Don't divide by zero in Line2D.segment_hits. #17282
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QuLogic
approved these changes
May 1, 2020
Instead of changing the numpy errstate, replace `a / b <= 1` by `a <= b` and use np.hypot() for `sqrt(x**2+y**2)` (which avoids overflows from `x**2`). Otherwise a call to segment_hits should "always" be protected by manipulating the numpy errstate.
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timhoffm
reviewed
May 1, 2020
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| # Note that there is a little area near one side of each point | ||
| # which will be near neither segment, and another which will | ||
| # be near both, depending on the angle of the lines. The | ||
| # following radius test eliminates these ambiguities. | ||
| point_hits = (cx - x) ** 2 + (cy - y) ** 2 <= radius ** 2 |
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Do we have an estimate how many elements this typically works on?
np.hypot scales worse than the squares, likely because taking the root is expensive.
import numpy as np
import matplotlib.pyplot as plt
ns = [10, 100, 200, 400,600, 1000]
v1 = []
v2 = []
for n in ns:
a = np.linspace(0, 1, n)
b = 2*a
a0 = 0.1
b0 = 0.2
r = 1.2
o1 = %timeit -o (a0 - a)**2 + (b0 - b)**2 < r**2
o2 = %timeit -o np.hypot(a0 - a, b0 - b) < r
v1.append(o1)
v2.append(o2)
plt.plot(ns, [v.average *1e6 for v in v1], 'o--', label='squares')
plt.plot(ns, [v.average *1e6 for v in v2], 'o--', label='np.hypot')
plt.legend()
plt.ylabel('duration [µs]')
plt.xlabel('array size')
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It is indeed slower, but on my machine the scaling is not so bad. Moreover skipping the call to errstate() is also quite helpful, as contextmanagers are slow (relatively speaking):
import numpy as np
import matplotlib.pyplot as plt
ns = [10, 100, 200, 400, 600, 1000]
v1 = []
v2 = []
v3 = []
for n in ns:
a = np.linspace(0, 1, n)
b = 2*a
a0 = 0.1
b0 = 0.2
r = 1.2
o1 = %timeit -o (a0 - a)**2 + (b0 - b)**2 < r**2
o2 = %timeit -o with np.errstate(all="ignore"): (a0 - a)**2 + (b0 - b)**2 < r**2
o3 = %timeit -o np.hypot(a0 - a, b0 - b) < r
v1.append(o1)
v2.append(o2)
v3.append(o3)
plt.plot(ns, [v.average *1e6 for v in v1], 'o--', label='squares')
plt.plot(ns, [v.average *1e6 for v in v2], 'o--', label='squares+errstate')
plt.plot(ns, [v.average *1e6 for v in v3], 'o--', label='np.hypot')
plt.legend()
plt.ylabel('duration [µs]')
plt.xlabel('array size')
(I know there's two calls to hypot vs a single errstate(), so I guess the real threshold where hypot becomes slower would be around 500 points.)
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Ok, let's assume we rarely deal with polygons with thousands of segments, so timing is not too different.
timhoffm
approved these changes
May 1, 2020
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| # Note that there is a little area near one side of each point | ||
| # which will be near neither segment, and another which will | ||
| # be near both, depending on the angle of the lines. The | ||
| # following radius test eliminates these ambiguities. | ||
| point_hits = (cx - x) ** 2 + (cy - y) ** 2 <= radius ** 2 |
There was a problem hiding this comment.
Ok, let's assume we rarely deal with polygons with thousands of segments, so timing is not too different.
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Instead of changing the numpy errstate, replace
a / b <= 1bya <= band use np.hypot() forsqrt(x**2+y**2)(which avoids overflows fromx**2).Otherwise a call to segment_hits should "always" be protected by
manipulating the numpy errstate.
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