areaPen.py: pen to calculate the area of a glyph (by Behdad)

https://github.com/behdad/fonttools/issues/617#issuecomment-225029592

Lib/fontTools/pens/areaPen.py

@@ -0,0 +1,57 @@
+"""Calculate the area of a glyph."""
+
+import math
+from fontTools.pens.basePen import BasePen
+from collections import namedtuple
+
+
+P = namedtuple('P', ('x', 'y'))
+
+
+def distance(p0, p1):
+    return math.hypot(p0.x - p1.x, p0.y - p1.y)
+
+
+def interpolate(p0, p1, t):
+    return P(p0.x * (1 - t) + p1.x * t, p0.y * (1 - t) + p1.y * t)
+
+
+def polygon_area(p0, p1):
+    return (p1.x - p0.x) * (p1.y + p0.y) * 0.5
+
+
+def quadratic_curve_area(p0, p1, p2):
+    new_p2 = interpolate(p2, p1, 2.0 / 3)
+    new_p1 = interpolate(p0, p1, 2.0 / 3)
+    return cubic_curve_area(p0, new_p1, new_p2, p2)
+
+
+def cubic_curve_area(p0, p1, p2, p3):
+    x0, y0 = p0.x, p0.y
+    x1, y1 = p1.x - x0, p1.y - y0
+    x2, y2 = p2.x - x0, p2.y - y0
+    x3, y3 = p3.x - x0, p3.y - y0
+    return (
+        x1 * (   -   y2 -   y3) +
+        x2 * (y1        - 2*y3) +
+        x3 * (y1 + 2*y2       )
+    ) * 0.15
+
+
+class AreaPen(BasePen):
+
+    def __init__(self, glyphset):
+        BasePen.__init__(self, glyphset)
+        self.value = 0
+
+    def _moveTo(self, p0):
+        pass
+
+    def _lineTo(self, p1):
+        p0 = self._getCurrentPoint()
+        self.value += polygon_area(P(*p0), P(*p1))
+
+    def _curveToOne(self, p1, p2, p3):
+        p0 = self._getCurrentPoint()
+        self.value += cubic_curve_area(P(*p0), P(*p1), P(*p2), P(*p3))
+        self.value += polygon_area(P(*p0), P(*p3))