111 lines
3.9 KiB
Python
111 lines
3.9 KiB
Python
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"""Helpers for manipulating 2D points and vectors in COLR table."""
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from math import copysign, cos, sqrt, pi
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from fontTools.misc.fixedTools import otRound
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def _vector_between_points(a, b):
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return (b[0] - a[0], b[1] - a[1])
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def _vector_length(vec):
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return sqrt(vec[0] * vec[0] + vec[1] * vec[1])
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def _distance_between_points(a, b):
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return _vector_length(_vector_between_points(a, b))
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def _round_point(pt):
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return (otRound(pt[0]), otRound(pt[1]))
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def _round_circle(centre, radius):
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return _round_point(centre), otRound(radius)
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def _unit_vector(vec):
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length = _vector_length(vec)
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if length == 0:
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return None
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return (vec[0] / length, vec[1] / length)
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# This is the same tolerance used by Skia's SkTwoPointConicalGradient.cpp to detect
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# when a radial gradient's focal point lies on the end circle.
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_NEARLY_ZERO = 1 / (1 << 12) # 0.000244140625
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def _is_circle_inside_circle(c0, r0, c1, r1):
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dist = r0 + _distance_between_points(c0, c1)
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return abs(r1 - dist) <= _NEARLY_ZERO or r1 > dist
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# The unit vector's X and Y components are respectively
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# U = (cos(α), sin(α))
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# where α is the angle between the unit vector and the positive x axis.
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_UNIT_VECTOR_THRESHOLD = cos(3 / 8 * pi) # == sin(1/8 * pi) == 0.38268343236508984
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def _nudge_point(pt, direction):
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# Nudge point coordinates -/+ 1.0 approximately based on the direction vector.
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# We divide the unit circle in 8 equal slices oriented towards the cardinal
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# (N, E, S, W) and intermediate (NE, SE, SW, NW) directions. To each slice we
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# map one of the possible cases: -1, 0, +1 for either X and Y coordinate.
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# E.g. Return (x + 1.0, y - 1.0) if unit vector is oriented towards SE, or
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# (x - 1.0, y) if it's pointing West, etc.
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uv = _unit_vector(direction)
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if not uv:
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return pt
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result = []
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for coord, uv_component in zip(pt, uv):
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if -_UNIT_VECTOR_THRESHOLD <= uv_component < _UNIT_VECTOR_THRESHOLD:
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# unit vector component near 0: direction almost orthogonal to the
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# direction of the current axis, thus keep coordinate unchanged
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result.append(coord)
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else:
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# nudge coord by +/- 1.0 in direction of unit vector
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result.append(coord + copysign(1.0, uv_component))
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return tuple(result)
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def nudge_start_circle_almost_inside(c0, r0, c1, r1):
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""" Nudge c0 so it continues to be inside/outside c1 after rounding.
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The rounding of circle coordinates to integers may cause an abrupt change
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if the start circle c0 is so close to the end circle c1's perimiter that
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it ends up falling outside (or inside) as a result of the rounding.
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To keep the gradient unchanged, we nudge it in the right direction.
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See:
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https://github.com/googlefonts/colr-gradients-spec/issues/204
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https://github.com/googlefonts/picosvg/issues/158
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"""
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inside_before_round = _is_circle_inside_circle(c0, r0, c1, r1)
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rc0, rr0 = _round_circle(c0, r0)
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rc1, rr1 = _round_circle(c1, r1)
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inside_after_round = _is_circle_inside_circle(rc0, rr0, rc1, rr1)
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if inside_before_round != inside_after_round:
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# at most 2 iterations ought to be enough to converge
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for _ in range(2):
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if rc0 == rc1: # nowhere to nudge along a zero vector, bail out
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break
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if inside_after_round:
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direction = _vector_between_points(rc1, rc0)
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else:
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direction = _vector_between_points(rc0, rc1)
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rc0 = _nudge_point(rc0, direction)
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inside_after_round = _is_circle_inside_circle(rc0, rr0, rc1, rr1)
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if inside_before_round == inside_after_round:
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break
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else: # ... or it's a bug
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raise AssertionError(
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f"Nudging circle <c0={c0}, r0={r0}> "
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f"{'inside' if inside_before_round else 'outside'} "
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f"<c1={c1}, r1={r1}> failed after two attempts!"
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)
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return rc0
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