#12827: Expand Animation class to accept more graphics types
-------------------------------------+-------------------------------------
Reporter: niles | Owner: jason, was
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.1
Component: graphics | Resolution:
Keywords: animate, | Merged in:
graphics, 3D | Reviewers:
Authors: Niles Johnson | Work issues: docstrings, testing,
Report Upstream: N/A | think about img protocol
Branch: | Commit:
u/niles/ticket/12827 | de5349040ebab566d5a0e35d99284e628ab21080
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Comment (by niles):
Attached some animated gifs to show what the new patch can do. Code is
below. It's also worth mentioning that this patch fixes some doctest
errors in the `Animation.ffmpeg()` method. These are caused by a change
in the way `tmp_filename` works, and the way file extensions are handled
('.gif' v.s. 'gif') elsewhere in sage. These bugs cause `animate` to
break when `convert` is not available but `ffmpeg` is (e.g. on the sage
cell servers).
Examples that this patch makes possible:
Animate graphics arrays show accumulation of area under a curve.
{{{
f(x) = 8*(x-4)^2 - 25
F(x) = f.integrate(x)
a,b = 0,7
M = max((_.find_local_maximum(a,b)[0] for _ in (f,F)))
m = min((_.find_local_minimum(a,b)[0] for _ in (f,F)))
bounding_pts = point([(a,0),(b,0),(0,m),(0,M)],color='black')
def fplot(t):
return plot(f,a,a + t*(b-a),fill=True) + plot(f,a,b) + \
line([(a + t*(b-a),0),(a + t*(b-a),f(a + t*(b-a)))],thickness=2) +
bounding_pts
def Fplot(t):
return plot(F,a,a + t*(b-a),color='green') + \
point((a + t*(b-a),F(a + t*(b-a))),color='green',size=15) +
bounding_pts
accumulation = animate((graphics_array([fplot(t),Fplot(t)]) for t in
sxrange(.01,1,.05)))
accumulation.show()
}}}
Animate parametric surfaces and curves to draw a torus knot.
{{{
var('u,v');
a,b = 2,1 # outer and inner radii
x = (a + b*cos(u))*cos(v)
y = (a + b*cos(u))*sin(v)
z = b*sin(u)
T = parametric_plot3d([x,y,z], (u,0,2*pi),(v,0,2*pi),
opacity=.6,aspect_ratio=1)
var('t');
c = (2*t,3*t)
s = [_.subs(dict(zip((u,v),c))) for _ in (x,y,z)]
curve = lambda d:
parametric_plot(s,(t,0,2*pi*d),color='red',thickness=2,plot_points=400)
K = animate((T+curve(d) for d in sxrange(.01,1.1,.05)))
K.show()
}}}
Animate Tachyon scenes to show the twisted cubic.
{{{
def tw_cubic(t):
q = Tachyon(camera_center=(-2,3,1),xres=500,yres=500)
q.light((1,1,11), 1,(1,0,1))
q.light((1,5,1), .5,(0,1,1))
q.texture('mirror', ambient=0.05, diffuse=0.05, specular=.9,
opacity=0.9, color=(.8,.8,.8))
q.texture('w',color=(1,1,1))
q.plane((0,0,-2),(0,0,1),'w')
q.plane((0,-2,0),(0,1,0),'w')
for i in srange(-1,t,0.05):
q.sphere((i,i^2-0.5,i^3), 0.1, 'mirror')
return q
W = animate([tw_cubic(t) for t in srange(-1,1.5,.1)])
W.show()
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/12827#comment:18>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/groups/opt_out.
