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@ -206,6 +206,18 @@ class Arc(Shape):
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return [poly]
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def get_bounds(self) -> numpy.ndarray:
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'''
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Equation for rotated ellipse is
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x = x0 + a * cos(t) * cos(rot) - b * sin(t) * sin(phi)
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y = y0 + a * cos(t) * sin(rot) + b * sin(t) * cos(rot)
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where t is our parameter.
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Differentiating and solving for 0 slope wrt. t, we find
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tan(t) = -+ b/a cot(phi)
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where -+ is for x, y cases, so that's where the extrema are.
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If the extrema are innaccessible due to arc constraints, check the arc endpoints instead.
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'''
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mins = []
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maxs = []
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for sgn in (+1, -1):
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@ -235,13 +247,18 @@ class Arc(Shape):
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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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xs = rx * sin_r
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yc = ry * cos_r
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sin_ax = yc / (yc * yc + xs * xs)
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cos_ax = xs / (yc * yc + xs * xs)
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xr = rx * cos_r * cos_ax - ry * sin_r * sin_ax
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yr = ry * sin_r * cos_ax + ry * cos_r * sin_ax
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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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yn, yp = sorted(rx * sin_r * cos_a + ry * cos_r * sin_a)
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# If
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if a0 < xpt < a1:
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xp = xr
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