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authorRoozbeh Pournader <roozbeh@google.com>2014-07-26 10:19:05 -0700
committerRoozbeh Pournader <roozbeh@google.com>2014-07-26 10:19:05 -0700
commit5a480b939b43dec473550292501a88518fe1208c (patch)
tree37e1d7f9a9795ed86211186ba2fc6bb5f9c918c3
parent1fbdd27fd4832645b44c726778817118d891d66f (diff)
Add fontcrunch to third_party.
-rw-r--r--third_party/fontcrunch/LICENSE202
-rw-r--r--third_party/fontcrunch/Makefile31
-rw-r--r--third_party/fontcrunch/README.md26
-rw-r--r--third_party/fontcrunch/README.third_party10
-rw-r--r--third_party/fontcrunch/fontcrunch.py412
-rw-r--r--third_party/fontcrunch/quadopt.cc484
6 files changed, 1165 insertions, 0 deletions
diff --git a/third_party/fontcrunch/LICENSE b/third_party/fontcrunch/LICENSE
new file mode 100644
index 0000000..ef51da2
--- /dev/null
+++ b/third_party/fontcrunch/LICENSE
@@ -0,0 +1,202 @@
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diff --git a/third_party/fontcrunch/Makefile b/third_party/fontcrunch/Makefile
new file mode 100644
index 0000000..e73ca38
--- /dev/null
+++ b/third_party/fontcrunch/Makefile
@@ -0,0 +1,31 @@
+# Copyright 2014 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.
+#
+# Contributor: Raph Levien
+
+SRC = $(wildcard */*.bz)
+OPT = $(patsubst %.bz, %.bzopt, $(SRC))
+
+dummy: $(OPT)
+
+quadopt: quadopt.cc
+ $(CXX) $< -O3 -o $@
+
+%.bzopt: %.bz quadopt
+ ./quadopt $< $@
+
+clean:
+ rm -f quadopt
+ find . -name '*.bz' -delete
+ find . -name '*.bzopt' -delete \ No newline at end of file
diff --git a/third_party/fontcrunch/README.md b/third_party/fontcrunch/README.md
new file mode 100644
index 0000000..98f3981
--- /dev/null
+++ b/third_party/fontcrunch/README.md
@@ -0,0 +1,26 @@
+# Fontcrunch
+
+By Raph Levien, Google
+
+This is a tool for TrueType font spline optimization - a "simplify" command.
+It tries to create a visual match for the spline using the smallest number of TrueType points.
+It is notable for counting on-curve points interpolated between two off-curve points as "free," making useful filesize savings.
+
+It depends on fonttools, and has some legacy dependencies on [spiro-0.01](http://www.levien.com/spiro/spiro-0.01.tar.gz)
+This code is available under the Apache v2 license. Spiro code is GNU GPL v2 or later, and Spiro curves are subject to a US patent.
+
+Create 256 directories named 00 .. ff, and populate them with lots of files with .bz extension.
+Each of these is a nontrivial segment of quad beziers cut from the font, stored as a `x0 y0 x1 y1 x2 y2` line per bezier.
+Lines are represented with `(x1, y1)` at the midpoint of the two endpoints.
+
+`python fontcrunch.py gen yourfont.ttf`
+
+Runs the optimizer on each of the .bz files, producing a .bzopt.
+You can control the level of precision by editing "penalty" in the code (should of course be a parameter).
+On a fast computer, it should go through about 5 glyphs a second, depending on complexity.
+
+`make -j16 # or whatever level of parallelism makes sense on your computer`
+
+Regenerate a new TrueType font. You can look at the outlines to check the quality of the result.
+
+`python fontcrunch.py pack yourfont.ttf > /tmp/outlines.ps newfont.ttf`
diff --git a/third_party/fontcrunch/README.third_party b/third_party/fontcrunch/README.third_party
new file mode 100644
index 0000000..7680eae
--- /dev/null
+++ b/third_party/fontcrunch/README.third_party
@@ -0,0 +1,10 @@
+URL: https://github.com/googlefonts/fontbakery/archive/182512a19071f38f5fe1e26a67c69a671fdad2d8.zip
+Version: 182512a19071f38f5fe1e26a67c69a671fdad2d8
+License: Apache 2.0
+License File: LICENSE
+
+Description:
+Fontcrunch is a TrueType outline simplification tool.
+
+Local Modifications:
+Only the fontcrunch directory is included from fontbakery.
diff --git a/third_party/fontcrunch/fontcrunch.py b/third_party/fontcrunch/fontcrunch.py
new file mode 100644
index 0000000..d129452
--- /dev/null
+++ b/third_party/fontcrunch/fontcrunch.py
@@ -0,0 +1,412 @@
+# Copyright 2014 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.
+#
+# Contributor: Raph Levien
+
+from fontTools import ttLib
+from fontTools.ttLib.tables import _g_l_y_f
+import fromcubic
+import tocubic
+import pcorn
+import math
+import md5
+
+import sys
+import os
+
+def lerppt(t, p0, p1):
+ return (p0[0] + t * (p1[0] - p0[0]), p0[1] + t * (p1[1] - p0[1]))
+
+def glyph_to_bzs(g):
+ bzs = []
+ for i in range(g.numberOfContours):
+ beg = 0 if i == 0 else g.endPtsOfContours[i - 1] + 1
+ end = g.endPtsOfContours[i] + 1
+ n = end - beg
+ pts = g.coordinates[beg:end]
+ flags = g.flags[beg:end]
+ bz = []
+ for j in range(n):
+ x1, y1 = pts[(j+1) % n]
+ if flags[j] and flags[(j+1) % n]:
+ bz.append((pts[j], (x1, y1)))
+ elif not flags[j]:
+ if flags[j - 1]:
+ x0, y0 = pts[j - 1]
+ else:
+ x0, y0 = lerppt(0.5, pts[j - 1], pts[j])
+ if not flags[(j+1) % n]:
+ x1, y1 = lerppt(0.5, (x1, y1), pts[j])
+ if pts[j] == (x0, y0) or pts[j] == (x1, y1):
+ # degenerate quad, treat as line
+ bz.append(((x0, y0), (x1, y1)))
+ else:
+ bz.append(((x0, y0), pts[j], (x1, y1)))
+ bzs.append(bz)
+ return bzs
+
+# convert all quadratics to cubics
+def raise_to_cubic(bzs):
+ result = []
+ for sp in bzs:
+ r = []
+ for bz in sp:
+ if len(bz) == 3:
+ r.append((bz[0], lerppt(2./3, bz[0], bz[1]), lerppt(2./3, bz[2], bz[1]), bz[2]))
+ else:
+ r.append(bz)
+ result.append(r)
+ return result
+
+def plot(bzs):
+ tocubic.plot_prolog()
+ print '/ss 1.5 def'
+ print '/circle { ss 0 moveto currentpoint exch ss sub exch ss 0 360 arc } bind def'
+ fromcubic.plot_bzs(bzs, (100, 100), 0.25, fancy = True)
+ print 'showpage'
+
+def getbreaks(curve):
+ extrema = curve.find_extrema()
+ extrema.extend(curve.find_breaks())
+ extrema.append(0)
+ extrema.append(curve.arclen)
+ extrema.sort()
+ result = []
+ for i in range(len(extrema)):
+ if i == 0 or extrema[i] > extrema[i-1] + 0.1:
+ result.append(extrema[i])
+ print result
+ return result
+
+class Pt:
+ def __init__(self, curve, s):
+ self.s = s
+ x, y = curve.xy(s)
+ self.xy = (round(x), round(y))
+ self.th = curve.th(s)
+
+class MiniState:
+ def __init__(self, score, sp):
+ self.score = score
+ self.sp = sp
+ def combine(self, score, bz):
+ newscore = self.score + score + penalty * (len(bz) - 1)
+ if len(bz) == 3 and len(self.sp):
+ lastbz = self.sp[-1]
+ if len(lastbz) == 3:
+ if lerppt(0.5, lastbz[1], bz[1]) == bz[0]:
+ newscore -= penalty
+ return MiniState(newscore, self.sp + [bz])
+
+class State:
+ def __init__(self, base):
+ self.base = base # a MiniState
+ self.map = {}
+
+penalty = 0.05
+
+def measure_bz(curve, s0, s1, bz):
+ bz_arclen = tocubic.bz_arclength_rk4(bz)
+ if bz_arclen == 0: return 1e9
+ arclen_scale = (s1 - s0) / bz_arclen
+ def th_fn(s):
+ return curve.th(s0 + arclen_scale * s, s == 0)
+ return tocubic.measure_bz_rk4(bz, bz_arclen, th_fn)
+
+def measure_line(curve, st, pt0, pt1):
+ bz = (pt0.xy, pt1.xy)
+ return st.combine(measure_bz(curve, pt0.s, pt1.s, bz), bz)
+
+def intersect(xy0, th0, xy1, th1):
+ x0, y0 = xy0
+ x1, y1 = xy1
+ dx0 = math.cos(th0)
+ dy0 = math.sin(th0)
+ dx1 = math.cos(th1)
+ dy1 = math.sin(th1)
+ det = dx0 * dy1 - dy0 * dx1
+ if abs(det) < 1e-6: return None
+ det = 1 / det
+ a = y0 * dx0 - x0 * dy0
+ b = y1 * dx1 - x1 * dy1
+ x = (a * dx1 - b * dx0) * det
+ y = (a * dy1 - b * dy0) * det
+ return (x, y)
+
+def measure_quad(curve, st, pt0, pt1):
+ xy = intersect(pt0.xy, pt0.th, pt1.xy, pt1.th)
+ if xy is None: return None
+ x, y = xy
+ x = round(x)
+ y = round(y)
+ bz = (pt0.xy, (x, y), pt1.xy)
+ return st.combine(measure_bz(curve, pt0.s, pt1.s, bz), bz)
+
+class Thcache:
+ mult = 1
+ def __init__(self, curve, s0, s1):
+ self.s0 = s0
+ self.s1 = s1
+ self.ths1 = curve.th(s1, False)
+ self.vals = []
+ scale = 1.0 / self.mult
+ for i in range(int(self.mult * (s1 - s0)) + 2):
+ s = min(s1, s0 + i * scale)
+ self.vals.append(curve.th(s, i == 0))
+ def th(self, s, ds):
+ if s > self.s1: return self.ths1
+ s = self.mult * (s - self.s0)
+ bucket = int(s)
+ v0 = self.vals[bucket]
+ v1 = self.vals[bucket + 1]
+ return v0 + (s - bucket) * (v1 - v0)
+
+# produce an optimized sequence of quadratics from s0 to s1 of the curve
+def optimize_run(curve, s0, s1):
+ print s0, s1
+ n = int(round(1 * (s1 - s0)))
+ pts = []
+ for i in range(n + 1):
+ pts.append(Pt(curve, s0 + (s1 - s0) * i / n))
+ cache = Thcache(curve, s0, s1)
+ states = [MiniState(0, [])]
+ newst = measure_line(cache, states[0], pts[0], pts[n])
+ bestst = newst
+ newst = measure_quad(cache, states[0], pts[0], pts[n])
+ if newst and newst.score < bestst.score:
+ bestst = newst
+ if bestst.score <= 3 * penalty:
+ return bestst.sp
+ # Quick scan for two-quad sections
+ # Note, could do line+quad and quad+line too, but less likely to win
+ for i in range(1, n):
+ st1 = measure_quad(cache, states[0], pts[0], pts[i])
+ if st1:
+ st2 = measure_quad(cache, st1, pts[i], pts[n])
+ if st2 and st2.score < bestst.score:
+ bestst = st2
+ if bestst.score <= 4 * penalty:
+ return bestst.sp
+ for i in range(1, n + 1):
+ best = 1e9
+ badcount = 0
+ for j in range(i - 1, -1, -1):
+ newst = measure_line(cache, states[j], pts[j], pts[i])
+ if newst and newst.score < best:
+ best, bestst = newst.score, newst
+ newst = measure_quad(cache, states[j], pts[j], pts[i])
+ if newst and newst.score < best:
+ best, bestst = newst.score, newst
+ if newst is None or newst.score - states[j].score > 10 * penalty:
+ badcount += 1
+ if badcount == 20:
+ break
+ else:
+ badcount = 0
+ states.append(bestst)
+ return states[n].sp
+
+def optimize(bzs):
+ result = []
+ for sp in fromcubic.bzs_to_pcorn(bzs):
+ r = []
+ curve = pcorn.Curve(sp)
+ breaks = getbreaks(curve)
+ for i in range(len(breaks) - 1):
+ r.extend(optimize_run(curve, breaks[i], breaks[i + 1]))
+ result.append(r)
+ return result
+
+def plot_tt_raw(bzs, fancy = True):
+ x0 = 100
+ y0 = 100
+ scale = 0.25
+ fromcubic.plot_bzs(raise_to_cubic(bzs), (x0, y0), scale)
+ if fancy:
+ for sp in bzs:
+ for i in range(len(sp)):
+ lastbz = sp[i - 1]
+ bz = sp[i]
+ if len(bz) != 3 or len(lastbz) != 3 or lerppt(0.5, lastbz[1], bz[1]) != bz[0]:
+ x, y = bz[0]
+ print 'gsave %f %f translate circle fill grestore' % (x * scale + x0, y * scale + y0)
+ if len(bz) == 3:
+ x, y = bz[1]
+ print 'gsave %f %f translate circle stroke grestore' % (x * scale + x0, y * scale + y0)
+
+def plot_tt(bzs, orig = None, style = 'redcyan'):
+ tocubic.plot_prolog()
+ print '/ss 2 def'
+ print '/circle { ss 0 moveto currentpoint exch ss sub exch ss 0 360 arc } bind def'
+ if style == 'redcyan':
+ print 'true setoverprint true setoverprintmode'
+ x0 = 100
+ y0 = 100
+ scale = 0.25
+ if orig:
+ print '0 1 1 0 setcmykcolor'
+ fancy = (style == 'redcyan')
+ plot_tt_raw(orig, fancy)
+ if style == 'redcyan':
+ print '1 0 0 0 setcmykcolor'
+ elif style == 'redblack':
+ print '0 0 0 1 setcmykcolor'
+ plot_tt_raw(bzs)
+ print 'showpage'
+
+def segment_sp(sp):
+ bks = set()
+
+ # direction changes
+ xsg = 0
+ ysg = 0
+ for i in range(2 * len(sp)):
+ imod = i % len(sp)
+ xsg1 = sp[imod][-1][0] - sp[imod][0][0]
+ ysg1 = sp[imod][-1][1] - sp[imod][0][1]
+ if xsg * xsg1 < 0 or ysg * ysg1 < 0:
+ bks.add(imod)
+ xsg = xsg1
+ ysg = ysg1
+ else:
+ if xsg == 0: xsg = xsg1
+ if ysg == 0: ysg = ysg1
+
+ # angle breaks
+ for i in range(len(sp)):
+ dx0 = sp[i-1][-1][0] - sp[i-1][-2][0]
+ dy0 = sp[i-1][-1][1] - sp[i-1][-2][1]
+ dx1 = sp[i][1][0] - sp[i][0][0]
+ dy1 = sp[i][1][1] - sp[i][0][1]
+ bend = dx1 * dy0 - dx0 * dy1
+ if (dx0 == 0 and dy0 == 0) or (dx1 == 0 and dy1 == 0):
+ bks.add(i)
+ else:
+ bend = bend / (math.hypot(dx0, dy0) * math.hypot(dx1, dy1))
+ # for small angles, bend is in units of radians
+ if abs(bend) > 0.02:
+ bks.add(i)
+
+ return sorted(bks)
+
+def seg_to_string(sp, bk0, bk1):
+ if bk1 < bk0:
+ bk1 += len(sp)
+ res = []
+ for i in range(bk0, bk1):
+ bz = sp[i % len(sp)]
+ if len(bz) == 2:
+ # just represent lines as quads
+ bz = (bz[0], lerppt(0.5, bz[0], bz[1]), bz[1])
+ res.append(' '.join(['%g' % z for xy in bz for z in xy]) + '\n')
+ return ''.join(res)
+
+USE_SUBDIRS = True
+
+# get filename, ensuring directory exists
+def seg_fn(segstr):
+ fn = md5.new(segstr).hexdigest()[:16]
+ if USE_SUBDIRS:
+ dirname = fn[:2]
+ if not os.path.exists(dirname):
+ os.mkdir(dirname)
+ fn = dirname + '/' + fn[2:]
+ fn += '.bz'
+ return fn
+
+def gen_segs(glyph):
+ bzs = glyph_to_bzs(glyph)
+ for sp in bzs:
+ bks = segment_sp(sp)
+ for i in range(len(bks)):
+ bk0, bk1 = bks[i], bks[(i + 1) % len(bks)]
+ if bk1 != (bk0 + 1) % len(sp) or len(sp[bk0]) != 2:
+ segstr = seg_to_string(sp, bk0, bk1)
+ fn = seg_fn(segstr)
+ file(fn, 'w').write(segstr)
+
+def generate(fn):
+ f = ttLib.TTFont(fn)
+ glyf = f['glyf']
+ for name, g in glyf.glyphs.iteritems():
+ print 'generating', name
+ gen_segs(g)
+
+def read_bzs(fn):
+ result = []
+ for l in file(fn):
+ z = [float(z) for z in l.split()]
+ bz = ((z[0], z[1]), (z[2], z[3]), (z[4], z[5]))
+ if bz[1] == lerppt(0.5, bz[0], bz[2]):
+ bz = (bz[0], bz[2])
+ result.append(bz)
+ return result
+
+def pt_to_int(pt):
+ # todo: should investigate non-int points
+ return (int(round(pt[0])), int(round(pt[1])))
+
+def bzs_to_glyph(bzs, glyph):
+ coordinates = []
+ flags = []
+ endPtsOfContours = []
+ for sp in bzs:
+ for i in range(len(sp)):
+ lastbz = sp[i - 1]
+ bz = sp[i]
+ if len(bz) != 3 or len(lastbz) != 3 or lerppt(0.5, lastbz[1], bz[1]) != bz[0]:
+ coordinates.append(pt_to_int(bz[0]))
+ flags.append(1)
+ if len(bz) == 3:
+ coordinates.append(pt_to_int(bz[1]))
+ flags.append(0)
+ endPtsOfContours.append(len(coordinates) - 1)
+ glyph.coordinates = _g_l_y_f.GlyphCoordinates(coordinates)
+ glyph.flags = flags
+ glyph.endPtsOfContours = endPtsOfContours
+
+def repack_glyph(glyph):
+ bzs = glyph_to_bzs(glyph)
+ newbzs = []
+ for sp in bzs:
+ bks = segment_sp(sp)
+ newsp = []
+ for i in range(len(bks)):
+ bk0, bk1 = bks[i], bks[(i + 1) % len(bks)]
+ if bk1 != (bk0 + 1) % len(sp) or len(sp[bk0]) != 2:
+ segstr = seg_to_string(sp, bk0, bk1)
+ fn = seg_fn(segstr) + 'opt'
+ newsp.extend(read_bzs(fn))
+ else:
+ newsp.append(sp[bk0])
+ newbzs.append(newsp)
+ bzs_to_glyph(newbzs, glyph)
+ plot_tt(newbzs, bzs, style = 'redblack')
+
+def repack(fn, newfn):
+ f = ttLib.TTFont(fn)
+ glyf = f['glyf']
+ for name, g in glyf.glyphs.iteritems():
+ if not g.isComposite():
+ repack_glyph(g)
+ if newfn:
+ f.save(newfn)
+
+def main(argv):
+ if argv[1] == 'gen':
+ generate(sys.argv[2])
+ elif argv[1] == 'pack':
+ repack(sys.argv[2], sys.argv[3] if len(argv) >= 3 else None)
+
+main(sys.argv)
diff --git a/third_party/fontcrunch/quadopt.cc b/third_party/fontcrunch/quadopt.cc
new file mode 100644
index 0000000..59f3523
--- /dev/null
+++ b/third_party/fontcrunch/quadopt.cc
@@ -0,0 +1,484 @@
+/*
+ * Copyright 2014 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.
+ *
+ * Contributor: Raph Levien
+ */
+
+#include <iostream>
+#include <fstream>
+#include <cmath>
+#include <vector>
+#include <algorithm>
+
+using std::vector;
+
+#define HALF_STEP 1
+
+class Point {
+public:
+ Point() : x(0), y(0) { }
+ Point(double x, double y) : x(x), y(y) { }
+ double x, y;
+};
+
+bool operator==(const Point& p0, const Point& p1) {
+ return p0.x == p1.x && p0.y == p1.y;
+}
+
+std::ostream& operator<<(std::ostream& os, const Point& p) {
+ os << "(" << p.x << ", " << p.y << ")";
+ return os;
+}
+
+double dist(Point p0, Point p1) {
+ return std::hypot(p0.x - p1.x, p0.y - p1.y);
+}
+
+double dist2(Point p0, Point p1) {
+ double dx = p0.x - p1.x;
+ double dy = p0.y - p1.y;
+ return dx * dx + dy * dy;
+}
+
+Point lerp(double t, Point p0, Point p1) {
+ return Point(p0.x + t * (p1.x - p0.x), p0.y + t * (p1.y - p0.y));
+}
+
+Point unitize(Point p) {
+ double scale = 1/std::hypot(p.x, p.y);
+ return Point(p.x * scale, p.y * scale);
+}
+
+Point round(Point p) {
+ return Point(std::round(p.x), std::round(p.y));
+}
+
+class Quad {
+public:
+ Quad() : p() { }
+ Quad(Point p0, Point p1, Point p2) : p() {
+ p[0] = p0;
+ p[1] = p1;
+ p[2] = p2;
+ }
+ Point p[3];
+ double arclen() const;
+ Point eval(double t) const;
+ bool isLine() const;
+ void print(std::ostream& o) const {
+ o << p[0].x << " " << p[0].y << " " << p[1].x << " " << p[1].y << " "
+ << p[2].x << " " << p[2].y << std::endl;
+ }
+};
+
+bool Quad::isLine() const {
+ return p[1] == lerp(0.5, p[0], p[2]);
+}
+
+// One step of a 4th-order Runge-Kutta numerical integration
+template <size_t n, typename F>
+void rk4(double y[n], double x, double h, F& derivs) {
+ double dydx[n];
+ double dyt[n];
+ double dym[n];
+ double yt[n];
+ derivs(dydx, x, y);
+ double hh = h * .5;
+ double h6 = h * (1./6);
+ for (size_t i = 0; i < n; i++) {
+ yt[i] = y[i] + hh * dydx[i];
+ }
+ derivs(dyt, x + hh, yt);
+ for (size_t i = 0; i < n; i++) {
+ yt[i] = y[i] + hh * dyt[i];
+ }
+ derivs(dym, x + hh, yt);
+ for (size_t i = 0; i < n; i++) {
+ yt[i] = y[i] + h * dym[i];
+ dym[i] += dyt[i];
+ }
+ derivs(dyt, x + h, yt);
+ for (size_t i = 0; i < n; i++) {
+ y[i] += h6 * (dydx[i] + dyt[i] + 2 * dym[i]);
+ }
+}
+
+class ArclenFunctor {
+public:
+ ArclenFunctor(const Quad& q)
+ : dx0(2 * (q.p[1].x - q.p[0].x))
+ , dx1(2 * (q.p[2].x - q.p[1].x))
+ , dy0(2 * (q.p[1].y - q.p[0].y))
+ , dy1(2 * (q.p[2].y - q.p[1].y)) { }
+ void operator()(double dydx[1], double t, const double y[1]) {
+ Point p(deriv(t));
+ dydx[0] = std::hypot(p.x, p.y);
+ }
+ Point deriv(double t) const {
+ return Point(dx0 + t * (dx1 - dx0), dy0 + t * (dy1 - dy0));
+ }
+private:
+ double dx0, dy0, dx1, dy1;
+};
+
+double Quad::arclen() const {
+ ArclenFunctor derivs(*this);
+ const int n = 10;
+ double dt = 1./n;
+ double t = 0;
+ double y[1] = { 0 };
+ for (int i = 0; i < n; i++) {
+ rk4<1>(y, t, dt, derivs);
+ t += dt;
+ }
+ return y[0];
+}
+
+Point Quad::eval(double t) const {
+ Point p01(lerp(t, p[0], p[1]));
+ Point p12(lerp(t, p[1], p[2]));
+ return lerp(t, p01, p12);
+}
+
+class Thetas {
+public:
+ void init(const vector<Quad>& qs);
+ Point xy(double s) const;
+ Point dir(double s) const;
+ double arclen;
+private:
+ vector<Point> xys;
+ vector<Point> dirs;
+};
+
+void Thetas::init(const vector<Quad>& qs) {
+ xys.clear();
+ dirs.clear();
+ double s = 0;
+ int ix = 0;
+ Point lastxy;
+ Point lastd;
+ double lasts = -1;
+ for (size_t i = 0; i < qs.size(); i++) {
+ const Quad& q = qs[i];
+ ArclenFunctor derivs(q);
+ const int n = 100;
+ double dt = 1./n;
+ double t = 0;
+ double y[1];
+ y[0] = s;
+ for (int j = 0; j < n; j++) {
+ Point thisxy(q.eval(t));
+ Point thisd(derivs.deriv(t));
+ while (ix <= y[0]) {
+ double u = (ix - lasts) / (y[0] - lasts);
+ xys.push_back(lerp(u, lastxy, thisxy));
+ dirs.push_back(unitize(lerp(u, lastd, thisd)));
+ ix++;
+ }
+ lasts = y[0];
+ rk4<1>(y, t, dt, derivs);
+ t += dt;
+ lastxy = thisxy;
+ lastd = thisd;
+ }
+ s = y[0];
+ }
+ const Quad& q = qs[qs.size() - 1];
+ Point thisxy(q.p[2]);
+ Point thisd(ArclenFunctor(q).deriv(1));
+ while (ix <= s + 1) {
+ double u = (ix - lasts) / (s - lasts);
+ xys.push_back(lerp(u, lastxy, thisxy));
+ dirs.push_back(unitize(lerp(u, lastd, thisd)));
+ ix++;
+ }
+ arclen = s;
+}
+
+Point Thetas::xy(double s) const {
+ int bucket = (int)s;
+ double frac = s - bucket;
+ return lerp(frac, xys[bucket], xys[bucket + 1]);
+}
+
+Point Thetas::dir(double s) const {
+ int bucket = (int)s;
+ double frac = s - bucket;
+ return lerp(frac, dirs[bucket], dirs[bucket + 1]);
+}
+
+#define NORM_LEVEL 2
+
+// L1 angle norm, 2, L2 angle norm, 0.05
+// L1 distance norm, 200
+double penalty = 1;
+double dist_factor = .005;
+double angle_factor = 5;
+
+
+class MeasureFunctor {
+public:
+ MeasureFunctor(const Thetas& curve, double s0, double ss, const ArclenFunctor& af,
+ Quad q)
+ : curve(curve), s0(s0), ss(ss), af(af), q(q) { }
+ void operator()(double dydx[2], double t, const double y[2]) {
+ Point dxy(af.deriv(t));
+ dydx[0] = std::hypot(dxy.x, dxy.y);
+
+ // distance error
+ Point curvexy = curve.xy(s0 + y[0] * ss);
+#if NORM_LEVEL == 1
+ double disterr = dist(q.eval(t), curvexy);
+#endif
+#if NORM_LEVEL == 2
+ double disterr = dist2(q.eval(t), curvexy);
+#endif
+ disterr *= dydx[0];
+
+ // angle error
+ Point dir = curve.dir(s0 + y[0] * ss);
+ double angleerr = dir.x * dxy.y - dir.y * dxy.x;
+#if NORM_LEVEL == 1
+ angleerr = std::abs(angleerr);
+#endif
+#if NORM_LEVEL == 2
+ angleerr = (angleerr * angleerr) / dydx[0];
+#endif
+
+ dydx[1] = dist_factor * disterr + angle_factor * angleerr;
+ }
+private:
+ const Thetas& curve;
+ double s0;
+ double ss;
+ const ArclenFunctor& af;
+ Quad q;
+};
+
+// measure how closely the quad fits the section of curve, using L1 norm
+// of angle mismatch
+double measureQuad(const Thetas& curve, double s0, double s1, const Quad& q) {
+ ArclenFunctor derivs(q);
+ double ss = (s1 - s0) / q.arclen();
+ MeasureFunctor err(curve, s0, ss, derivs, q);
+ const int n = 10;
+ double dt = 1./n;
+ double t = 0;
+ double y[2] = { 0, 0 };
+ for (int i = 0; i < n; i++) {
+ rk4<2>(y, t, dt, err);
+ t += dt;
+ }
+ return y[1];
+}
+
+struct Break {
+ Break(double s, Point xy, Point dir) : s(s), xy(xy), dir(dir) { }
+ double s;
+ Point xy;
+ Point dir;
+};
+
+struct Statelet {
+ void combine(const Statelet* prev, double score, Quad q);
+ const Statelet* prev;
+ double score;
+ Quad q;
+};
+
+void Statelet::combine(const Statelet* newprev, double newscore, Quad newq) {
+ prev = newprev;
+ double pmul = 2;
+ if (newq.isLine()) {
+ pmul = 1;
+ } else if (newprev != 0 && !newprev->q.isLine()
+ && lerp(0.5, newprev->q.p[1], newq.p[1]) == newq.p[0]) {
+ pmul = 1;
+ }
+ score = (newprev == 0 ? 0 : newprev->score) + penalty * pmul + newscore;
+ q = newq;
+}
+
+struct State {
+ void combine(const State* prev, double score, Quad q);
+ vector<Statelet> sts;
+ bool init;
+};
+
+void State::combine(const State* prev, double score, Quad q) {
+ const Statelet* prevsl = prev->sts.empty() ? 0 : &prev->sts[0];
+ if (prevsl == 0 && !prev->init) {
+ return;
+ }
+ Statelet sl;
+ sl.combine(prevsl, score, q);
+ if (sts.empty()) {
+ sts.push_back(sl);
+ } else {
+ if (sl.score < sts[0].score) {
+ sts[0] = sl;
+ }
+ }
+}
+
+bool isInt(double x) {
+ return x == (int) x;
+}
+
+bool okForHalf(const State* prev, Quad q) {
+ if (isInt(q.p[0].x) && isInt(q.p[0].y)) {
+ return true;
+ }
+ if (q.isLine()) {
+ return false;
+ }
+ const Statelet* prevsl = prev->sts.empty() ? 0 : &prev->sts[0];
+
+ if (prevsl == 0 || prevsl->q.isLine()) {
+ return false;
+ }
+ return lerp(0.5, prevsl->q.p[1], q.p[1]) == q.p[0];
+}
+
+void findBreaks(vector<Break>* breaks, const Thetas& curve) {
+ breaks->clear();
+ double lastd;
+ int n = round(10 * curve.arclen);
+ for (int i = 0; i <= n; i++) {
+ double s = curve.arclen * i / n;
+ Point origp = curve.xy(s);
+#if HALF_STEP
+ Point p(.5 * std::round(2 * origp.x), .5 * std::round(2 * origp.y));
+#else
+ Point p = round(origp);
+#endif
+ double d = dist(p, origp);
+ if (i == 0 || !(p == (*breaks)[breaks->size() - 1].xy)) {
+ Break bk(s, p, curve.dir(s));
+ breaks->push_back(bk);
+ lastd = d;
+ } else if (d < lastd) {
+ (*breaks)[breaks->size() - 1] = Break(s, p, curve.dir(s));
+ lastd = d;
+ }
+ }
+}
+
+bool intersect(Point* result, Point p0, Point dir0, Point p1, Point dir1) {
+ double det = dir0.x * dir1.y - dir0.y * dir1.x;
+ if (std::abs(det) < 1e-6) return false;
+ det = 1 / det;
+ double a = p0.y * dir0.x - p0.x * dir0.y;
+ double b = p1.y * dir1.x - p1.x * dir1.y;
+ result->x = (a * dir1.x - b * dir0.x) * det;
+ result->y = (a * dir1.y - b * dir0.y) * det;
+ return true;
+}
+
+void tryQuad(const State* prev, State* st, const Thetas& curve,
+ const Break& bk0, const Break& bk1, const Quad& q) {
+ double score = measureQuad(curve, bk0.s, bk1.s, q);
+ st->combine(prev, score, q);
+}
+
+void tryLineQuad(const State* prev, State* st, const Thetas& curve,
+ const Break& bk0, const Break& bk1) {
+ if (isInt(bk0.xy.x) && isInt(bk0.xy.y)) {
+ Quad line(bk0.xy, lerp(0.5, bk0.xy, bk1.xy), bk1.xy);
+ tryQuad(prev, st, curve, bk0, bk1, line);
+ }
+ Point pmid;
+ if (intersect(&pmid, bk0.xy, bk0.dir, bk1.xy, bk1.dir)) {
+ Quad q(bk0.xy, round(pmid), bk1.xy);
+ if (okForHalf(prev, q)) {
+ tryQuad(prev, st, curve, bk0, bk1, q);
+ }
+ }
+}
+
+vector<Quad> optimize(const Thetas& curve) {
+ vector<Break> breaks;
+ findBreaks(&breaks, curve);
+ int n = breaks.size() - 1;
+ vector<State> states;
+ states.resize(n + 1);
+ states[0].init = true;
+ tryLineQuad(&states[0], &states[n], curve, breaks[0], breaks[n]);
+ if (states[n].sts[0].score <= 3 * penalty) {
+ goto done;
+ }
+ for (int i = 1; i < n; i++) {
+ tryLineQuad(&states[0], &states[i], curve, breaks[0], breaks[i]);
+ tryLineQuad(&states[i], &states[n], curve, breaks[i], breaks[n]);
+ }
+ if (states[n].sts[0].score <= 4 * penalty) {
+ goto done;
+ }
+ for (int i = 1; i <= n; i++) {
+ for (int j = i - 1; j >= 0; j--) {
+ tryLineQuad(&states[j], &states[i], curve, breaks[j], breaks[i]);
+ }
+ }
+done:
+ vector<Quad> result;
+ for (const Statelet* sl = &states[n].sts[0]; sl != 0; sl = sl->prev) {
+ result.push_back(sl->q);
+ }
+ std::reverse(result.begin(), result.end());
+ return result;
+}
+
+void readBzs(vector<Quad>* result, std::istream& is) {
+ double x0, y0, x1, y1, x2, y2;
+ while (is >> x0 >> y0 >> x1 >> y1 >> x2 >> y2) {
+ result->push_back(Quad(Point(x0, y0), Point(x1, y1), Point(x2, y2)));
+ }
+ // Round the endpoints, they must be on integers
+ (*result)[0].p[0] = round((*result)[0].p[0]);
+ Quad* lastq = &(*result)[(*result).size()];
+ lastq->p[2] = round(lastq->p[2]);
+}
+
+int main(int argc, char** argv) {
+ if (argc != 3) {
+ std::cerr << "usage: quadopt in out\n";
+ return 1;
+ }
+#if 0
+ Quad q(Point(100, 0), Point(0, 0), Point(0, 100));
+ std::cout.precision(8);
+ std::cout << q.arclen() << "\n";
+#endif
+ vector<Quad> bzs;
+ std::ifstream is;
+ is.open(argv[1]);
+ readBzs(&bzs, is);
+ Thetas thetas;
+ thetas.init(bzs);
+#if 0
+ for (int i = 0; i < thetas.arclen; i++) {
+ Point xy = thetas.dir(i);
+ std::cout << xy.x << " " << xy.y << std::endl;
+ }
+#endif
+ vector<Quad> optbzs = optimize(thetas);
+ std::ofstream os;
+ os.open(argv[2]);
+ for (size_t i = 0; i < optbzs.size(); i++) {
+ optbzs[i].print(os);
+ }
+ return 0;
+}