.assertAlmostEqual(arc2.point(0.2), (-80.9016994375 + 20.6107373854j), delta=TOL) self.assertAlmostEqual(arc2.point(0.3), (-98.7688340595 + 42.178276748j), delta=TOL) self.assertAlmostEqual(arc2.point(0.4), (-95.1056516295 + 65.4508497187j), delta=TOL) self.assertAlmostEqual(arc2.point(0.5), (-70.7106781187 + 85.3553390593j), delta=TOL) self.assertAlmostEqual(arc2.point(0.6), (-30.9016994375 + 97.5528258148j), delta=TOL) self.assertAlmostEqual(arc2.point(0.7), (15.643446504 + 99.3844170298j), delta=TOL) self.assertAlmostEqual(arc2.point(0.8), (58.7785252292 + 90.4508497187j), delta=TOL) self.assertAlmostEqual(arc2.point(0.9), (89.1006524188 + 72.699524987j), delta=TOL) self.assertAlmostEqual(arc2.point(1.0), (100 + 50j), delta=TOL) arc3 = Arc(0j, 100 + 50j, 0, 0, 1, 100 + 50j) self.assertAlmostEqual(arc3.center, 50j, delta=TOL) self.assertAlmostEqual(arc3.theta, -90.0, delta=TOL) self.assertAlmostEqual(arc3.delta, 90.0, delta=TOL) self.assertAlmostEqual(arc3.point(0.0), 0j, delta=TOL) self.assertAlmostEqual(arc3.point(0.1), (15.643446504 + 0.615582970243j), delta=TOL) self.assertAlmostEqual(arc3.point(0.2), (30.9016994375 + 2.44717418524j), delta=TOL) self.assertAlmostEqual(arc3.point(0.3), (45.399049974 + 5.44967379058j), delta=TOL) self.assertAlmostEqual(arc3.point(0.4), (58.7785252292 + 9.54915028125j), delta=TOL) self.assertAlmostEqual(arc3.point(0.5), (70.7106781187 + 14.6446609407j), delta=TOL) self.assertAlmostEqual(arc3.point(0.6), (80.9016994375 + 20.6107373854j), delta=TOL) self.assertAlmostEqual(arc3.point(0.7), (89.1006524188 + 27.300475013j), delta=TOL) self.assertAlmostEqual(arc3.point(0.8), (95.1056516295 + 34.5491502813j), delta=TOL) self.assertAlmostEqual(arc3.point(0.9), (98.7688340595 + 42.178276748j), delta=TOL) self.assertAlmostEqual(arc3.point(1.0), (100 + 50j), delta=TOL) arc4 = Arc(0j, 100 + 50j, 0, 1, 1, 100 + 50j) self.assertAlmostEqual(arc4.center, 100 + 0j, delta=TOL) self.assertAlmostEqual(arc4.theta, 180.0, delta=TOL) self.assertAlmostEqual(arc4.delta, 270.0, delta=TOL) self.assertAlmostEqual(arc4.point(0.0), 0j, delta=TOL) self.assertAlmostEqual(arc4.point(0.1), (10.8993475812 - 22.699524987j), delta=TOL) self.assertAlmostEqual(arc4.point(0.2), (41.2214747708 - 40.4508497187j), delta=TOL) self.assertAlmostEqual(arc4.point(0.3), (84.3565534960 - 49.3844170298j), delta=TOL) self.assertAlmostEqual(arc4.point(0.4), (130.901699437 - 47.5528258148j), delta=TOL) self.assertAlmostEqual(arc4.point(0.5), (170.710678119 - 35.3553390593j), delta=TOL) self.assertAlmostEqual(arc4.point(0.6), (195.105651630 - 15.4508497187j), delta=TOL) self.assertAlmostEqual(arc4.point(0.7), (198.768834060 + 7.82172325201j), delta=TOL) self.assertAlmostEqual(arc4.point(0.8), (180.901699437 + 29.3892626146j), delta=TOL) self.assertAlmostEqual(arc4.point(0.9), (145.399049974 + 44.5503262094j), delta=TOL) self.assertAlmostEqual(arc4.point(1.0), (100 + 50j), delta=TOL) 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), delta=TOL) 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, delta=TOL) self.assertAlmostEqual(arc2.length(), pi * 100, delta=TOL) 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)) def test_point_to_t(self): tol = 1e-4 a = Arc(start=(0+0j), radius=(5+5j), rotation=0.0, large_arc=True, sweep=True, end=(0+10j)) self.assertEqual(a.point_to_t(0+0j), 0.0) self.assertAlmostEqual(a.point_to_t(5+5j), 0.5, delta=tol) self.assertEqual(a.point_to_t(0+10j), 1.0) self.assertIsNone(a.point_to_t(-5+5j)) self.assertIsNone(a.point_to_t(0+5j)) self.assertIsNone(a.point_to_t(1+0j)) self.assertIsNone(a.point_to_t(0-1j)) self.assertIsNone(a.point_to_t(0+11j)) a = Arc(start=(0+0j), radius=(5+5j), rotation=0.0, large_arc=True, sweep=False, end=(0+10j)) self.assertEqual(a.point_to_t(0+0j), 0.0) self.assertAlmostEqual(a.point_to_t(-5+5j), 0.5, delta=tol) self.assertEqual(a.point_to_t(0+10j), 1.0) self.assertIsNone(a.point_to_t(5+5j)) self.assertIsNone(a.point_to_t(0+5j)) self.assertIsNone(a.point_to_t(1+0j)) self.assertIsNone(a.point_to_t(0-1j)) self.assertIsNone(a.point_to_t(0+11j)) a = Arc(start=(-10+0j), radius=(10+20j), rotation=0.0, large_arc=True, sweep=True, end=(10+0j)) self.assertEqual(a.point_to_t(-10+0j), 0.0) self.assertAlmostEqual(a.point_to_t(0-20j), 0.5, delta=tol) self.assertEqual(a.point_to_t(10+0j), 1.0) self.assertIsNone(a.point_to_t(0+20j)) self.assertIsNone(a.point_to_t(-5+5j)) self.assertIsNone(a.point_to_t(0+5j)) self.assertIsNone(a.point_to_t(1+0j)) self.assertIsNone(a.point_to_t(0-1j)) self.assertIsNone(a.point_to_t(0+11j)) a = Arc(start=(100.834+27.987j), radius=(60.6+60.6j), rotation=0.0, large_arc=False, sweep=False, end=(40.234-32.613j)) self.assertEqual(a.point_to_t(100.834+27.987j), 0.0) self.assertAlmostEqual(a.point_to_t(96.2210993246+4.7963831644j), 0.25, delta=tol) self.assertAlmostEqual(a.point_to_t(83.0846703014-14.8636715784j), 0.50, delta=tol) self.assertAlmostEqual(a.point_to_t(63.4246151671-28.0001000158j), 0.75, delta=tol) self.assertEqual(a.point_to_t(40.234-32.613j), 1.00) self.assertIsNone(a.point_to_t(-10+0j)) self.assertIsNone(a.point_to_t(0+0j)) a = Arc(start=(423.049961698-41.3779390229j), radius=(904.283878032+597.298520765j), rotation=0.0, large_arc=True, sweep=False, end=(548.984030235-312.385118044j)) orig_t = 0.854049465076 p = a.point(orig_t) computed_t = a.point_to_t(p) self.assertAlmostEqual(orig_t, computed_t, delta=TOL) a = Arc(start=(-1-750j), radius=(750+750j), rotation=0.0, large_arc=True, sweep=False, end=1-750j) self.assertAlmostEqual(a.point_to_t(730.5212132777968+169.8191111892562j), 0.71373858, delta=tol) self.assertIsNone(a.point_to_t(730.5212132777968+169j)) self.assertIsNone(a.point_to_t(730.5212132777968+171j)) random.seed() for arc_index in range(100): a = random_arc() for t_index in np.linspace(0, 1, 100): orig_t = random.random() p = a.point(orig_t) computed_t = a.point_to_t(p) msg = "arc %s at t=%f is point %s, but got %f back" \ "" % (a, orig_t, p, computed_t) self.assertAlmostEqual(orig_t, computed_t, msg=msg, delta=tol) def test_approx_quad(self): n = 100 for i in range(n): arc = random_arc() if arc.radius.real > 2000 or arc.radius.imag > 2000: continue # Random Arc too large, by autoscale. path1 = Path(arc) path2 = Path(*path1) path2.approximate_arcs_with_quads(error=0.05) d = abs(path1.length() - path2.length()) # Error less than 1% typically less than 0.5% self.assertAlmostEqual(d, 0.0, delta=20) def test_approx_cubic(self): n = 100 for i in range(n): arc = random_arc() if arc.radius.real > 2000 or arc.radius.imag > 2000: continue # Random Arc too large, by autoscale. path1 = Path(arc) path2 = Path(*path1) path2.approximate_arcs_with_cubics(error=0.1) d = abs(path1.length() - path2.length()) # Error less than 0.1% typically less than 0.001% self.assertAlmostEqual(d, 0.0, delta=2) class TestPath(unittest.TestCase): def test_hash(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] # this is necessary due to changes to the builtin `hash` function if sys.version_info.major == 2: expected_hashes = [ -5762846476463470127, -138736730317965290, -2005041722222729058, 8448700906794235291, -5178990533869800243, -4003140762934044601, 8575549467429100514, 5166859065265868968, 1373103287265872323, -1022491904150314631, 4188352014604112779, -5090374009174854814, -7093907105533857815, 2036243740727202243, -8108488067585685407] else: expected_hashes = [ -6073024107272494569, -2519772625496438197, 8726412907710383506, 2132930052750006195, 3112548573593977871, 991446120749438306, -5589397644574569777, -4438808571483114580, -3125333407400456536, -4418099728831808951, 702646573139378041, -6331016786776229094, 5053050772929443013, 6102272282813527681, -5385294438006156225, ] for c, h in zip(test_curves, expected_hashes): self.assertTrue(hash(c) == h, msg="hash {} was expected for curve = {}".format(h, c)) 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, delta=TOL) self.assertAlmostEqual(path.point(0.25), (100 + 100j), delta=TOL) self.assertAlmostEqual(path.point(0.5), (200 + 0j), delta=TOL) self.assertAlmostEqual(path.point(0.75), (100 - 100j), delta=TOL) self.assertAlmostEqual(path.point(1.0), 0j, delta=TOL) self.assertAlmostEqual(path.length(), pi * 200, delta=TOL) 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), delta=TOL) self.assertAlmostEqual(path.point(0.14897825542), (150 + 200j), delta=TOL) self.assertAlmostEqual(path.point(0.5), (406.066017177 + 306.066017177j), delta=TOL) self.assertAlmostEqual(path.point(1 - 0.14897825542), (300 + 50j), delta=TOL) self.assertAlmostEqual(path.point(1.0), (300 + 200j), delta=TOL) # 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), delta=TOL) self.assertAlmostEqual(path.point(0.2800495767557787), (275 + 25j), delta=TOL) self.assertAlmostEqual(path.point(0.5), (168.93398282201787 + 68.93398282201787j)) self.assertAlmostEqual(path.point(1 - 0.2800495767557787), (125 + 175j), delta=TOL) self.assertAlmostEqual(path.point(1.0), (275 + 175j), delta=TOL) # 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), delta=TOL) # self.assertAlmostEqual(path.point(0.3), (755.239799276+212.182020958j), delta=TOL) # self.assertAlmostEqual(path.point(0.5), (827.730749264+147.824157418j), delta=TOL) # self.assertAlmostEqual(path.point(0.9), (971.284357806+106.302352605j), delta=TOL) # self.assertAlmostEqual(path.point(1), (1050+125j), delta=TOL) # # The errors seem to accumulate. Still 6 decimal places is more # # than good enough. # self.assertAlmostEqual(path.length(), 928.3886394081095, delta=TOL) 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] def scale_a_point(pt, sx, sy=None, origin=0j): if sy is None: sy = sx zeta = pt - origin pt_vec = [[zeta.real], [zeta.imag], [1]] transform = [[sx, 0, origin.real], [0, sy, origin.imag]] return complex(*np.dot(transform, pt_vec).ravel()) for curve in test_curves: # generate a random point and a random scaling t = np.random.rand() pt = curve.point(t) # random diagonal transformation sx = 2 * np.random.rand() sy = 2 * np.random.rand() # random origin origin = (10 * (np.random.rand() - 0.5) + 10j * (np.random.rand() - 0.5)) # Note: `sx != sy` cases are not implemented for `Arc` objects has_arc = (isinstance(curve, Arc) or isinstance(curve, Path) and any(isinstance(seg, Arc) for seg in curve)) # find seg which t lands on for failure reporting seg = curve if isinstance(curve, Path): seg_idx, seg_t = curve.T2t(t) seg = curve[seg_idx] _fail_msg = "Failure!\nseg {}\n".format(seg) # case where no `sy` and no `origin` given curve_scaled = curve.scaled(sx) if isinstance(curve, Path): res = curve_scaled[seg_idx].point(seg_t) else: res = curve_scaled.point(t) ans = scale_a_point(pt, sx, None) fail_msg = _fail_msg + ("curve.scaled({}, {}, {}) = \n{}\n" "".format(sx, None, None, curve_scaled)) fail_msg += "seg_scaled.point({}) = {}\n".format(seg_t, res) fail_msg += "ans = {}".format(ans) self.assertAlmostEqual(ans, res, places=4, msg=fail_msg) # case where random `origin` given but no `sy` ans = scale_a_point(pt, sx, None, origin) curve_scaled = curve.scaled(sx, origin=origin) if isinstance(curve, Path): res = curve_scaled[seg_idx].point(seg_t) else: res = curve_scaled.point(t) fail_msg = _fail_msg + ("curve.scaled({}, {}, {}) = \n{}\n" "".format(sx, None, origin, curve_scaled)) fail_msg += "seg_scaled.point({}) = {}\n".format(seg_t, res) fail_msg += "ans = {}".format(ans) self.assertAlmostEqual(ans, res, places=4, msg=fail_msg) # case where `sx != sy`, and no `origin` given ans = scale_a_point(pt, sx, sy) if has_arc: # the cases with sx != sy are not yet imp for arcs with self.assertRaises(Exception): curve.scaled(sx, sy).point(t) else: curve_scaled = curve.scaled(sx, sy) seg_scaled = seg.scaled(sx, sy) if isinstance(curve, Path): res = curve_scaled[seg_idx].point(seg_t) else: res = curve_scaled.point(t) fail_msg = _fail_msg + ("curve.scaled({}, {}, {}) = \n{}\n" "".format(sx, sy, None, curve_scaled)) fail_msg += "seg_scaled.point({}) = {}\n".format(seg_t, res) fail_msg += "ans = {}".format(ans) self.assertAlmostEqual(ans, res, places=4, msg=fail_msg) # case where `sx != sy`, and random `origin` given ans = scale_a_point(pt, sx, sy, origin) if has_arc: # the cases with sx != sy are not yet imp for arcs with self.assertRaises(Exception): curve.scaled(sx, sy, origin).point(t) else: curve_scaled = curve.scaled(sx, sy, origin) if isinstance(curve, Path): res = curve_scaled[seg_idx].point(seg_t) else: res = curve_scaled.point(t) fail_msg = _fail_msg + ("curve.scaled({}, {}, {}) = \n{}\n" "".format(sx, sy, origin, curve_scaled)) fail_msg += "seg_scaled.point({}) = {}\n".format(seg_t, res) fail_msg += "ans = {}".format(ans) self.assertAlmostEqual(ans, res, places=4, msg=fail_msg) # more tests for scalar (i.e. `sx == sy`) case for curve in test_curves: # scale by 2 around (100, 100) scaled_curve = curve.scaled(2.0, origin=complex(100, 100)) # expected length len_orig = curve.length() len_trns = scaled_curve.length() self.assertAlmostEqual(len_orig * 2.0, len_trns, delta=TOL) # expected positions for T in np.linspace(0.0, 1.0, num=100): pt_orig = curve.point(T) pt_trns = scaled_curve.point(T) pt_xpct = (pt_orig - complex(100, 100)) * 2.0 + complex(100, 100) self.assertAlmostEqual(pt_xpct, pt_trns, delta=TOL) # scale by 0.3 around (0, -100) # the 'almost equal' test fails at the 7th decimal place for # some length and position tests here. scaled_curve = curve.scaled(0.3, origin=complex(0, -100)) # expected length len_orig = curve.length() len_trns = scaled_curve.length() self.assertAlmostEqual(len_orig * 0.3, len_trns, delta=0.000001) # expected positions for T in np.linspace(0.0, 1.0, num=100): pt_orig = curve.point(T) pt_trns = scaled_curve.point(T) pt_xpct = (pt_orig - complex(0, -100)) * 0.3 + complex(0, -100) self.assertAlmostEqual(pt_xpct, pt_trns, delta=0.000001) def test_d(self): # the following two path represent the same path but in absolute and relative forms abs_s = 'M 38.0,130.0 C 37.0,132.0 38.0,136.0 40.0,137.0 L 85.0,161.0 C 87.0,162.0 91.0,162.0 93.0,160.0 L 127.0,133.0 C 129.0,131.0 129.0,128.0 127.0,126.0 L 80.0,70.0 C 78.0,67.0 75.0,68.0 74.0,70.0 Z' rel_s = 'm 38.0,130.0 c -1.0,2.0 0.0,6.0 2.0,7.0 l 45.0,24.0 c 2.0,1.0 6.0,1.0 8.0,-1.0 l 34.0,-27.0 c 2.0,-2.0 2.0,-5.0 0.0,-7.0 l -47.0,-56.0 c -2.0,-3.0 -5.0,-2.0 -6.0,0.0 z' path1 = parse_path(abs_s) path2 = parse_path(rel_s) self.assertEqual(path1.d(use_closed_attrib=True), abs_s) self.assertEqual(path2.d(use_closed_attrib=True), abs_s) self.assertEqual(path1.d(use_closed_attrib=True, rel=True), rel_s) self.assertEqual(path2.d(use_closed_attrib=True, rel=True), rel_s) 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, delta=TOL) 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, delta=TOL) 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, delta=TOL) 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, delta=TOL) 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: try: self.assertAlmostEqual(c.ilength(s), t, msg=str((c, t, s)), delta=TOL) except: # These test case values were generated using a system # with scipy installed -- if scipy is not installed, # then in cases where `t == 1`, `s` may be slightly # greater than the length computed previously. # Thus this try/except block exists as a workaround. if c.length() < s: with self.assertRaises(ValueError): c.ilength(s) else: raise # 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], delta=TOL) self.assertAlmostEqual(xy[1], yx[0], delta=TOL) self.assertAlmostEqual(x.point(xy[0]), y.point(yx[0]), delta=TOL) self.assertTrue(len(xiy) == len(yix)) # 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], delta=TOL) self.assertAlmostEqual(xy[1], yx[0], delta=TOL) self.assertAlmostEqual(x.point(xy[0]), y.point(yx[0]), delta=TOL) 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) def test_arc_line(self): l = Line(start=(-20+1j), end=(20+1j)) a = Arc(start=(-10+0), radius=(10+10j), rotation=0.0, large_arc=True, sweep=False, end=(10+0j)) intersections = a.intersect(l) assert_intersections(self, a, l, intersections, 2) l = Line(start=(-20-1j), end=(20-1j)) a = Arc(start=(-10+0), radius=(10+10j), rotation=0.0, large_arc=True, sweep=False, end=(10+0j)) intersections = a.intersect(l) assert_intersections(self, a, l, intersections, 0) l = Line(start=(-20+1j), end=(20+1j)) a = Arc(start=(-10+0), radius=(10+10j), rotation=0.0, large_arc=True, sweep=True, end=(10+0j)) intersections = a.intersect(l) assert_intersections(self, a, l, intersections, 0) l = Line(start=(-20-1j), end=(20-1j)) a = Arc(start=(-10+0), radius=(10+10j), rotation=0.0, large_arc=True, sweep=True, end=(10+0j)) intersections = a.intersect(l) assert_intersections(self, a, l, intersections, 2) l = Line(start=(-20+0j), end=(20+0j)) a = Arc(start=(-10+0), radius=(10+10j), rotation=0.0, large_arc=True, sweep=True, end=(10+0j)) intersections = a.intersect(l) assert_intersections(self, a, l, intersections, 2) l = Line(start=(-20+0j), end=(20+0j)) a = Arc(start=(-10+0), radius=(10+10j), rotation=0.0, large_arc=True, sweep=False, end=(10+0j)) intersections = a.intersect(l) assert_intersections(self, a, l, intersections, 2) l = Line(start=(-20+10j), end=(20+10j)) a = Arc(start=(-10+0), radius=(10+10j), rotation=0.0, large_arc=True, sweep=False, end=(10+0j)) intersections = a.intersect(l) assert_intersections(self, a, l, intersections, 1) l = Line(start=(229.226097475-282.403591377j), end=(751.681212592+188.907748894j)) a = Arc(start=(-1-750j), radius=(750+750j), rotation=0.0, large_arc=True, sweep=False, end=(1-750j)) intersections = a.intersect(l) assert_intersections(self, a, l, intersections, 1) # end of arc touches start of horizontal line l = Line(start=(40.234-32.613j), end=(12.7-32.613j)) a = Arc(start=(100.834+27.987j), radius=(60.6+60.6j), rotation=0.0, large_arc=False, sweep=False, end=(40.234-32.613j)) intersections = a.intersect(l) assert_intersections(self, a, l, intersections, 1) # vertical line, intersects half-arc once l = Line(start=(1-100j), end=(1+100j)) a = Arc(start=(10.0+0j), radius=(10+10j), rotation=0, large_arc=False, sweep=True, end=(-10.0+0j)) intersections = a.intersect(l) assert_intersections(self, a, l, intersections, 1) # vertical line, intersects nearly-full arc twice l = Line(start=(1-100j), end=(1+100j)) a = Arc(start=(0.1-10j), radius=(10+10j), rotation=0, large_arc=True, sweep=True, end=(-0.1-10j)) intersections = a.intersect(l) assert_intersections(self, a, l, intersections, 2) # vertical line, start of line touches end of arc l = Line(start=(15.4+100j), end=(15.4+90.475j)) a = Arc(start=(25.4+90j), radius=(10+10j), rotation=0, large_arc=False, sweep=True, end=(15.4+100j)) intersections = a.intersect(l) assert_intersections(self, a, l, intersections, 1) l = Line(start=(100-60.913j), end=(40+59j)) a = Arc(start=(100.834+27.987j), radius=(60.6+60.6j), rotation=0.0, large_arc=False, sweep=False, end=(40.234-32.613j)) intersections = a.intersect(l) assert_intersections(self, a, l, intersections, 1) l = Line(start=(128.57143 + 380.93364j), end=(300.00001 + 389.505069j)) a = Arc(start=(214.28572 + 598.07649j), radius=(85.714287 + 108.57143j), rotation=0.0, large_arc=False, sweep=True, end=(128.57143 + 489.50507j)) intersections = a.intersect(l) assert_intersections(self, a, l, intersections, 0) random.seed() for arc_index in range(50): a = random_arc() for line_index in range(100): l = random_line() intersections = a.intersect(l) msg = 'Generated: arc = {}, line = {}'.format(a, l) assert_intersections(self, a, l, intersections, None, msg=msg) def test_intersect_arc_line_1(self): """Verify the return value of intersects() when an Arc ends at the starting point of a Line.""" a = Arc(start=(0+0j), radius=(10+10j), rotation=0, large_arc=False, sweep=False, end=(10+10j), autoscale_radius=False) l = Line(start=(10+10j), end=(20+10j)) i = a.intersect(l) self.assertEqual(len(i), 1) self.assertEqual(i[0][0], 1.0) self.assertEqual(i[0][1], 0.0) def test_intersect_arc_line_2(self): """Verify the return value of intersects() when an Arc is pierced once by a Line.""" a = Arc(start=(0+0j), radius=(10+10j), rotation=0, large_arc=False, sweep=False, end=(10+10j), autoscale_radius=False) l = Line(start=(0+9j), end=(20+9j)) i = a.intersect(l) self.assertEqual(len(i), 1) self.assertGreaterEqual(i[0][0], 0.0) self.assertLessEqual(i[0][0], 1.0) self.assertGreaterEqual(i[0][1], 0.0) self.assertLessEqual(i[0][1], 1.0) def test_intersect_arc_line_3(self): """Verify the return value of intersects() when an Arc misses a Line, but the circle that the Arc is part of hits the Line.""" a = Arc(start=(0+0j), radius=(10+10j), rotation=0, large_arc=False, sweep=False, end=(10+10j), autoscale_radius=False) l = Line(start=(11+100j), end=(11-100j)) i = a.intersect(l) self.assertEqual(len(i), 0) def test_intersect_arc_line_disjoint_bboxes(self): # The arc is very short, which contributes to the problem here. l = Line(start=(125.314540561+144.192926144j), end=(125.798713132+144.510685287j)) a = Arc(start=(128.26640649+146.908463323j), radius=(2+2j), rotation=0, large_arc=False, sweep=True, end=(128.26640606+146.90846449j)) i = l.intersect(a) self.assertEqual(i, []) def test_arc_arc_0(self): # These arcs cross at a single point. a0 = Arc(start=(114.648+27.4280898219j), radius=(22+22j), rotation=0, large_arc=False, sweep=True, end=(118.542+39.925j)) a1 = Arc(start=(118.542+15.795j), radius=(22+22j), rotation=0, large_arc=False, sweep=True, end=(96.542+37.795j)) intersections = a0.intersect(a1) assert_intersections(self, a0, a1, intersections, 1) def test_arc_arc_1(self): # These touch at an endpoint, and are *nearly* segments of a larger arc. a0 = Arc(start=(-12.8272110776+72.6464538932j), radius=(44.029+44.029j), rotation=0.0, large_arc=False, sweep=False, end=(-60.6807543328+75.3104334473j)) a1 = Arc(start=(-60.6807101078+75.3104011248j), radius=(44.029+44.029j), rotation=0.0, large_arc=False, sweep=False, end=(-77.7490636234+120.096609353j)) intersections = a0.intersect(a1) assert_intersections(self, a0, a1, intersections, 1) def test_arc_arc_2(self): # These arcs cross at a single point. a0 = Arc(start=(112.648+5j), radius=(24+24j), rotation=0, large_arc=False, sweep=True, end=(136.648+29j)) a1 = Arc(start=(112.648+6.33538520071j), radius=(24+24j), rotation=0, large_arc=False, sweep=True, end=(120.542+5j)) intersections = a0.intersect(a1) assert_intersections(self, a0, a1, intersections, 1) # The Arcs in this test are part of the same circle. def test_arc_arc_same_circle(self): # These touch at one endpoint, and go in the same direction. a0 = Arc(start=(0+0j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(-10+10j)) a1 = Arc(start=(-10+10j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(0+20j)) intersections = a0.intersect(a1) assert_intersections(self, a0, a1, intersections, 1) # These touch at both endpoints, and go in the same direction. a0 = Arc(start=(0+0j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(-10+10j)) a1 = Arc(start=(-10+10j), radius=(10+10j), rotation=0.0, large_arc=True, sweep=False, end=(0+0j)) intersections = a0.intersect(a1) assert_intersections(self, a0, a1, intersections, 2) # These touch at one endpoint, and go in opposite directions. a0 = Arc(start=(0+0j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(0+20j)) a1 = Arc(start=(0+20j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=True, end=(-10+10j)) intersections = a0.intersect(a1) assert_intersections(self, a0, a1, intersections, 0) # These touch at both endpoints, and go in opposite directions. a0 = Arc(start=(0+0j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(-10+10j)) a1 = Arc(start=(-10+10j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=True, end=(0+0j)) intersections = a0.intersect(a1) assert_intersections(self, a0, a1, intersections, 0) # These are totally disjoint. a0 = Arc(start=(0+0j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(-10+10j)) a1 = Arc(start=(0+20j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(10+10j)) intersections = a0.intersect(a1) assert_intersections(self, a0, a1, intersections, 0) # These overlap at one end and don't touch at the other. a0 = Arc(start=(0+0j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(0+20j)) a1 = Arc(start=(-10+10j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(10+10j)) intersections = a0.intersect(a1) assert_intersections(self, a0, a1, intersections, 0) # These overlap at one end and touch at the other. a0 = Arc(start=(0+0j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(0+20j)) a1 = Arc(start=(-10+10j), radius=(10+10j), rotation=0.0, large_arc=True, sweep=False, end=(0+0j)) intersections = a0.intersect(a1) assert_intersections(self, a0, a1, intersections, 0) # The Arcs in this test are part of tangent circles, outside each other. def test_arc_arc_tangent_circles_outside(self): a0 = Arc(start=(0+0j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(0+20j)) a1 = Arc(start=(-20+0j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=True, end=(-20+20j)) intersections = a0.intersect(a1) assert_intersections(self, a0, a1, intersections, 1) a0 = Arc(start=(0+0j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(0+20j)) a1 = Arc(start=(-20+0j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(-20+20j)) intersections = a0.intersect(a1) assert_intersections(self, a0, a1, intersections, 0) a0 = Arc(start=(10-10j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(10+10j)) a1 = Arc(start=(-10-0j), radius=(5+5j), rotation=0.0, large_arc=True, sweep=True, end=(-5+5j)) intersections = a0.intersect(a1) assert_intersections(self, a0, a1, intersections, 1) # The Arcs in this test are part of tangent circles, one inside the other. def test_arc_arc_tangent_circles_inside(self): a0 = Arc(start=(10-10j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(10+10j)) a1 = Arc(start=(10-0j), radius=(5+5j), rotation=0.0, large_arc=True, sweep=True, end=(5+5j)) intersections = a0.intersect(a1) assert_intersections(self, a0, a1, intersections, 1) a0 = Arc(start=(10-10j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(10+10j)) a1 = Arc(start=(10-0j), radius=(5+5j), rotation=0.0, large_arc=True, sweep=False, end=(5+5j)) intersections = a0.intersect(a1) assert_intersections(self, a0, a1, intersections, 1) a0 = Arc(start=(10-10j), radius=(10+10j), rotation=0.0, large_arc=False, sweep=False, end=(10+10j)) a1 = Arc(start=(10-0j), radius=(5+5j), rotation=0.0, large_arc=False, sweep=False, end=(5+5j)) intersections = a0.intersect(a1) assert_intersections(self, a0, a1, intersections, 0) 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 = np.poly1d(pcoeffs) correct_bpoints = [(6+2j), (4.3+0j)] # Input np.poly1d object bez = poly2bez(p) bpoints = bez.bpoints() self.assertAlmostEqual(distfcn(bpoints, correct_bpoints), 0, delta=TOL) # Input list of coefficients bpoints = poly2bez(pcoeffs, return_bpoints=True) self.assertAlmostEqual(distfcn(bpoints, correct_bpoints), 0, delta=TOL) # Case: Quadratic pcoeffs = [(29.5+15.5j), (-31-19j), (7.5+5.5j)] p = np.poly1d(pcoeffs) correct_bpoints = [(7.5+5.5j), (-8-4j), (6+2j)] # Input np.poly1d object bez = poly2bez(p) bpoints = bez.bpoints() self.assertAlmostEqual(distfcn(bpoints, correct_bpoints), 0, delta=TOL) # Input list of coefficients bpoints = poly2bez(pcoeffs, return_bpoints=True) self.assertAlmostEqual(distfcn(bpoints, correct_bpoints), 0, delta=TOL) # Case: Cubic pcoeffs = [(-18.5-12.5j), (34.5+16.5j), (-18-6j), (6+2j)] p = np.poly1d(pcoeffs) correct_bpoints = [(6+2j), 0j, (5.5+3.5j), (4+0j)] # Input np.poly1d object bez = poly2bez(p) bpoints = bez.bpoints() self.assertAlmostEqual(distfcn(bpoints, correct_bpoints), 0, delta=TOL) # Input list of coefficients object bpoints = poly2bez(pcoeffs, return_bpoints=True) self.assertAlmostEqual(distfcn(bpoints, correct_bpoints), 0, delta=TOL) 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, delta=TOL) # 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, delta=TOL) 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, delta=TOL) # 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, delta=TOL) 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) def test_path_area(self): if not RUN_SLOW_TESTS: warnings.warn("Skipping `test_path_area` as RUN_SLOW_TESTS is false.") return cw_square = Path() cw_square.append(Line((0+0j), (0+100j))) cw_square.append(Line((0+100j), (100+100j))) cw_square.append(Line((100+100j), (100+0j))) cw_square.append(Line((100+0j), (0+0j))) self.assertEqual(cw_square.area(), -10000.0) ccw_square = Path() ccw_square.append(Line((0+0j), (100+0j))) ccw_square.append(Line((100+0j), (100+100j))) ccw_square.append(Line((100+100j), (0+100j))) ccw_square.append(Line((0+100j), (0+0j))) self.assertEqual(ccw_square.area(), 10000.0) cw_half_circle = Path() cw_half_circle.append(Line((0+0j), (0+100j))) cw_half_circle.append(Arc(start=(0+100j), radius=(50+50j), rotation=0, large_arc=False, sweep=False, end=(0+0j))) self.assertAlmostEqual(cw_half_circle.area(), -3926.9908169872415, places=3) self.assertAlmostEqual(cw_half_circle.area(chord_length=1e-3), -3926.9908169872415, places=6) ccw_half_circle = Path() ccw_half_circle.append(Line((0+100j), (0+0j))) ccw_half_circle.append(Arc(start=(0+0j), radius=(50+50j), rotation=0, large_arc=False, sweep=True, end=(0+100j))) self.assertAlmostEqual(ccw_half_circle.area(), 3926.9908169872415, places=3) self.assertAlmostEqual(ccw_half_circle.area(chord_length=1e-3), 3926.9908169872415, places=6) def test_is_contained_by(self): enclosing_shape = Path() enclosing_shape.append(Line((0+0j), (0+100j))) enclosing_shape.append(Line((0+100j), (100+100j))) enclosing_shape.append(Line((100+100j), (100+0j))) enclosing_shape.append(Line((100+0j), (0+0j))) enclosed_path = Path() enclosed_path.append(Line((10+10j), (90+90j))) self.assertTrue(enclosed_path.is_contained_by(enclosing_shape)) not_enclosed_path = Path() not_enclosed_path.append(Line((200+200j), (200+0j))) self.assertFalse(not_enclosed_path.is_contained_by(enclosing_shape)) intersecting_path = Path() intersecting_path.append(Line((50+50j), (200+50j))) self.assertFalse(intersecting_path.is_contained_by(enclosing_shape)) larger_shape = Path() larger_shape.append(Line((-10-10j), (-10+110j))) larger_shape.append(Line((-10+110j), (110+110j))) larger_shape.append(Line((110+110j), (110+-10j))) larger_shape.append(Line((110-10j), (-10-10j))) self.assertFalse(larger_shape.is_contained_by(enclosing_shape)) self.assertTrue(enclosing_shape.is_contained_by(larger_shape)) class TestPathBugs(unittest.TestCase): def test_issue_113(self): """ Tests against issue regebro/svg.path#61 mathandy/svgpathtools#113 """ p = Path('M 206.5,525 Q 162.5,583 162.5,583') self.assertAlmostEqual(p.length(), 72.80109889280519, delta=TOL) p = Path('M 425.781 446.289 Q 410.40000000000003 373.047 410.4 373.047') self.assertAlmostEqual(p.length(), 74.83959997888816, delta=TOL) p = Path('M 639.648 568.115 Q 606.6890000000001 507.568 606.689 507.568') self.assertAlmostEqual(p.length(), 68.93645544992873, delta=TOL) p = Path('M 288.818 616.699 Q 301.025 547.3629999999999 301.025 547.363') self.assertAlmostEqual(p.length(), 70.40235610403947, delta=TOL) p = Path('M 339.927 706.25 Q 243.92700000000002 806.25 243.927 806.25') self.assertAlmostEqual(p.length(), 138.6217876093077, delta=TOL) p = Path('M 539.795 702.637 Q 548.0959999999999 803.4669999999999 548.096 803.467') self.assertAlmostEqual(p.length(), 101.17111989594662, delta=TOL) p = Path('M 537.815 555.042 Q 570.1680000000001 499.1600000000001 570.168 499.16') self.assertAlmostEqual(p.length(), 64.57177814649368, delta=TOL) p = Path('M 615.297 470.503 Q 538.797 694.5029999999999 538.797 694.503') self.assertAlmostEqual(p.length(), 236.70287281737836, delta=TOL) def test_issue_71(self): p = Path("M327 468z") m = p.closed q = p.d() # Failing to Crash is good. def test_issue_95(self): """ Corrects: https://github.com/mathandy/svgpathtools/issues/95 """ p = Path('M261 166 L261 166') self.assertEqual(p.length(), 0) def test_issue_94(self): # clipping rectangle p1 = Path('M0.0 0.0 L27.84765625 0.0 L27.84765625 242.6669922 L0.0 242.6669922 z') # clipping rectangle p2 = Path('M166.8359375,235.5478516c0,3.7773438-3.0859375,6.8691406-6.8701172,6.8691406H7.1108398c-3.7749023,0-6.8608398-3.0917969-6.8608398-6.8691406V7.1201172C0.25,3.3427734,3.3359375,0.25,7.1108398,0.25h152.8549805c3.7841797,0,6.8701172,3.0927734,6.8701172,6.8701172v228.4277344z') self.assertEqual(len(p1.intersect(p2)), len(p2.intersect(p1))) if __name__ == '__main__': unittest.main()