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@ -74,7 +74,7 @@ class Arc(Shape):
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def angles(self) -> vector2:
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"""
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Return the start and stop angles [a_start, a_stop].
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Angles are measured from x-axis after rotation, and are stored mod 2*pi
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Angles are measured from x-axis after rotation
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:return: [a_start, a_stop]
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"""
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@ -168,7 +168,12 @@ class Arc(Shape):
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' (default was also overridden)')
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r0, r1 = self.radii
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a0, a1 = self.angles
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# Convert from polar angle to ellipse parameter (for [rx*cos(t), ry*sin(t)] representation)
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a0, a1 = (numpy.arctan2(r0*numpy.sin(a), r1*numpy.cos(a)) for a in self.angles)
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sign = numpy.sign(self.angles[1] - self.angles[0])
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if sign != numpy.sign(a1 - a0):
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a1 += sign * 2 * pi
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# Approximate perimeter
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# Ramanujan, S., "Modular Equations and Approximations to ,"
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@ -201,8 +206,6 @@ class Arc(Shape):
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return [poly]
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def get_bounds(self) -> numpy.ndarray:
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a = self.angles - 0.5 * pi
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mins = []
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maxs = []
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for sgn in (+1, -1):
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@ -210,33 +213,45 @@ class Arc(Shape):
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rx = self.radius_x + wh
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ry = self.radius_y + wh
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# Create paremeter 'a' for parametrized ellipse
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a0, a1 = (numpy.arctan2(rx*numpy.sin(a), ry*numpy.cos(a)) for a in self.angles)
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sign = numpy.sign(self.angles[1] - self.angles[0])
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if sign != numpy.sign(a1 - a0):
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a1 += sign * 2 * pi
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a = numpy.array((a0, a1))
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a0_offset = a0 - (a0 % (2 * pi))
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sin_r = numpy.sin(self.rotation)
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cos_r = numpy.cos(self.rotation)
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tan_r = numpy.tan(self.rotation)
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sin_a = numpy.sin(a)
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cos_a = numpy.cos(a)
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xpt = numpy.arctan(-ry / rx * tan_r)
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ypt = numpy.arctan(+ry / rx / tan_r)
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xnt = numpy.arcsin(numpy.sin(xpt - pi))
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ynt = numpy.arcsin(numpy.sin(ypt - pi))
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# Cutoff angles
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xpt = (-self.rotation) % (2 * pi) + a0_offset
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ypt = self.rotation % (2 * pi) + a0_offset
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xnt = (xpt - pi) % (2 * pi) + a0_offset
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ynt = (ypt - pi) % (2 * pi) + a0_offset
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# Points along coordinate axes
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xr = numpy.sqrt((rx * cos_r) ** 2 + (ry * sin_r) ** 2)
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yr = numpy.sqrt((rx * sin_r) ** 2 + (ry * cos_r) ** 2)
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# Arc endpoints
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xn, xp = sorted(rx * cos_r * cos_a - ry * sin_r * sin_a)
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yn, yp = sorted(rx * sin_r * cos_a - ry * cos_r * sin_a)
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if min(a) < xpt < max(a):
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if a0 < xpt < a1:
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xp = xr
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if min(a) < xnt < max(a):
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if a0 < xnt < a1:
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xn = -xr
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if min(a) < ypt < max(a):
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if a0 < ypt < a1:
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yp = yr
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if min(a) < ynt < max(a):
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if a0 < ynt < a1:
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yn = -yr
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mins.append([xn, yn])
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