Marshall Hampton wrote:
> I think the culprit is the "pi" in the srange, which gets Maxima too
> involved (and maxima as called through sage is slow). This may
> improve very soon as there is some work being done to shift basic
> symbolic things like "pi" to a more python-based backend.
>
> Anyway for the moment you can avoid this by declaring your own numeric
> pi. The fastest I could do this without using "fast_float" was:
>
> pts=[];
> number_of_points=500
> mypi = n(pi)
> for t1 in srange(0, mypi, n(pi/sqrt(number_of_points))):
> st1 = sin(t1)
> ct1 = cos(t1)
> for t2 in srange(0, 2*mypi, n(2*pi/sqrt(number_of_points))):
> pts.append((st1*cos(t2), st1*sin(t2), ct1))
> show(point3d(pts))
>
> ...taking the sin(t1) and cos(t1) calc out of the inner loop helps a
> bit as well. That was much faster for me than your original code.
>
Here's a version that's about 6x faster yet again by avoiding yet more
calculations in the inner loop and using the python sin/cos instead of
the sage sin/cos:
pts=[];
number_of_points=500
twopi = 2*RR(pi)
mystep = twopi/math.sqrt(number_of_points)
mysin,mycos = math.sin,math.cos
for t1 in srange(0, twopi/2, mystep/2):
st1 = mysin(t1)
ct1 = mycos(t1)
for t2 in srange(0, twopi, mystep):
pts.append((st1*mycos(t2), st1*mysin(t2), ct1))
Thanks,
Jason
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