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Improve arc arclength estimation (untested)

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jan 2023-09-17 21:33:34 -07:00
parent e2c7f8c8cc
commit c2008f2719
1 changed files with 36 additions and 13 deletions
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masque/shapes/arc.py
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@ -202,32 +202,55 @@ class Arc(Shape):
# Convert from polar angle to ellipse parameter (for [rx*cos(t), ry*sin(t)] representation) # Convert from polar angle to ellipse parameter (for [rx*cos(t), ry*sin(t)] representation)
a_ranges = self._angles_to_parameters() a_ranges = self._angles_to_parameters()
# Approximate outer perimeter via numerical integration # Approximate perimeter via numerical integration
a0, a1 = a_ranges[1] # use outer arc
t, dt = numpy.linspace(a0, a1, 10_000, retstep=True) # NOTE: could probably use an adaptive number of points
r0sin = r0 * numpy.sin(t)
r1cos = r1 * numpy.cos(t)
perimeter = numpy.trapz(numpy.sqrt(r0sin * r0sin + r1cos * r1cos), dx=dt)
#perimeter1 = numpy.trapz(numpy.sqrt(r0sin * r0sin + r1cos * r1cos), dx=dt)
#from scipy.special import ellipeinc #from scipy.special import ellipeinc
#m = 1 - (r1 / r0) ** 2 #m = 1 - (r1 / r0) ** 2
#t1 = ellipeinc(a1 - pi / 2, m) #t1 = ellipeinc(a1 - pi / 2, m)
#t0 = ellipeinc(a0 - pi / 2, m) #t0 = ellipeinc(a0 - pi / 2, m)
#perimeter2 = r0 * (t1 - t0) #perimeter2 = r0 * (t1 - t0)
n = [] def get_arclens(n_pts: int, a0: float, a1: float) -> NDArray[numpy.float64]:
""" Get `n_pts` arclengths """
t, dt = numpy.linspace(a0, a1, n_pts, retstep=True) # NOTE: could probably use an adaptive number of points
r0sin = r0 * numpy.sin(t)
r1cos = r1 * numpy.cos(t)
arc_dl = numpy.sqrt(r0sin * r0sin + r1cos * r1cos)
#arc_lengths = numpy.diff(t) * (v[1:] + v[:-1]) / 2
arc_lengths = (v[1:] + v[:-1]) * dt / 2
return arc_lengths, t
if num_vertices is not None: if num_vertices is not None:
n += [num_vertices] n_pts = max(self.radii) / min(self.radii) * num_vertices * 100
if max_arclen is not None: perimeter_inner = get_arclens(n_pts, *a_ranges[0])[0].sum()
n += [perimeter / max_arclen] perimeter_outer = get_arclens(n_pts, *a_ranges[1])[0].sum()
num_vertices = int(round(max(n))) implied_arclen = (perimeter_outer + perimeter_inner + self.width * 2) / num_vertices
max_arclen = min(implied_arclen, max_arclen if max_arclen is not None else numpy.inf)
def get_thetas(inner: bool) -> NDArray[numpy.float64]:
""" Figure out the parameter values at which we should place vertices to meet the arclength constraint"""
dr = -self.width / 2.0 * (-1 if inner else 1)
n_pts = 2 * pi * max(self.radii) / max_arclen
arc_lengths, thetas = get_arclens(n_pts, *a_ranges[0 if inner else 1])
keep = []
removable = (numpy.cumsum(arc_lengths) <= max_arclen)
start = 0
while True:
next_to_keep = start + numpy.where(removable)[0][-1] # TODO: any chance we haven't sampled finely enough?
keep.append(next_to_keep)
removable = (numpy.cumsum(arc_lengths[next_to_keep + 1:]) <= max_arclen)
start = next_to_keep + 1
return thetas[keep]
wh = self.width / 2.0 wh = self.width / 2.0
if wh == r0 or wh == r1: if wh == r0 or wh == r1:
thetas_inner = numpy.zeros(1) # Don't generate multiple vertices if we're at the origin thetas_inner = numpy.zeros(1) # Don't generate multiple vertices if we're at the origin
else: else:
thetas_inner = numpy.linspace(a_ranges[0][1], a_ranges[0][0], num_vertices, endpoint=True) thetas_inner = get_thetas(inner=True)
thetas_outer = numpy.linspace(a_ranges[1][0], a_ranges[1][1], num_vertices, endpoint=True) thetas_outer = get_thetas(inner=False)
sin_th_i, cos_th_i = (numpy.sin(thetas_inner), numpy.cos(thetas_inner)) sin_th_i, cos_th_i = (numpy.sin(thetas_inner), numpy.cos(thetas_inner))
sin_th_o, cos_th_o = (numpy.sin(thetas_outer), numpy.cos(thetas_outer)) sin_th_o, cos_th_o = (numpy.sin(thetas_outer), numpy.cos(thetas_outer))