| """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 |
| import math |
| |
| |
| def _distance(p0, p1): |
| return math.hypot(p0[0] - p1[0], p0[1] - p1[1]) |
| def _dot(v1, v2): |
| return (v1 * v2.conjugate()).real |
| def _intSecAtan(x): |
| # In : sympy.integrate(sp.sec(sp.atan(x))) |
| # Out: x*sqrt(x**2 + 1)/2 + asinh(x)/2 |
| return x * math.sqrt(x**2 + 1)/2 + math.asinh(x)/2 |
| |
| 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 |
| |
| def _moveTo(self, p0): |
| self.__startPoint = p0 |
| |
| def _lineTo(self, p1): |
| p0 = self._getCurrentPoint() |
| self.value += _distance(p0, p1) |
| |
| def _qCurveToOne(self, p1, p2): |
| # Analytical solution to the length of a quadratic bezier. |
| # I'll explain how I arrived at this later. |
| p0 = self._getCurrentPoint() |
| _p1 = complex(*p1) |
| d0 = _p1 - complex(*p0) |
| d1 = complex(*p2) - _p1 |
| d = d1 - d0 |
| n = d * 1j |
| scale = abs(n) |
| if scale == 0.: |
| self._lineTo(p2) |
| return |
| origDist = _dot(n,d0) |
| if origDist == 0.: |
| if _dot(d0,d1) >= 0: |
| self._lineTo(p2) |
| return |
| assert 0 # TODO handle cusps |
| x0 = _dot(d,d0) / origDist |
| x1 = _dot(d,d1) / origDist |
| Len = abs(2 * (_intSecAtan(x1) - _intSecAtan(x0)) * origDist / (scale * (x1 - x0))) |
| self.value += Len |
| |
| def _addCubic(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._addCubic(*one) |
| self._addCubic(*two) |
| |
| def _curveToOne(self, p1, p2, p3): |
| p0 = self._getCurrentPoint() |
| self._addCubic(complex(*p0), complex(*p1), complex(*p2), complex(*p3)) |
| |
| def _closePath(self): |
| p0 = self._getCurrentPoint() |
| if p0 != self.__startPoint: |
| self.value += _distance(p0, self.__startPoint) |
