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