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Improve arclength calculation for elliptical arcs

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This commit is contained in:
Jan Petykiewicz 2023-07-17 21:23:44 -07:00
parent fcbf651694
commit b95e9de1ee
1 changed files with 11 additions and 6 deletions
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17
masque/shapes/arc.py
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@ -202,13 +202,18 @@ class Arc(Shape):
# Convert from polar angle to ellipse parameter (for [rx*cos(t), ry*sin(t)] representation)
a_ranges = self._angles_to_parameters()
# Approximate perimeter
# Ramanujan, S., "Modular Equations and Approximations to ,"
# Quart. J. Pure. Appl. Math., vol. 45 (1913-1914), pp. 350-372
# Approximate outer perimeter via numerical integration
a0, a1 = a_ranges[1] # use outer arc
h = ((r1 - r0) / (r1 + r0)) ** 2
ellipse_perimeter = pi * (r1 + r0) * (1 + 3 * h / (10 + math.sqrt(4 - 3 * h)))
perimeter = abs(a0 - a1) / (2 * pi) * ellipse_perimeter # TODO: make this more accurate
t = numpy.linspace(a0, a1, 10_000) # 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=t[1] - t[0])
#from scipy.special import ellipeinc
#m = 1 - (r1 / r0) ** 2
#t1 = ellipeinc(a1 - pi / 2, m)
#t0 = ellipeinc(a0 - pi / 2, m)
#perimeter2 = r0 * (t1 - t0)
n = []
if num_vertices is not None: