323 lines
10 KiB
Python
323 lines
10 KiB
Python
# Copyright 2015 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.
|
|
|
|
|
|
"""Converts cubic bezier curves to quadratic splines.
|
|
|
|
Conversion is performed such that the quadratic splines keep the same end-curve
|
|
tangents as the original cubics. The approach is iterative, increasing the
|
|
number of segments for a spline until the error gets below a bound.
|
|
|
|
If necessary, respective curves from multiple fonts will be converted at once to
|
|
ensure that the resulting splines are interpolation-compatible.
|
|
"""
|
|
|
|
|
|
from math import hypot
|
|
|
|
from fontTools.misc import bezierTools
|
|
from robofab.objects.objectsRF import RSegment, RPoint
|
|
|
|
|
|
def replace_segments(contour, segments):
|
|
try:
|
|
contour.replace_segments(segments)
|
|
return
|
|
except AttributeError:
|
|
pass
|
|
|
|
while len(contour):
|
|
contour.removeSegment(0)
|
|
for s in segments:
|
|
contour.appendSegment(s.type, [(p.x, p.y) for p in s.points], s.smooth)
|
|
|
|
|
|
def as_quadratic(segment, points):
|
|
try:
|
|
return segment.as_quadratic(points)
|
|
except AttributeError:
|
|
return RSegment(
|
|
'qcurve', [[int(i) for i in p] for p in points], segment.smooth)
|
|
|
|
|
|
_zip = zip
|
|
def zip(*args):
|
|
"""Ensure each argument to zip has the same length."""
|
|
if len(set(len(a) for a in args)) != 1:
|
|
msg = 'Args to zip in convert_curves.py should have equal lengths: '
|
|
raise ValueError(msg + ' '.join(str(a) for a in args))
|
|
return _zip(*args)
|
|
|
|
|
|
class Point:
|
|
"""An arithmetic-compatible 2D vector.
|
|
We use this because arithmetic with RoboFab's RPoint is prohibitively slow.
|
|
"""
|
|
|
|
def __init__(self, p):
|
|
self.p = map(float, p)
|
|
|
|
def __getitem__(self, key):
|
|
return self.p[key]
|
|
|
|
def __add__(self, other):
|
|
return Point([a + b for a, b in zip(self.p, other.p)])
|
|
|
|
def __sub__(self, other):
|
|
return Point([a - b for a, b in zip(self.p, other.p)])
|
|
|
|
def __mul__(self, n):
|
|
return Point([a * n for a in self.p])
|
|
|
|
def dist(self, other):
|
|
"""Calculate the distance between two points."""
|
|
return hypot(self[0] - other[0], self[1] - other[1])
|
|
|
|
def dot(self, other):
|
|
"""Return the dot product of two points."""
|
|
return self[0] * other[0] + self[1] * other[1]
|
|
|
|
|
|
def lerp(p1, p2, t):
|
|
"""Linearly interpolate between p1 and p2 at time t."""
|
|
return p1 * (1 - t) + p2 * t
|
|
|
|
|
|
def quadratic_bezier_at(p, t):
|
|
"""Return the point on a quadratic bezier curve at time t."""
|
|
|
|
return Point([
|
|
lerp(lerp(p[0][0], p[1][0], t), lerp(p[1][0], p[2][0], t), t),
|
|
lerp(lerp(p[0][1], p[1][1], t), lerp(p[1][1], p[2][1], t), t)])
|
|
|
|
|
|
def cubic_bezier_at(p, t):
|
|
"""Return the point on a cubic bezier curve at time t."""
|
|
|
|
return Point([
|
|
lerp(lerp(lerp(p[0][0], p[1][0], t), lerp(p[1][0], p[2][0], t), t),
|
|
lerp(lerp(p[1][0], p[2][0], t), lerp(p[2][0], p[3][0], t), t), t),
|
|
lerp(lerp(lerp(p[0][1], p[1][1], t), lerp(p[1][1], p[2][1], t), t),
|
|
lerp(lerp(p[1][1], p[2][1], t), lerp(p[2][1], p[3][1], t), t), t)])
|
|
|
|
|
|
def cubic_approx(p, t):
|
|
"""Approximate a cubic bezier curve with a quadratic one."""
|
|
|
|
p1 = lerp(p[0], p[1], 1.5)
|
|
p2 = lerp(p[3], p[2], 1.5)
|
|
return [p[0], lerp(p1, p2, t), p[3]]
|
|
|
|
|
|
def calc_intersect(p):
|
|
"""Calculate the intersection of ab and cd, given [a, b, c, d]."""
|
|
|
|
a, b, c, d = p
|
|
ab = b - a
|
|
cd = d - c
|
|
p = Point([-ab[1], ab[0]])
|
|
try:
|
|
h = p.dot(a - c) / p.dot(cd)
|
|
except ZeroDivisionError:
|
|
raise ValueError('Parallel vectors given to calc_intersect.')
|
|
return c + cd * h
|
|
|
|
|
|
def cubic_approx_spline(p, n):
|
|
"""Approximate a cubic bezier curve with a spline of n quadratics.
|
|
|
|
Returns None if n is 1 and the cubic's control vectors are parallel, since
|
|
no quadratic exists with this cubic's tangents."""
|
|
|
|
if n == 1:
|
|
try:
|
|
p1 = calc_intersect(p)
|
|
except ValueError:
|
|
return None
|
|
return p[0], p1, p[3]
|
|
|
|
spline = [p[0]]
|
|
ts = [(float(i) / n) for i in range(1, n)]
|
|
segments = [
|
|
map(Point, segment)
|
|
for segment in bezierTools.splitCubicAtT(p[0], p[1], p[2], p[3], *ts)]
|
|
for i in range(len(segments)):
|
|
segment = cubic_approx(segments[i], float(i) / (n - 1))
|
|
spline.append(segment[1])
|
|
spline.append(p[3])
|
|
return spline
|
|
|
|
|
|
def curve_spline_dist(bezier, spline):
|
|
"""Max distance between a bezier and quadratic spline at sampled ts."""
|
|
|
|
TOTAL_STEPS = 20
|
|
error = 0
|
|
n = len(spline) - 2
|
|
steps = TOTAL_STEPS / n
|
|
for i in range(1, n + 1):
|
|
segment = [
|
|
spline[0] if i == 1 else segment[2],
|
|
spline[i],
|
|
spline[i + 1] if i == n else lerp(spline[i], spline[i + 1], 0.5)]
|
|
for j in range(steps):
|
|
p1 = cubic_bezier_at(bezier, (float(j) / steps + i - 1) / n)
|
|
p2 = quadratic_bezier_at(segment, float(j) / steps)
|
|
error = max(error, p1.dist(p2))
|
|
return error
|
|
|
|
|
|
def convert_to_quadratic(p0, p1, p2, p3, max_n, max_err):
|
|
"""Return a quadratic spline approximating this cubic bezier."""
|
|
|
|
if not isinstance(p0, RPoint):
|
|
return convert_collection_to_quadratic(p0, p1, p2, p3, max_n, max_err)
|
|
|
|
p = [Point([i.x, i.y]) for i in [p0, p1, p2, p3]]
|
|
for n in range(1, max_n + 1):
|
|
spline = cubic_approx_spline(p, n)
|
|
if spline and curve_spline_dist(p, spline) <= max_err:
|
|
break
|
|
return spline
|
|
|
|
|
|
def convert_collection_to_quadratic(p0, p1, p2, p3, max_n, max_err):
|
|
"""Return quadratic splines approximating these cubic beziers."""
|
|
|
|
curves = [[Point([i.x, i.y]) for i in p] for p in zip(p0, p1, p2, p3)]
|
|
for n in range(1, max_n + 1):
|
|
splines = [cubic_approx_spline(c, n) for c in curves]
|
|
if (all(splines) and
|
|
max(curve_spline_dist(c, s)
|
|
for c, s in zip(curves, splines)) <= max_err):
|
|
break
|
|
return splines
|
|
|
|
|
|
def cubic_segment_to_quadratic(c, sid, max_n, max_err, report):
|
|
"""Return a quadratic approximation of a cubic segment."""
|
|
|
|
segment = c[sid]
|
|
if segment.type != 'curve':
|
|
raise TypeError('Segment type not curve')
|
|
|
|
# assumes that a curve type will always be proceeded by another point on the
|
|
# same contour
|
|
prev_segment = c[sid - 1]
|
|
points = convert_to_quadratic(prev_segment.points[-1], segment.points[0],
|
|
segment.points[1], segment.points[2],
|
|
max_n, max_err)
|
|
|
|
if isinstance(points[0][0], float): # just one spline
|
|
n = str(len(points))
|
|
points = points[1:]
|
|
|
|
else: # collection of splines
|
|
n = str(len(points[0]))
|
|
points = [p[1:] for p in points]
|
|
|
|
report[n] = report.get(n, 0) + 1
|
|
return as_quadratic(segment, points)
|
|
|
|
|
|
def glyph_curves_to_quadratic(g, max_n, max_err, report):
|
|
"""Convert a glyph's curves to quadratic, in place."""
|
|
|
|
for c in g:
|
|
segments = []
|
|
for i in range(len(c)):
|
|
s = c[i]
|
|
if s.type == 'curve':
|
|
segments.append(cubic_segment_to_quadratic(
|
|
c, i, max_n, max_err, report))
|
|
else:
|
|
segments.append(s)
|
|
replace_segments(c, segments)
|
|
|
|
|
|
def fonts_to_quadratic(fonts, compatible=False, max_n=10, max_err=5):
|
|
"""Convert the curves of a collection of fonts to quadratic.
|
|
|
|
If compatibility is required, all curves will be converted to quadratic
|
|
at once. Otherwise the glyphs will be converted one font at a time,
|
|
which should be slightly more optimized.
|
|
"""
|
|
|
|
report = {}
|
|
if compatible:
|
|
fonts = [FontCollection(fonts)]
|
|
for font in fonts:
|
|
for glyph in font:
|
|
glyph_curves_to_quadratic(glyph, max_n, max_err, report)
|
|
|
|
spline_lengths = report.keys()
|
|
spline_lengths.sort()
|
|
return (
|
|
'New spline lengths:\n' +
|
|
'\n'.join('%s: %d' % (l, report[l]) for l in spline_lengths))
|
|
|
|
|
|
class FontCollection:
|
|
"""A collection of fonts, or font components from different fonts.
|
|
|
|
Behaves like a single instance of the component, allowing access into
|
|
multiple fonts simultaneously for purposes of ensuring interpolation
|
|
compatibility.
|
|
"""
|
|
|
|
def __init__(self, fonts):
|
|
self.init(fonts, GlyphCollection)
|
|
|
|
def __getitem__(self, key):
|
|
return self.children[key]
|
|
|
|
def __len__(self):
|
|
return len(self.children)
|
|
|
|
def __str__(self):
|
|
return str(self.instances)
|
|
|
|
def init(self, instances, child_collection_type, get_children=None):
|
|
self.instances = instances
|
|
children_by_instance = map(get_children, self.instances)
|
|
self.children = map(child_collection_type, zip(*children_by_instance))
|
|
|
|
|
|
class GlyphCollection(FontCollection):
|
|
def __init__(self, glyphs):
|
|
self.init(glyphs, ContourCollection)
|
|
self.name = glyphs[0].name
|
|
|
|
|
|
class ContourCollection(FontCollection):
|
|
def __init__(self, contours):
|
|
self.init(contours, SegmentCollection)
|
|
|
|
def replace_segments(self, segment_collections):
|
|
segments_by_contour = zip(*[s.instances for s in segment_collections])
|
|
for contour, segments in zip(self.instances, segments_by_contour):
|
|
replace_segments(contour, segments)
|
|
|
|
|
|
class SegmentCollection(FontCollection):
|
|
def __init__(self, segments):
|
|
self.init(segments, None, lambda s: s.points)
|
|
self.points = self.children
|
|
self.type = segments[0].type
|
|
|
|
def as_quadratic(self, new_points=None):
|
|
points = new_points or self.children
|
|
return SegmentCollection([
|
|
as_quadratic(s, pts) for s, pts in zip(self.instances, points)])
|