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Diffstat (limited to 'Lib/fontTools/colorLib/geometry.py')
| -rw-r--r-- | Lib/fontTools/colorLib/geometry.py | 145 |
1 files changed, 145 insertions, 0 deletions
diff --git a/Lib/fontTools/colorLib/geometry.py b/Lib/fontTools/colorLib/geometry.py new file mode 100644 index 00000000..ec647535 --- /dev/null +++ b/Lib/fontTools/colorLib/geometry.py @@ -0,0 +1,145 @@ +"""Helpers for manipulating 2D points and vectors in COLR table.""" + +from math import copysign, cos, hypot, pi +from fontTools.misc.fixedTools import otRound + + +def _vector_between(origin, target): + return (target[0] - origin[0], target[1] - origin[1]) + + +def _round_point(pt): + return (otRound(pt[0]), otRound(pt[1])) + + +def _unit_vector(vec): + length = hypot(*vec) + if length == 0: + return None + return (vec[0] / length, vec[1] / length) + + +# This is the same tolerance used by Skia's SkTwoPointConicalGradient.cpp to detect +# when a radial gradient's focal point lies on the end circle. +_NEARLY_ZERO = 1 / (1 << 12) # 0.000244140625 + + +# The unit vector's X and Y components are respectively +# U = (cos(α), sin(α)) +# where α is the angle between the unit vector and the positive x axis. +_UNIT_VECTOR_THRESHOLD = cos(3 / 8 * pi) # == sin(1/8 * pi) == 0.38268343236508984 + + +def _rounding_offset(direction): + # Return 2-tuple of -/+ 1.0 or 0.0 approximately based on the direction vector. + # We divide the unit circle in 8 equal slices oriented towards the cardinal + # (N, E, S, W) and intermediate (NE, SE, SW, NW) directions. To each slice we + # map one of the possible cases: -1, 0, +1 for either X and Y coordinate. + # E.g. Return (+1.0, -1.0) if unit vector is oriented towards SE, or + # (-1.0, 0.0) if it's pointing West, etc. + uv = _unit_vector(direction) + if not uv: + return (0, 0) + + result = [] + for uv_component in uv: + if -_UNIT_VECTOR_THRESHOLD <= uv_component < _UNIT_VECTOR_THRESHOLD: + # unit vector component near 0: direction almost orthogonal to the + # direction of the current axis, thus keep coordinate unchanged + result.append(0) + else: + # nudge coord by +/- 1.0 in direction of unit vector + result.append(copysign(1.0, uv_component)) + return tuple(result) + + +class Circle: + def __init__(self, centre, radius): + self.centre = centre + self.radius = radius + + def __repr__(self): + return f"Circle(centre={self.centre}, radius={self.radius})" + + def round(self): + return Circle(_round_point(self.centre), otRound(self.radius)) + + def inside(self, outer_circle): + dist = self.radius + hypot(*_vector_between(self.centre, outer_circle.centre)) + return ( + abs(outer_circle.radius - dist) <= _NEARLY_ZERO + or outer_circle.radius > dist + ) + + def concentric(self, other): + return self.centre == other.centre + + def move(self, dx, dy): + self.centre = (self.centre[0] + dx, self.centre[1] + dy) + + +def round_start_circle_stable_containment(c0, r0, c1, r1): + """Round start circle so that it stays inside/outside end circle after rounding. + + The rounding of circle coordinates to integers may cause an abrupt change + if the start circle c0 is so close to the end circle c1's perimiter that + it ends up falling outside (or inside) as a result of the rounding. + To keep the gradient unchanged, we nudge it in the right direction. + + See: + https://github.com/googlefonts/colr-gradients-spec/issues/204 + https://github.com/googlefonts/picosvg/issues/158 + """ + start, end = Circle(c0, r0), Circle(c1, r1) + + inside_before_round = start.inside(end) + + round_start = start.round() + round_end = end.round() + inside_after_round = round_start.inside(round_end) + + if inside_before_round == inside_after_round: + return round_start + elif inside_after_round: + # start was outside before rounding: we need to push start away from end + direction = _vector_between(round_end.centre, round_start.centre) + radius_delta = +1.0 + else: + # start was inside before rounding: we need to push start towards end + direction = _vector_between(round_start.centre, round_end.centre) + radius_delta = -1.0 + dx, dy = _rounding_offset(direction) + + # At most 2 iterations ought to be enough to converge. Before the loop, we + # know the start circle didn't keep containment after normal rounding; thus + # we continue adjusting by -/+ 1.0 until containment is restored. + # Normal rounding can at most move each coordinates -/+0.5; in the worst case + # both the start and end circle's centres and radii will be rounded in opposite + # directions, e.g. when they move along a 45 degree diagonal: + # c0 = (1.5, 1.5) ===> (2.0, 2.0) + # r0 = 0.5 ===> 1.0 + # c1 = (0.499, 0.499) ===> (0.0, 0.0) + # r1 = 2.499 ===> 2.0 + # In this example, the relative distance between the circles, calculated + # as r1 - (r0 + distance(c0, c1)) is initially 0.57437 (c0 is inside c1), and + # -1.82842 after rounding (c0 is now outside c1). Nudging c0 by -1.0 on both + # x and y axes moves it towards c1 by hypot(-1.0, -1.0) = 1.41421. Two of these + # moves cover twice that distance, which is enough to restore containment. + max_attempts = 2 + for _ in range(max_attempts): + if round_start.concentric(round_end): + # can't move c0 towards c1 (they are the same), so we change the radius + round_start.radius += radius_delta + assert round_start.radius >= 0 + else: + round_start.move(dx, dy) + if inside_before_round == round_start.inside(round_end): + break + else: # likely a bug + raise AssertionError( + f"Rounding circle {start} " + f"{'inside' if inside_before_round else 'outside'} " + f"{end} failed after {max_attempts} attempts!" + ) + + return round_start |