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155 lines
5.7 KiB
Python
155 lines
5.7 KiB
Python
"""Convert SVG Path's elliptical arcs to Bezier curves.
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The code is mostly adapted from Blink's SVGPathNormalizer::DecomposeArcToCubic
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https://github.com/chromium/chromium/blob/93831f2/third_party/
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blink/renderer/core/svg/svg_path_parser.cc#L169-L278
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"""
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from fontTools.misc.transform import Identity, Scale
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from math import atan2, ceil, cos, fabs, isfinite, pi, radians, sin, sqrt, tan
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TWO_PI = 2 * pi
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PI_OVER_TWO = 0.5 * pi
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def _map_point(matrix, pt):
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# apply Transform matrix to a point represented as a complex number
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r = matrix.transformPoint((pt.real, pt.imag))
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return r[0] + r[1] * 1j
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class EllipticalArc(object):
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def __init__(self, current_point, rx, ry, rotation, large, sweep, target_point):
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self.current_point = current_point
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self.rx = rx
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self.ry = ry
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self.rotation = rotation
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self.large = large
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self.sweep = sweep
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self.target_point = target_point
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# SVG arc's rotation angle is expressed in degrees, whereas Transform.rotate
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# uses radians
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self.angle = radians(rotation)
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# these derived attributes are computed by the _parametrize method
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self.center_point = self.theta1 = self.theta2 = self.theta_arc = None
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def _parametrize(self):
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# convert from endopoint to center parametrization:
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# https://www.w3.org/TR/SVG/implnote.html#ArcConversionEndpointToCenter
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# If rx = 0 or ry = 0 then this arc is treated as a straight line segment (a
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# "lineto") joining the endpoints.
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# http://www.w3.org/TR/SVG/implnote.html#ArcOutOfRangeParameters
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rx = fabs(self.rx)
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ry = fabs(self.ry)
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if not (rx and ry):
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return False
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# If the current point and target point for the arc are identical, it should
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# be treated as a zero length path. This ensures continuity in animations.
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if self.target_point == self.current_point:
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return False
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mid_point_distance = (self.current_point - self.target_point) * 0.5
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point_transform = Identity.rotate(-self.angle)
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transformed_mid_point = _map_point(point_transform, mid_point_distance)
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square_rx = rx * rx
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square_ry = ry * ry
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square_x = transformed_mid_point.real * transformed_mid_point.real
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square_y = transformed_mid_point.imag * transformed_mid_point.imag
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# Check if the radii are big enough to draw the arc, scale radii if not.
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# http://www.w3.org/TR/SVG/implnote.html#ArcCorrectionOutOfRangeRadii
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radii_scale = square_x / square_rx + square_y / square_ry
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if radii_scale > 1:
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rx *= sqrt(radii_scale)
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ry *= sqrt(radii_scale)
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self.rx, self.ry = rx, ry
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point_transform = Scale(1 / rx, 1 / ry).rotate(-self.angle)
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point1 = _map_point(point_transform, self.current_point)
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point2 = _map_point(point_transform, self.target_point)
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delta = point2 - point1
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d = delta.real * delta.real + delta.imag * delta.imag
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scale_factor_squared = max(1 / d - 0.25, 0.0)
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scale_factor = sqrt(scale_factor_squared)
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if self.sweep == self.large:
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scale_factor = -scale_factor
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delta *= scale_factor
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center_point = (point1 + point2) * 0.5
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center_point += complex(-delta.imag, delta.real)
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point1 -= center_point
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point2 -= center_point
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theta1 = atan2(point1.imag, point1.real)
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theta2 = atan2(point2.imag, point2.real)
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theta_arc = theta2 - theta1
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if theta_arc < 0 and self.sweep:
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theta_arc += TWO_PI
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elif theta_arc > 0 and not self.sweep:
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theta_arc -= TWO_PI
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self.theta1 = theta1
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self.theta2 = theta1 + theta_arc
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self.theta_arc = theta_arc
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self.center_point = center_point
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return True
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def _decompose_to_cubic_curves(self):
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if self.center_point is None and not self._parametrize():
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return
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point_transform = Identity.rotate(self.angle).scale(self.rx, self.ry)
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# Some results of atan2 on some platform implementations are not exact
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# enough. So that we get more cubic curves than expected here. Adding 0.001f
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# reduces the count of sgements to the correct count.
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num_segments = int(ceil(fabs(self.theta_arc / (PI_OVER_TWO + 0.001))))
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for i in range(num_segments):
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start_theta = self.theta1 + i * self.theta_arc / num_segments
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end_theta = self.theta1 + (i + 1) * self.theta_arc / num_segments
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t = (4 / 3) * tan(0.25 * (end_theta - start_theta))
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if not isfinite(t):
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return
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sin_start_theta = sin(start_theta)
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cos_start_theta = cos(start_theta)
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sin_end_theta = sin(end_theta)
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cos_end_theta = cos(end_theta)
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point1 = complex(
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cos_start_theta - t * sin_start_theta,
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sin_start_theta + t * cos_start_theta,
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)
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point1 += self.center_point
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target_point = complex(cos_end_theta, sin_end_theta)
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target_point += self.center_point
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point2 = target_point
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point2 += complex(t * sin_end_theta, -t * cos_end_theta)
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point1 = _map_point(point_transform, point1)
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point2 = _map_point(point_transform, point2)
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target_point = _map_point(point_transform, target_point)
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yield point1, point2, target_point
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def draw(self, pen):
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for point1, point2, target_point in self._decompose_to_cubic_curves():
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pen.curveTo(
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(point1.real, point1.imag),
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(point2.real, point2.imag),
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(target_point.real, target_point.imag),
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)
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