Lib/fontTools/pens/perimeterPen.py

# -*- coding: utf-8 -*-
"""Calculate the perimeter of a glyph."""

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
import math


__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

		# Choose which algorithm to use for quadratic and for cubic.
		# Quadrature is faster but has fixed error characteristic with no strong
		# error bound.  The cutoff points are derived empirically.
		self._addCubic = self._addCubicQuadrature if tolerance >= 0.0015 else self._addCubicRecursive
		self._addQuadratic = self._addQuadraticQuadrature if tolerance >= 0.00075 else self._addQuadraticExact

	def _moveTo(self, p0):
		self.__startPoint = p0

	def _closePath(self):
		p0 = self._getCurrentPoint()
		if p0 != self.__startPoint:
			self._lineTo(self.__startPoint)

	def _lineTo(self, p1):
		p0 = self._getCurrentPoint()
		self.value += _distance(p0, p1)

	def _addQuadraticExact(self, c0, c1, c2):
		self.value += calcQuadraticArcLengthC(c0, c1, c2)

	def _addQuadraticQuadrature(self, c0, c1, c2):
		self.value += approximateQuadraticArcLengthC(c0, c1, c2)

	def _qCurveToOne(self, p1, p2):
		p0 = self._getCurrentPoint()
		self._addQuadratic(complex(*p0), complex(*p1), complex(*p2))

	def _addCubicRecursive(self, p0, p1, p2, p3):
		arch = abs(p0-p3)
		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)

	def _curveToOne(self, p1, p2, p3):
		p0 = self._getCurrentPoint()
		self._addCubic(complex(*p0), complex(*p1), complex(*p2), complex(*p3))