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venv/lib/python3.12/site-packages/fontTools/qu2cu/__init__.py

@@ -0,0 +1,15 @@
+# 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.
+
+from .qu2cu import *

venv/lib/python3.12/site-packages/fontTools/qu2cu/__main__.py

@@ -0,0 +1,7 @@
+import sys
+
+from .cli import _main as main
+
+
+if __name__ == "__main__":
+    sys.exit(main())

venv/lib/python3.12/site-packages/fontTools/qu2cu/benchmark.py

@@ -0,0 +1,56 @@
+"""Benchmark the qu2cu algorithm performance."""
+
+from .qu2cu import *
+from fontTools.cu2qu import curve_to_quadratic
+import random
+import timeit
+
+MAX_ERR = 0.5
+NUM_CURVES = 5
+
+
+def generate_curves(n):
+    points = [
+        tuple(float(random.randint(0, 2048)) for coord in range(2))
+        for point in range(1 + 3 * n)
+    ]
+    curves = []
+    for i in range(n):
+        curves.append(tuple(points[i * 3 : i * 3 + 4]))
+    return curves
+
+
+def setup_quadratic_to_curves():
+    curves = generate_curves(NUM_CURVES)
+    quadratics = [curve_to_quadratic(curve, MAX_ERR) for curve in curves]
+    return quadratics, MAX_ERR
+
+
+def run_benchmark(module, function, setup_suffix="", repeat=25, number=1):
+    setup_func = "setup_" + function
+    if setup_suffix:
+        print("%s with %s:" % (function, setup_suffix), end="")
+        setup_func += "_" + setup_suffix
+    else:
+        print("%s:" % function, end="")
+
+    def wrapper(function, setup_func):
+        function = globals()[function]
+        setup_func = globals()[setup_func]
+
+        def wrapped():
+            return function(*setup_func())
+
+        return wrapped
+
+    results = timeit.repeat(wrapper(function, setup_func), repeat=repeat, number=number)
+    print("\t%5.1fus" % (min(results) * 1000000.0 / number))
+
+
+def main():
+    run_benchmark("qu2cu", "quadratic_to_curves")
+
+
+if __name__ == "__main__":
+    random.seed(1)
+    main()

venv/lib/python3.12/site-packages/fontTools/qu2cu/cli.py

@@ -0,0 +1,125 @@
+import os
+import argparse
+import logging
+from fontTools.misc.cliTools import makeOutputFileName
+from fontTools.ttLib import TTFont
+from fontTools.pens.qu2cuPen import Qu2CuPen
+from fontTools.pens.ttGlyphPen import TTGlyphPen
+import fontTools
+
+
+logger = logging.getLogger("fontTools.qu2cu")
+
+
+def _font_to_cubic(input_path, output_path=None, **kwargs):
+    font = TTFont(input_path)
+    logger.info("Converting curves for %s", input_path)
+
+    stats = {} if kwargs["dump_stats"] else None
+    qu2cu_kwargs = {
+        "stats": stats,
+        "max_err": kwargs["max_err_em"] * font["head"].unitsPerEm,
+        "all_cubic": kwargs["all_cubic"],
+    }
+
+    assert "gvar" not in font, "Cannot convert variable font"
+    glyphSet = font.getGlyphSet()
+    glyphOrder = font.getGlyphOrder()
+    glyf = font["glyf"]
+    for glyphName in glyphOrder:
+        glyph = glyphSet[glyphName]
+        ttpen = TTGlyphPen(glyphSet)
+        pen = Qu2CuPen(ttpen, **qu2cu_kwargs)
+        glyph.draw(pen)
+        glyf[glyphName] = ttpen.glyph(dropImpliedOnCurves=True)
+
+    font["head"].glyphDataFormat = 1
+
+    if kwargs["dump_stats"]:
+        logger.info("Stats: %s", stats)
+
+    logger.info("Saving %s", output_path)
+    font.save(output_path)
+
+
+def _main(args=None):
+    """Convert an OpenType font from quadratic to cubic curves"""
+    parser = argparse.ArgumentParser(prog="qu2cu")
+    parser.add_argument("--version", action="version", version=fontTools.__version__)
+    parser.add_argument(
+        "infiles",
+        nargs="+",
+        metavar="INPUT",
+        help="one or more input TTF source file(s).",
+    )
+    parser.add_argument("-v", "--verbose", action="count", default=0)
+    parser.add_argument(
+        "-e",
+        "--conversion-error",
+        type=float,
+        metavar="ERROR",
+        default=0.001,
+        help="maxiumum approximation error measured in EM (default: 0.001)",
+    )
+    parser.add_argument(
+        "-c",
+        "--all-cubic",
+        default=False,
+        action="store_true",
+        help="whether to only use cubic curves",
+    )
+
+    output_parser = parser.add_mutually_exclusive_group()
+    output_parser.add_argument(
+        "-o",
+        "--output-file",
+        default=None,
+        metavar="OUTPUT",
+        help=("output filename for the converted TTF."),
+    )
+    output_parser.add_argument(
+        "-d",
+        "--output-dir",
+        default=None,
+        metavar="DIRECTORY",
+        help="output directory where to save converted TTFs",
+    )
+
+    options = parser.parse_args(args)
+
+    if not options.verbose:
+        level = "WARNING"
+    elif options.verbose == 1:
+        level = "INFO"
+    else:
+        level = "DEBUG"
+    logging.basicConfig(level=level)
+
+    if len(options.infiles) > 1 and options.output_file:
+        parser.error("-o/--output-file can't be used with multile inputs")
+
+    if options.output_dir:
+        output_dir = options.output_dir
+        if not os.path.exists(output_dir):
+            os.mkdir(output_dir)
+        elif not os.path.isdir(output_dir):
+            parser.error("'%s' is not a directory" % output_dir)
+        output_paths = [
+            os.path.join(output_dir, os.path.basename(p)) for p in options.infiles
+        ]
+    elif options.output_file:
+        output_paths = [options.output_file]
+    else:
+        output_paths = [
+            makeOutputFileName(p, overWrite=True, suffix=".cubic")
+            for p in options.infiles
+        ]
+
+    kwargs = dict(
+        dump_stats=options.verbose > 0,
+        max_err_em=options.conversion_error,
+        all_cubic=options.all_cubic,
+    )
+
+    for input_path, output_path in zip(options.infiles, output_paths):
+        _font_to_cubic(input_path, output_path, **kwargs)

venv/lib/python3.12/site-packages/fontTools/qu2cu/qu2cu.py

@@ -0,0 +1,408 @@
+# cython: language_level=3
+# distutils: define_macros=CYTHON_TRACE_NOGIL=1
+
+# Copyright 2023 Google Inc. All Rights Reserved.
+# Copyright 2023 Behdad Esfahbod. 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.
+
+try:
+    import cython
+
+    COMPILED = cython.compiled
+except (AttributeError, ImportError):
+    # if cython not installed, use mock module with no-op decorators and types
+    from fontTools.misc import cython
+
+    COMPILED = False
+
+from fontTools.misc.bezierTools import splitCubicAtTC
+from collections import namedtuple
+import math
+from typing import (
+    List,
+    Tuple,
+    Union,
+)
+
+
+__all__ = ["quadratic_to_curves"]
+
+
+# Copied from cu2qu
+@cython.cfunc
+@cython.returns(cython.int)
+@cython.locals(
+    tolerance=cython.double,
+    p0=cython.complex,
+    p1=cython.complex,
+    p2=cython.complex,
+    p3=cython.complex,
+)
+@cython.locals(mid=cython.complex, deriv3=cython.complex)
+def cubic_farthest_fit_inside(p0, p1, p2, p3, tolerance):
+    """Check if a cubic Bezier lies within a given distance of the origin.
+
+    "Origin" means *the* origin (0,0), not the start of the curve. Note that no
+    checks are made on the start and end positions of the curve; this function
+    only checks the inside of the curve.
+
+    Args:
+        p0 (complex): Start point of curve.
+        p1 (complex): First handle of curve.
+        p2 (complex): Second handle of curve.
+        p3 (complex): End point of curve.
+        tolerance (double): Distance from origin.
+
+    Returns:
+        bool: True if the cubic Bezier ``p`` entirely lies within a distance
+        ``tolerance`` of the origin, False otherwise.
+    """
+    # First check p2 then p1, as p2 has higher error early on.
+    if abs(p2) <= tolerance and abs(p1) <= tolerance:
+        return True
+
+    # Split.
+    mid = (p0 + 3 * (p1 + p2) + p3) * 0.125
+    if abs(mid) > tolerance:
+        return False
+    deriv3 = (p3 + p2 - p1 - p0) * 0.125
+    return cubic_farthest_fit_inside(
+        p0, (p0 + p1) * 0.5, mid - deriv3, mid, tolerance
+    ) and cubic_farthest_fit_inside(mid, mid + deriv3, (p2 + p3) * 0.5, p3, tolerance)
+
+
+@cython.locals(
+    p0=cython.complex,
+    p1=cython.complex,
+    p2=cython.complex,
+    p1_2_3=cython.complex,
+)
+def elevate_quadratic(p0, p1, p2):
+    """Given a quadratic bezier curve, return its degree-elevated cubic."""
+
+    # https://pomax.github.io/bezierinfo/#reordering
+    p1_2_3 = p1 * (2 / 3)
+    return (
+        p0,
+        (p0 * (1 / 3) + p1_2_3),
+        (p2 * (1 / 3) + p1_2_3),
+        p2,
+    )
+
+
+@cython.cfunc
+@cython.locals(
+    start=cython.int,
+    n=cython.int,
+    k=cython.int,
+    prod_ratio=cython.double,
+    sum_ratio=cython.double,
+    ratio=cython.double,
+    t=cython.double,
+    p0=cython.complex,
+    p1=cython.complex,
+    p2=cython.complex,
+    p3=cython.complex,
+)
+def merge_curves(curves, start, n):
+    """Give a cubic-Bezier spline, reconstruct one cubic-Bezier
+    that has the same endpoints and tangents and approxmates
+    the spline."""
+
+    # Reconstruct the t values of the cut segments
+    prod_ratio = 1.0
+    sum_ratio = 1.0
+    ts = [1]
+    for k in range(1, n):
+        ck = curves[start + k]
+        c_before = curves[start + k - 1]
+
+        # |t_(k+1) - t_k| / |t_k - t_(k - 1)| = ratio
+        assert ck[0] == c_before[3]
+        ratio = abs(ck[1] - ck[0]) / abs(c_before[3] - c_before[2])
+
+        prod_ratio *= ratio
+        sum_ratio += prod_ratio
+        ts.append(sum_ratio)
+
+    # (t(n) - t(n - 1)) / (t_(1) - t(0)) = prod_ratio
+
+    ts = [t / sum_ratio for t in ts[:-1]]
+
+    p0 = curves[start][0]
+    p1 = curves[start][1]
+    p2 = curves[start + n - 1][2]
+    p3 = curves[start + n - 1][3]
+
+    # Build the curve by scaling the control-points.
+    p1 = p0 + (p1 - p0) / (ts[0] if ts else 1)
+    p2 = p3 + (p2 - p3) / ((1 - ts[-1]) if ts else 1)
+
+    curve = (p0, p1, p2, p3)
+
+    return curve, ts
+
+
+@cython.locals(
+    count=cython.int,
+    num_offcurves=cython.int,
+    i=cython.int,
+    off1=cython.complex,
+    off2=cython.complex,
+    on=cython.complex,
+)
+def add_implicit_on_curves(p):
+    q = list(p)
+    count = 0
+    num_offcurves = len(p) - 2
+    for i in range(1, num_offcurves):
+        off1 = p[i]
+        off2 = p[i + 1]
+        on = off1 + (off2 - off1) * 0.5
+        q.insert(i + 1 + count, on)
+        count += 1
+    return q
+
+
+Point = Union[Tuple[float, float], complex]
+
+
+@cython.locals(
+    cost=cython.int,
+    is_complex=cython.int,
+)
+def quadratic_to_curves(
+    quads: List[List[Point]],
+    max_err: float = 0.5,
+    all_cubic: bool = False,
+) -> List[Tuple[Point, ...]]:
+    """Converts a connecting list of quadratic splines to a list of quadratic
+    and cubic curves.
+
+    A quadratic spline is specified as a list of points.  Either each point is
+    a 2-tuple of X,Y coordinates, or each point is a complex number with
+    real/imaginary components representing X,Y coordinates.
+
+    The first and last points are on-curve points and the rest are off-curve
+    points, with an implied on-curve point in the middle between every two
+    consequtive off-curve points.
+
+    Returns:
+        The output is a list of tuples of points. Points are represented
+        in the same format as the input, either as 2-tuples or complex numbers.
+
+        Each tuple is either of length three, for a quadratic curve, or four,
+        for a cubic curve.  Each curve's last point is the same as the next
+        curve's first point.
+
+    Args:
+        quads: quadratic splines
+
+        max_err: absolute error tolerance; defaults to 0.5
+
+        all_cubic: if True, only cubic curves are generated; defaults to False
+    """
+    is_complex = type(quads[0][0]) is complex
+    if not is_complex:
+        quads = [[complex(x, y) for (x, y) in p] for p in quads]
+
+    q = [quads[0][0]]
+    costs = [1]
+    cost = 1
+    for p in quads:
+        assert q[-1] == p[0]
+        for i in range(len(p) - 2):
+            cost += 1
+            costs.append(cost)
+            costs.append(cost)
+        qq = add_implicit_on_curves(p)[1:]
+        costs.pop()
+        q.extend(qq)
+        cost += 1
+        costs.append(cost)
+
+    curves = spline_to_curves(q, costs, max_err, all_cubic)
+
+    if not is_complex:
+        curves = [tuple((c.real, c.imag) for c in curve) for curve in curves]
+    return curves
+
+
+Solution = namedtuple("Solution", ["num_points", "error", "start_index", "is_cubic"])
+
+
+@cython.locals(
+    i=cython.int,
+    j=cython.int,
+    k=cython.int,
+    start=cython.int,
+    i_sol_count=cython.int,
+    j_sol_count=cython.int,
+    this_sol_count=cython.int,
+    tolerance=cython.double,
+    err=cython.double,
+    error=cython.double,
+    i_sol_error=cython.double,
+    j_sol_error=cython.double,
+    all_cubic=cython.int,
+    is_cubic=cython.int,
+    count=cython.int,
+    p0=cython.complex,
+    p1=cython.complex,
+    p2=cython.complex,
+    p3=cython.complex,
+    v=cython.complex,
+    u=cython.complex,
+)
+def spline_to_curves(q, costs, tolerance=0.5, all_cubic=False):
+    """
+    q: quadratic spline with alternating on-curve / off-curve points.
+
+    costs: cumulative list of encoding cost of q in terms of number of
+      points that need to be encoded.  Implied on-curve points do not
+      contribute to the cost. If all points need to be encoded, then
+      costs will be range(1, len(q)+1).
+    """
+
+    assert len(q) >= 3, "quadratic spline requires at least 3 points"
+
+    # Elevate quadratic segments to cubic
+    elevated_quadratics = [
+        elevate_quadratic(*q[i : i + 3]) for i in range(0, len(q) - 2, 2)
+    ]
+
+    # Find sharp corners; they have to be oncurves for sure.
+    forced = set()
+    for i in range(1, len(elevated_quadratics)):
+        p0 = elevated_quadratics[i - 1][2]
+        p1 = elevated_quadratics[i][0]
+        p2 = elevated_quadratics[i][1]
+        if abs(p1 - p0) + abs(p2 - p1) > tolerance + abs(p2 - p0):
+            forced.add(i)
+
+    # Dynamic-Programming to find the solution with fewest number of
+    # cubic curves, and within those the one with smallest error.
+    sols = [Solution(0, 0, 0, False)]
+    impossible = Solution(len(elevated_quadratics) * 3 + 1, 0, 1, False)
+    start = 0
+    for i in range(1, len(elevated_quadratics) + 1):
+        best_sol = impossible
+        for j in range(start, i):
+            j_sol_count, j_sol_error = sols[j].num_points, sols[j].error
+
+            if not all_cubic:
+                # Solution with quadratics between j:i
+                this_count = costs[2 * i - 1] - costs[2 * j] + 1
+                i_sol_count = j_sol_count + this_count
+                i_sol_error = j_sol_error
+                i_sol = Solution(i_sol_count, i_sol_error, i - j, False)
+                if i_sol < best_sol:
+                    best_sol = i_sol
+
+                if this_count <= 3:
+                    # Can't get any better than this in the path below
+                    continue
+
+            # Fit elevated_quadratics[j:i] into one cubic
+            try:
+                curve, ts = merge_curves(elevated_quadratics, j, i - j)
+            except ZeroDivisionError:
+                continue
+
+            # Now reconstruct the segments from the fitted curve
+            reconstructed_iter = splitCubicAtTC(*curve, *ts)
+            reconstructed = []
+
+            # Knot errors
+            error = 0
+            for k, reconst in enumerate(reconstructed_iter):
+                orig = elevated_quadratics[j + k]
+                err = abs(reconst[3] - orig[3])
+                error = max(error, err)
+                if error > tolerance:
+                    break
+                reconstructed.append(reconst)
+            if error > tolerance:
+                # Not feasible
+                continue
+
+            # Interior errors
+            for k, reconst in enumerate(reconstructed):
+                orig = elevated_quadratics[j + k]
+                p0, p1, p2, p3 = tuple(v - u for v, u in zip(reconst, orig))
+
+                if not cubic_farthest_fit_inside(p0, p1, p2, p3, tolerance):
+                    error = tolerance + 1
+                    break
+            if error > tolerance:
+                # Not feasible
+                continue
+
+            # Save best solution
+            i_sol_count = j_sol_count + 3
+            i_sol_error = max(j_sol_error, error)
+            i_sol = Solution(i_sol_count, i_sol_error, i - j, True)
+            if i_sol < best_sol:
+                best_sol = i_sol
+
+            if i_sol_count == 3:
+                # Can't get any better than this
+                break
+
+        sols.append(best_sol)
+        if i in forced:
+            start = i
+
+    # Reconstruct solution
+    splits = []
+    cubic = []
+    i = len(sols) - 1
+    while i:
+        count, is_cubic = sols[i].start_index, sols[i].is_cubic
+        splits.append(i)
+        cubic.append(is_cubic)
+        i -= count
+    curves = []
+    j = 0
+    for i, is_cubic in reversed(list(zip(splits, cubic))):
+        if is_cubic:
+            curves.append(merge_curves(elevated_quadratics, j, i - j)[0])
+        else:
+            for k in range(j, i):
+                curves.append(q[k * 2 : k * 2 + 3])
+        j = i
+
+    return curves
+
+
+def main():
+    from fontTools.cu2qu.benchmark import generate_curve
+    from fontTools.cu2qu import curve_to_quadratic
+
+    tolerance = 0.05
+    reconstruct_tolerance = tolerance * 1
+    curve = generate_curve()
+    quadratics = curve_to_quadratic(curve, tolerance)
+    print(
+        "cu2qu tolerance %g. qu2cu tolerance %g." % (tolerance, reconstruct_tolerance)
+    )
+    print("One random cubic turned into %d quadratics." % len(quadratics))
+    curves = quadratic_to_curves([quadratics], reconstruct_tolerance)
+    print("Those quadratics turned back into %d cubics. " % len(curves))
+    print("Original curve:", curve)
+    print("Reconstructed curve(s):", curves)
+
+
+if __name__ == "__main__":
+    main()