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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]
proposed_point = 0
reverse = False
min_cost = first_cost = 1
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]
if min_cost < first_cost * tolerance:
this_tolerance = min_cost / first_cost
# 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.
proposed_point = contour1[min_cost_idx][1]
reverse = contour1[min_cost_idx][2]
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
return proposed_point, reverse, min_cost, first_cost
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