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@ -202,32 +202,55 @@ class Arc(Shape):
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# Convert from polar angle to ellipse parameter (for [rx*cos(t), ry*sin(t)] representation)
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a_ranges = self._angles_to_parameters()
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# Approximate outer perimeter via numerical integration
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a0, a1 = a_ranges[1] # use outer arc
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t, dt = numpy.linspace(a0, a1, 10_000, retstep=True) # NOTE: could probably use an adaptive number of points
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r0sin = r0 * numpy.sin(t)
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r1cos = r1 * numpy.cos(t)
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perimeter = numpy.trapz(numpy.sqrt(r0sin * r0sin + r1cos * r1cos), dx=dt)
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# Approximate perimeter via numerical integration
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#perimeter1 = numpy.trapz(numpy.sqrt(r0sin * r0sin + r1cos * r1cos), dx=dt)
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#from scipy.special import ellipeinc
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#m = 1 - (r1 / r0) ** 2
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#t1 = ellipeinc(a1 - pi / 2, m)
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#t0 = ellipeinc(a0 - pi / 2, m)
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#perimeter2 = r0 * (t1 - t0)
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n = []
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def get_arclens(n_pts: int, a0: float, a1: float) -> NDArray[numpy.float64]:
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""" Get `n_pts` arclengths """
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t, dt = numpy.linspace(a0, a1, n_pts, retstep=True) # NOTE: could probably use an adaptive number of points
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r0sin = r0 * numpy.sin(t)
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r1cos = r1 * numpy.cos(t)
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arc_dl = numpy.sqrt(r0sin * r0sin + r1cos * r1cos)
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#arc_lengths = numpy.diff(t) * (v[1:] + v[:-1]) / 2
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arc_lengths = (v[1:] + v[:-1]) * dt / 2
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return arc_lengths, t
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if num_vertices is not None:
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n += [num_vertices]
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if max_arclen is not None:
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n += [perimeter / max_arclen]
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num_vertices = int(round(max(n)))
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n_pts = max(self.radii) / min(self.radii) * num_vertices * 100
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perimeter_inner = get_arclens(n_pts, *a_ranges[0])[0].sum()
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perimeter_outer = get_arclens(n_pts, *a_ranges[1])[0].sum()
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implied_arclen = (perimeter_outer + perimeter_inner + self.width * 2) / num_vertices
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max_arclen = min(implied_arclen, max_arclen if max_arclen is not None else numpy.inf)
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def get_thetas(inner: bool) -> NDArray[numpy.float64]:
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""" Figure out the parameter values at which we should place vertices to meet the arclength constraint"""
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dr = -self.width / 2.0 * (-1 if inner else 1)
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n_pts = 2 * pi * max(self.radii) / max_arclen
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arc_lengths, thetas = get_arclens(n_pts, *a_ranges[0 if inner else 1])
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keep = []
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removable = (numpy.cumsum(arc_lengths) <= max_arclen)
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start = 0
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while True:
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next_to_keep = start + numpy.where(removable)[0][-1] # TODO: any chance we haven't sampled finely enough?
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keep.append(next_to_keep)
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removable = (numpy.cumsum(arc_lengths[next_to_keep + 1:]) <= max_arclen)
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start = next_to_keep + 1
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return thetas[keep]
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wh = self.width / 2.0
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if wh == r0 or wh == r1:
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thetas_inner = numpy.zeros(1) # Don't generate multiple vertices if we're at the origin
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else:
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thetas_inner = numpy.linspace(a_ranges[0][1], a_ranges[0][0], num_vertices, endpoint=True)
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thetas_outer = numpy.linspace(a_ranges[1][0], a_ranges[1][1], num_vertices, endpoint=True)
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thetas_inner = get_thetas(inner=True)
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thetas_outer = get_thetas(inner=False)
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sin_th_i, cos_th_i = (numpy.sin(thetas_inner), numpy.cos(thetas_inner))
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sin_th_o, cos_th_o = (numpy.sin(thetas_outer), numpy.cos(thetas_outer))
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jan
8 months ago