[varLib] Start implementing optimal IUP solution

Not optimal right now, since first and last point are always included.
Also rather slow.  Takes about 12s for NotoSansArabic, and saves just
one percent in gvar size with a tolerance of 0.5 font units.

Lib/fontTools/varLib/__init__.py

@@ -202,6 +202,16 @@ def _SetCoordinates(font, glyphName, coord):
 	font["hmtx"].metrics[glyphName] = horizontalAdvanceWidth, leftSideBearing
 
 
+def _all_interpolatable_in_between(deltas, coords, j, i, tolerance):
+	assert i - j >= 2
+	from fontTools.varLib.mutator import _iup_segment
+	interp = _iup_segment(coords[j+1:i], coords[j], deltas[j], coords[i], deltas[i])
+	deltas = deltas[j+1:i]
+
+	assert len(deltas) == len(interp)
+
+	return all(abs(x-p) <= tolerance >= abs(y-q) for (x,y),(p,q) in zip(deltas, interp))
+
 def _optimize_contour(delta, coords, tolerance=0.):
 	n = len(delta)
 	if all(abs(x) <= tolerance >= abs(y) for x,y in delta):
@@ -212,9 +222,34 @@ def _optimize_contour(delta, coords, tolerance=0.):
 	if all(d0 == d for d in delta):
 		return [d0] + [None] * (n-1)
 
-	# TODO
+	# TODO Handle circularity in Dynamic-Programming.
 
-	return delta
+	dp = [(1, None)]
+	for i in range(1, len(delta)):
+		best_cost, best_i = dp[i-1][0]+1, i-1
+		for j in range(i-2, -1, -1):
+			cost, _ = dp[j]
+			cost += 1
+			if cost >= best_cost:
+				continue
+
+			valid = _all_interpolatable_in_between(delta, coords, j, i, tolerance)
+
+			if not valid:
+				continue
+
+			best_cost, best_i = cost, j
+
+		dp.append((best_cost, best_i))
+
+	i = n - 1
+	sol = set()
+	while i is not None:
+		sol.add(i)
+		_, i = dp[i]
+	assert len(sol) > 1
+
+	return [delta[i] if i in sol else None for i in range(n)]
 
 def _optimize_delta(delta, coords, ends, tolerance=0.):
 	assert sorted(ends) == ends and len(coords) == (ends[-1]+1 if ends else 0) + 4
@@ -224,12 +259,13 @@ def _optimize_delta(delta, coords, ends, tolerance=0.):
 	start = 0
 	for end in ends:
 		contour = _optimize_contour(delta[start:end+1], coords[start:end+1], tolerance)
+		assert len(contour) == end - start + 1
 		out.extend(contour)
 		start = end+1
 
 	return out
 
-def _add_gvar(font, model, master_ttfs, tolerance=.5, optimize=True):
+def _add_gvar(font, model, master_ttfs, tolerance=0.5, optimize=True):
 
 	assert tolerance >= 0