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# Copyright 2016 Google Inc. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import collections
import math
import unittest
import os
import json
from fontTools.cu2qu import curve_to_quadratic, curves_to_quadratic
DATADIR = os.path.join(os.path.dirname(__file__), "data")
MAX_ERR = 5
class CurveToQuadraticTest(unittest.TestCase):
@classmethod
def setUpClass(cls):
"""Do the curve conversion ahead of time, and run tests on results."""
with open(os.path.join(DATADIR, "curves.json"), "r") as fp:
curves = json.load(fp)
cls.single_splines = [curve_to_quadratic(c, MAX_ERR) for c in curves]
cls.single_errors = [
cls.curve_spline_dist(c, s) for c, s in zip(curves, cls.single_splines)
]
curve_groups = [curves[i : i + 3] for i in range(0, 300, 3)]
cls.compat_splines = [
curves_to_quadratic(c, [MAX_ERR] * 3) for c in curve_groups
]
cls.compat_errors = [
[cls.curve_spline_dist(c, s) for c, s in zip(curve_group, splines)]
for curve_group, splines in zip(curve_groups, cls.compat_splines)
]
cls.results = []
@classmethod
def tearDownClass(cls):
"""Print stats from conversion, as determined during tests."""
for tag, results in cls.results:
print(
"\n%s\n%s"
% (
tag,
"\n".join(
"%s: %s (%d)" % (k, "#" * (v // 10 + 1), v)
for k, v in sorted(results.items())
),
)
)
def test_results_unchanged(self):
"""Tests that the results of conversion haven't changed since the time
of this test's writing. Useful as a quick check whenever one modifies
the conversion algorithm.
"""
expected = {2: 6, 3: 26, 4: 82, 5: 232, 6: 360, 7: 266, 8: 28}
results = collections.defaultdict(int)
for spline in self.single_splines:
n = len(spline) - 2
results[n] += 1
self.assertEqual(results, expected)
self.results.append(("single spline lengths", results))
def test_results_unchanged_multiple(self):
"""Test that conversion results are unchanged for multiple curves."""
expected = {5: 11, 6: 35, 7: 49, 8: 5}
results = collections.defaultdict(int)
for splines in self.compat_splines:
n = len(splines[0]) - 2
for spline in splines[1:]:
self.assertEqual(
len(spline) - 2, n, "Got incompatible conversion results"
)
results[n] += 1
self.assertEqual(results, expected)
self.results.append(("compatible spline lengths", results))
def test_does_not_exceed_tolerance(self):
"""Test that conversion results do not exceed given error tolerance."""
results = collections.defaultdict(int)
for error in self.single_errors:
results[round(error, 1)] += 1
self.assertLessEqual(error, MAX_ERR)
self.results.append(("single errors", results))
def test_does_not_exceed_tolerance_multiple(self):
"""Test that error tolerance isn't exceeded for multiple curves."""
results = collections.defaultdict(int)
for errors in self.compat_errors:
for error in errors:
results[round(error, 1)] += 1
self.assertLessEqual(error, MAX_ERR)
self.results.append(("compatible errors", results))
@classmethod
def curve_spline_dist(cls, bezier, spline, total_steps=20):
"""Max distance between a bezier and quadratic spline at sampled points."""
error = 0
n = len(spline) - 2
steps = total_steps // n
for i in range(0, n - 1):
p1 = spline[0] if i == 0 else p3
p2 = spline[i + 1]
if i < n - 1:
p3 = cls.lerp(spline[i + 1], spline[i + 2], 0.5)
else:
p3 = spline[n + 2]
segment = p1, p2, p3
for j in range(steps):
error = max(
error,
cls.dist(
cls.cubic_bezier_at(bezier, (j / steps + i) / n),
cls.quadratic_bezier_at(segment, j / steps),
),
)
return error
@classmethod
def lerp(cls, p1, p2, t):
(x1, y1), (x2, y2) = p1, p2
return x1 + (x2 - x1) * t, y1 + (y2 - y1) * t
@classmethod
def dist(cls, p1, p2):
(x1, y1), (x2, y2) = p1, p2
return math.hypot(x1 - x2, y1 - y2)
@classmethod
def quadratic_bezier_at(cls, b, t):
(x1, y1), (x2, y2), (x3, y3) = b
_t = 1 - t
t2 = t * t
_t2 = _t * _t
_2_t_t = 2 * t * _t
return (_t2 * x1 + _2_t_t * x2 + t2 * x3, _t2 * y1 + _2_t_t * y2 + t2 * y3)
@classmethod
def cubic_bezier_at(cls, b, t):
(x1, y1), (x2, y2), (x3, y3), (x4, y4) = b
_t = 1 - t
t2 = t * t
_t2 = _t * _t
t3 = t * t2
_t3 = _t * _t2
_3_t2_t = 3 * t2 * _t
_3_t_t2 = 3 * t * _t2
return (
_t3 * x1 + _3_t_t2 * x2 + _3_t2_t * x3 + t3 * x4,
_t3 * y1 + _3_t_t2 * y2 + _3_t2_t * y3 + t3 * y4,
)
class AllQuadraticFalseTest(unittest.TestCase):
def test_cubic(self):
cubic = [(0, 0), (0, 1), (2, 1), (2, 0)]
result = curve_to_quadratic(cubic, 0.1, all_quadratic=False)
assert result == cubic
def test_quadratic(self):
cubic = [(0, 0), (2, 2), (4, 2), (6, 0)]
result = curve_to_quadratic(cubic, 0.1, all_quadratic=False)
quadratic = [(0, 0), (3, 3), (6, 0)]
assert result == quadratic
if __name__ == "__main__":
unittest.main()
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