From baecd8850b878b1cc5ccf140d884754c4b8d2e9b Mon Sep 17 00:00:00 2001
From: Behdad Esfahbod <behdad@behdad.org>
Date: Wed, 24 Aug 2022 16:13:16 -0600
Subject: [PATCH] [Snippets] Add statShape

---
 Snippets/statShape.py | 70 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 70 insertions(+)
 create mode 100644 Snippets/statShape.py

diff --git a/Snippets/statShape.py b/Snippets/statShape.py
new file mode 100644
index 000000000..7961a9950
--- /dev/null
+++ b/Snippets/statShape.py
@@ -0,0 +1,70 @@
+"""Draw statistical shape of a glyph as an ellipse."""
+
+from fontTools.ttLib import TTFont
+from fontTools.pens.recordingPen import RecordingPen
+from fontTools.pens.cairoPen import CairoPen
+from fontTools.pens.statisticsPen import StatisticsPen
+import cairo
+import math
+import sys
+
+
+font = TTFont(sys.argv[1])
+unicode = sys.argv[2]
+
+cmap = font['cmap'].getBestCmap()
+gid = cmap[ord(unicode)]
+
+hhea = font['hhea']
+glyphset = font.getGlyphSet()
+with cairo.SVGSurface("example.svg", hhea.advanceWidthMax, hhea.ascent-hhea.descent) as surface:
+    context = cairo.Context(surface)
+    context.translate(0, +font['hhea'].ascent)
+    context.scale(1, -1)
+
+    glyph = glyphset[gid]
+
+    recording = RecordingPen()
+    glyph.draw(recording)
+
+    context.translate((hhea.advanceWidthMax - glyph.width) * .5, 0)
+
+    pen = CairoPen(glyphset, context)
+    glyph.draw(pen)
+    context.fill()
+
+    stats = StatisticsPen()
+    glyph.draw(stats)
+
+    context.save()
+
+    # https://cookierobotics.com/007/
+    a = stats.varianceX
+    b = stats.covariance
+    c = stats.varianceY
+    delta = (((a - c) * .5) ** 2 + b * b) ** .5
+    lambda1 = (a + c) * .5 + delta  # Major eigenvalue
+    lambda2 = (a + c) * .5 - delta  # Minor eigenvalue
+    theta = (
+             math.atan2(lambda1 - a, b)
+             if b != 0 else
+             (math.pi * .5 if a < c else 0)
+            )
+    mult = 4  # Empirical by drawing '.'
+    transform = cairo.Matrix()
+    transform.translate(stats.meanX, stats.meanY)
+    transform.rotate(theta)
+    transform.scale(math.sqrt(lambda1), math.sqrt(lambda2))
+    transform.scale(mult, mult)
+
+    ellipse_area = math.sqrt(lambda1) * math.sqrt(lambda2) * math.pi/4 * mult * mult
+
+    context.set_line_cap(cairo.LINE_CAP_ROUND)
+    context.transform(transform)
+    context.move_to(0, 0)
+    context.line_to(0, 0)
+    context.set_line_width(1)
+    context.set_source_rgba(1, 0, 0, abs(stats.area / ellipse_area))
+    context.stroke()
+
+    context.restore()