[bezierTools] Add calcCubicArcLength() and calcCubicArcLengthC()

Fixes https://github.com/fonttools/fonttools/issues/1142

Lib/fontTools/misc/bezierTools.py

@@ -13,10 +13,12 @@ __all__ = [
     "approximateCubicArcLengthC",
     "approximateQuadraticArcLength",
     "approximateQuadraticArcLengthC",
+    "calcCubicArcLength",
+    "calcCubicArcLengthC",
     "calcQuadraticArcLength",
     "calcQuadraticArcLengthC",
-    "calcQuadraticBounds",
     "calcCubicBounds",
+    "calcQuadraticBounds",
     "splitLine",
     "splitQuadratic",
     "splitCubic",
@@ -27,6 +29,32 @@ __all__ = [
 ]
 
 
+def calcCubicArcLength(pt1, pt2, pt3, pt4, tolerance=0.005):
+    """Return the arc length for a cubic bezier segment."""
+    return calcCubicArcLengthC(complex(*pt1), complex(*pt2), complex(*pt3), complex(*pt4), tolerance)
+
+
+def _split_cubic_into_two(p0, p1, p2, p3):
+    mid = (p0 + 3 * (p1 + p2) + p3) * .125
+    deriv3 = (p3 + p2 - p1 - p0) * .125
+    return ((p0, (p0 + p1) * .5, mid - deriv3, mid),
+            (mid, mid + deriv3, (p2 + p3) * .5, p3))
+
+def _calcCubicArcLengthCRecurse(mult, p0, p1, p2, p3):
+	arch = abs(p0-p3)
+	box = abs(p0-p1) + abs(p1-p2) + abs(p2-p3)
+	if arch * mult >= box:
+		return (arch + box) * .5
+	else:
+		one,two = _split_cubic_into_two(p0,p1,p2,p3)
+		return _calcCubicArcLengthCRecurse(mult, *one) + _calcCubicArcLengthCRecurse(mult, *two)
+
+def calcCubicArcLengthC(pt1, pt2, pt3, pt4, tolerance=0.005):
+    """Return the arc length for a cubic bezier segment using complex points."""
+    mult = 1. + 1.5 * tolerance # The 1.5 is a empirical hack; no math
+    return _calcCubicArcLengthCRecurse(mult, pt1, pt2, pt3, pt4)
+
+
 epsilonDigits = 6
 epsilon = 1e-10
 

Lib/fontTools/pens/perimeterPen.py

@@ -4,7 +4,7 @@
 from __future__ import print_function, division, absolute_import
 from fontTools.misc.py23 import *
 from fontTools.pens.basePen import BasePen
-from fontTools.misc.bezierTools import splitQuadraticAtT, splitCubicAtT, approximateQuadraticArcLengthC, calcQuadraticArcLengthC, approximateCubicArcLengthC
+from fontTools.misc.bezierTools import approximateQuadraticArcLengthC, calcQuadraticArcLengthC, approximateCubicArcLengthC, calcCubicArcLengthC
 import math
 
 
@@ -14,18 +14,12 @@ __all__ = ["PerimeterPen"]
 def _distance(p0, p1):
 	return math.hypot(p0[0] - p1[0], p0[1] - p1[1])
 
-def _split_cubic_into_two(p0, p1, p2, p3):
-    mid = (p0 + 3 * (p1 + p2) + p3) * .125
-    deriv3 = (p3 + p2 - p1 - p0) * .125
-    return ((p0, (p0 + p1) * .5, mid - deriv3, mid),
-            (mid, mid + deriv3, (p2 + p3) * .5, p3))
-
 class PerimeterPen(BasePen):
 
 	def __init__(self, glyphset=None, tolerance=0.005):
 		BasePen.__init__(self, glyphset)
 		self.value = 0
-		self._mult = 1.+1.5*tolerance # The 1.5 is a empirical hack; no math
+		self.tolerance = tolerance
 
 		# Choose which algorithm to use for quadratic and for cubic.
 		# Quadrature is faster but has fixed error characteristic with no strong
@@ -55,15 +49,8 @@ class PerimeterPen(BasePen):
 		p0 = self._getCurrentPoint()
 		self._addQuadratic(complex(*p0), complex(*p1), complex(*p2))
 
-	def _addCubicRecursive(self, p0, p1, p2, p3):
+	def _addCubicRecursive(self, c0, c1, c2, c3):
-		arch = abs(p0-p3)
+		self.value += calcCubicArcLengthC(c0, c1, c2, c3, self.tolerance)
-		box = abs(p0-p1) + abs(p1-p2) + abs(p2-p3)
-		if arch * self._mult >= box:
-			self.value += (arch + box) * .5
-		else:
-			one,two = _split_cubic_into_two(p0,p1,p2,p3)
-			self._addCubicRecursive(*one)
-			self._addCubicRecursive(*two)
 
 	def _addCubicQuadrature(self, c0, c1, c2, c3):
 		self.value += approximateCubicArcLengthC(c0, c1, c2, c3)