1 files changed, 105 insertions, 0 deletions
diff --git a/Lib/fontTools/varLib/interpolatableTestStartingPoint.py b/Lib/fontTools/varLib/interpolatableTestStartingPoint.py
new file mode 100644
index 00000000..e7600066
--- /dev/null
+++ b/Lib/fontTools/varLib/interpolatableTestStartingPoint.py
@@ -0,0 +1,105 @@
+from .interpolatableHelpers import *
+
+
+def test_starting_point(glyph0, glyph1, ix, tolerance, matching):
+    if matching is None:
+        matching = list(range(len(glyph0.isomorphisms)))
+    contour0 = glyph0.isomorphisms[ix]
+    contour1 = glyph1.isomorphisms[matching[ix]]
+    m0Vectors = glyph0.greenVectors
+    m1Vectors = [glyph1.greenVectors[i] for i in matching]
+
+    c0 = contour0[0]
+    # Next few lines duplicated below.
+    costs = [vdiff_hypot2_complex(c0[0], c1[0]) for c1 in contour1]
+    min_cost_idx, min_cost = min(enumerate(costs), key=lambda x: x[1])
+    first_cost = costs[0]
+    proposed_point = contour1[min_cost_idx][1]
+    reverse = contour1[min_cost_idx][2]
+
+    if min_cost < first_cost * tolerance:
+        # c0 is the first isomorphism of the m0 master
+        # contour1 is list of all isomorphisms of the m1 master
+        #
+        # If the two shapes are both circle-ish and slightly
+        # rotated, we detect wrong start point. This is for
+        # example the case hundreds of times in
+        # RobotoSerif-Italic[GRAD,opsz,wdth,wght].ttf
+        #
+        # If the proposed point is only one off from the first
+        # point (and not reversed), try harder:
+        #
+        # Find the major eigenvector of the covariance matrix,
+        # and rotate the contours by that angle. Then find the
+        # closest point again.  If it matches this time, let it
+        # pass.
+
+        num_points = len(glyph1.points[ix])
+        leeway = 3
+        if not reverse and (
+            proposed_point <= leeway or proposed_point >= num_points - leeway
+        ):
+            # Try harder
+
+            # Recover the covariance matrix from the GreenVectors.
+            # This is a 2x2 matrix.
+            transforms = []
+            for vector in (m0Vectors[ix], m1Vectors[ix]):
+                meanX = vector[1]
+                meanY = vector[2]
+                stddevX = vector[3] * 0.5
+                stddevY = vector[4] * 0.5
+                correlation = vector[5] / abs(vector[0])
+
+                # https://cookierobotics.com/007/
+                a = stddevX * stddevX  # VarianceX
+                c = stddevY * stddevY  # VarianceY
+                b = correlation * stddevX * stddevY  # Covariance
+
+                delta = (((a - c) * 0.5) ** 2 + b * b) ** 0.5
+                lambda1 = (a + c) * 0.5 + delta  # Major eigenvalue
+                lambda2 = (a + c) * 0.5 - delta  # Minor eigenvalue
+                theta = atan2(lambda1 - a, b) if b != 0 else (pi * 0.5 if a < c else 0)
+                trans = Transform()
+                # Don't translate here. We are working on the complex-vector
+                # that includes more than just the points. It's horrible what
+                # we are doing anyway...
+                # trans = trans.translate(meanX, meanY)
+                trans = trans.rotate(theta)
+                trans = trans.scale(sqrt(lambda1), sqrt(lambda2))
+                transforms.append(trans)
+
+            trans = transforms[0]
+            new_c0 = (
+                [complex(*trans.transformPoint((pt.real, pt.imag))) for pt in c0[0]],
+            ) + c0[1:]
+            trans = transforms[1]
+            new_contour1 = []
+            for c1 in contour1:
+                new_c1 = (
+                    [
+                        complex(*trans.transformPoint((pt.real, pt.imag)))
+                        for pt in c1[0]
+                    ],
+                ) + c1[1:]
+                new_contour1.append(new_c1)
+
+            # Next few lines duplicate from above.
+            costs = [
+                vdiff_hypot2_complex(new_c0[0], new_c1[0]) for new_c1 in new_contour1
+            ]
+            min_cost_idx, min_cost = min(enumerate(costs), key=lambda x: x[1])
+            first_cost = costs[0]
+            if min_cost < first_cost * tolerance:
+                # Don't report this
+                # min_cost = first_cost
+                # reverse = False
+                # proposed_point = 0  # new_contour1[min_cost_idx][1]
+                pass
+
+    this_tolerance = min_cost / first_cost if first_cost else 1
+    log.debug(
+        "test-starting-point: tolerance %g",
+        this_tolerance,
+    )
+    return this_tolerance, proposed_point, reverse