Animations are generated from a list (or other iterable) of graphics objects. Images are produced by calling the save_image method on each input object, creating a sequence of PNG files. These are then assembled to various target formats using different tools. In particular, the convert program from ImageMagick can be used to generate an animated GIF file. FFmpeg (with the command line program ffmpeg) provides support for various video formats, but also an alternative method of generating animated GIFs. For browsers which support it, APNG can be used as another alternative which works without any extra dependencies.
Warning
Note that ImageMagick and FFmpeg are not included with Sage, and must be installed by the user. On unix systems, type which convert at a command prompt to see if convert (part of the ImageMagick suite) is installed. If it is, you will be given its location. Similarly, you can check for ffmpeg with which ffmpeg. See the websites of ImageMagick or FFmpeg for installation instructions.
EXAMPLES:
The sine function:
sage: sines = [plot(c*sin(x), (-2*pi,2*pi), color=Color(c,0,0), ymin=-1, ymax=1) for c in sxrange(0,1,.2)]
sage: a = animate(sines)
sage: a # optional -- ImageMagick
Animation with 5 frames
sage: a.show() # optional -- ImageMagick
Animate using FFmpeg instead of ImageMagick:
sage: f = tmp_filename(ext='.gif')
sage: a.save(filename=f, use_ffmpeg=True) # optional -- ffmpeg
Animate as an APNG:
sage: a.apng() # long time
doctest:...: DeprecationWarning: use tmp_filename instead
See http://trac.sagemath.org/17234 for details.
An animated sage.plot.graphics.GraphicsArray of rotating ellipses:
sage: E = animate((graphics_array([[ellipse((0,0),a,b,angle=t,xmin=-3,xmax=3)+circle((0,0),3,color='blue') for a in range(1,3)] for b in range(2,4)]) for t in sxrange(0,pi/4,.15)))
sage: str(E) # animations produced from a generator do not have a known length
'Animation with unknown number of frames'
sage: E.show() # optional -- ImageMagick
A simple animation of a circle shooting up to the right:
sage: c = animate([circle((i,i), 1-1/(i+1), hue=i/10) for i in srange(0,2,0.2)],
....: xmin=0,ymin=0,xmax=2,ymax=2,figsize=[2,2])
sage: c.show() # optional -- ImageMagick
Animations of 3d objects:
sage: var('s,t')
(s, t)
sage: def sphere_and_plane(x):
....: return sphere((0,0,0),1,color='red',opacity=.5)+parametric_plot3d([t,x,s],(s,-1,1),(t,-1,1),color='green',opacity=.7)
sage: sp = animate([sphere_and_plane(x) for x in sxrange(-1,1,.3)])
sage: sp[0] # first frame
Graphics3d Object
sage: sp[-1] # last frame
Graphics3d Object
sage: sp.show() # optional -- ImageMagick
sage: (x,y,z) = var('x,y,z')
sage: def frame(t):
....: return implicit_plot3d((x^2 + y^2 + z^2), (x, -2, 2), (y, -2, 2), (z, -2, 2), plot_points=60, contour=[1,3,5], region=lambda x,y,z: x<=t or y>=t or z<=t)
sage: a = animate([frame(t) for t in srange(.01,1.5,.2)])
sage: a[0] # long time
Graphics3d Object
sage: a.show() # optional -- ImageMagick
If the input objects do not have a save_image method, then the animation object attempts to make an image by calling its internal method sage.plot.animate.Animation.make_image(). This is illustrated by the following example:
sage: t = var('t')
sage: a = animate((sin(c*pi*t) for c in sxrange(1,2,.2)))
sage: a.show() # optional -- ImageMagick
AUTHORS:
Bases: object
Builds an APNG (Animated PNG) from a sequence of PNG files. This is used by the sage.plot.animate.Animation.apng() method.
This code is quite simple; it does little more than copying chunks from input PNG files to the output file. There is no optimization involved. This does not depend on external programs or libraries.
INPUT:
- out – a file opened for binary writing to which the data will be written
- num_frames – the number of frames in the animation
- num_plays – how often to iterate, 0 means infinitely
- delay – numerator of the delay fraction in seconds
- delay_denominator – denominator of the delay in seconds
EXAMPLES:
sage: from sage.plot.animate import APngAssembler
sage: def assembleAPNG():
....: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)],
....: xmin=0, xmax=2*pi, figsize=[2,1])
....: pngdir = a.png()
....: outfile = sage.misc.temporary_file.tmp_filename(ext='.png')
....: with open(outfile, "wb") as f:
....: apng = APngAssembler(f, len(a))
....: for i in range(len(a)):
....: png = os.path.join(pngdir, "{:08d}.png".format(i))
....: apng.add_frame(png, delay=10*i + 10)
....: return outfile
....:
sage: assembleAPNG() # long time
'...png'
Adds a single frame to the APNG file.
INPUT:
If the delay is not specified, the default from the constructor applies.
TESTS:
sage: from sage.plot.animate import APngAssembler
sage: from StringIO import StringIO
sage: buf = StringIO()
sage: apng = APngAssembler(buf, 2)
sage: fn = APngAssembler._testData("input1", True)
sage: apng.add_frame(fn, delay=0x567, delay_denominator=0x1234)
sage: fn = APngAssembler._testData("input2", True)
sage: apng.add_frame(fn)
sage: len(buf.getvalue())
217
sage: buf.getvalue() == APngAssembler._testData("anim12", False)
True
sage: apng.add_frame(fn)
Traceback (most recent call last):
...
RuntimeError: Already reached the declared number of frames
Adds a default image for the APNG file.
This image is used as a fallback in case some application does not understand the APNG format. This method must be called prior to any calls to the add_frame method, if it is called at all. If it is not called, then the first frame of the animation will be the default.
INPUT:
TESTS:
sage: from sage.plot.animate import APngAssembler
sage: from StringIO import StringIO
sage: buf = StringIO()
sage: apng = APngAssembler(buf, 1)
sage: fn = APngAssembler._testData("input1", True)
sage: apng.set_default(fn)
sage: fn = APngAssembler._testData("input2", True)
sage: apng.add_frame(fn, delay=0x567, delay_denominator=0x1234)
sage: len(buf.getvalue())
179
sage: buf.getvalue() == APngAssembler._testData("still1anim2", False)
True
sage: apng.add_frame(fn)
Traceback (most recent call last):
...
RuntimeError: Already reached the declared number of frames
Bases: sage.structure.sage_object.SageObject
Return an animation of a sequence of plots of objects.
INPUT:
EXAMPLES:
sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.3)],
....: xmin=0, xmax=2*pi, figsize=[2,1])
sage: a # optional -- ImageMagick
Animation with 21 frames
sage: a[:5] # optional -- ImageMagick
Animation with 5 frames
sage: a.show() # optional -- ImageMagick
sage: a[:5].show() # optional -- ImageMagick
The show() method takes arguments to specify the delay between frames (measured in hundredths of a second, default value 20) and the number of iterations (default value 0, which means to iterate forever). To iterate 4 times with half a second between each frame:
sage: a.show(delay=50, iterations=4) # optional -- ImageMagick
An animation of drawing a parabola:
sage: step = 0.1
sage: L = Graphics()
sage: v = []
sage: for i in srange(0,1,step):
....: L += line([(i,i^2),(i+step,(i+step)^2)], rgbcolor=(1,0,0), thickness=2)
....: v.append(L)
sage: a = animate(v, xmin=0, ymin=0)
sage: a.show() # optional -- ImageMagick
sage: show(L)
TESTS:
This illustrates that trac ticket #2066 is fixed (setting axes ranges when an endpoint is 0):
sage: animate([plot(sin, -1,1)], xmin=0, ymin=0)._kwds['xmin']
0
We check that trac ticket #7981 is fixed:
sage: a = animate([plot(sin(x + float(k)), (0, 2*pi), ymin=-5, ymax=5)
....: for k in srange(0,2*pi,0.3)])
sage: a.show() # optional -- ImageMagick
Do not convert input iterator to a list, but ensure that the frame count is known after rendering the frames:
sage: a = animate((plot(x^p, (x,0,2)) for p in sxrange(1,2,.1)))
sage: str(a)
'Animation with unknown number of frames'
sage: a.png() # long time
'.../'
sage: len(a) # long time
10
sage: a._frames
<generator object ...
Creates an animated PNG composed from rendering the graphics objects in self. Return the absolute path to that file.
Notice that not all web browsers are capable of displaying APNG files, though they should still present the first frame of the animation as a fallback.
The generated file is not optimized, so it may be quite large.
Input:
EXAMPLES:
sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)],
....: xmin=0, xmax=2*pi, figsize=[2,1])
sage: dir = tmp_dir()
sage: a.apng() # long time
sage: a.apng(savefile=dir + 'my_animation.png', delay=35, iterations=3) # long time
sage: a.apng(savefile=dir + 'my_animation.png', show_path=True) # long time
Animation saved to .../my_animation.png.
If the individual frames have different sizes, an error will be raised:
sage: a = animate([plot(sin(x), (x, 0, k)) for k in range(1,4)],
....: ymin=-1, ymax=1, aspect_ratio=1, figsize=[2,1])
sage: a.apng() # long time
Traceback (most recent call last):
...
ValueError: Chunk IHDR mismatch
Returns a movie showing an animation composed from rendering the frames in self.
This method will only work if ffmpeg is installed. See http://www.ffmpeg.org for information about ffmpeg.
INPUT:
If savefile is not specified: in notebook mode, display the animation; otherwise, save it to a default file name. Use sage.misc.misc.set_verbose() with level=1 to see additional output.
EXAMPLES:
sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)],
....: xmin=0, xmax=2*pi, ymin=-1, ymax=1, figsize=[2,1])
sage: td = tmp_dir()
sage: a.ffmpeg(savefile=td + 'new.mpg') # optional -- ffmpeg
sage: a.ffmpeg(savefile=td + 'new.avi') # optional -- ffmpeg
sage: a.ffmpeg(savefile=td + 'new.gif') # optional -- ffmpeg
sage: a.ffmpeg(savefile=td + 'new.mpg', show_path=True) # optional -- ffmpeg
Animation saved to .../new.mpg.
Note
If ffmpeg is not installed, you will get an error message like this:
Error: ffmpeg does not appear to be installed. Saving an animation to
a movie file in any format other than GIF requires this software, so
please install it and try again.
See www.ffmpeg.org for more information.
TESTS:
sage: a.ffmpeg(output_format='gif',delay=30,iterations=5) # optional -- ffmpeg
doctest:...: DeprecationWarning: use tmp_filename instead
See http://trac.sagemath.org/17234 for details.
Returns an animated gif composed from rendering the graphics objects in self.
This method will only work if either (a) the ImageMagick software suite is installed, i.e., you have the convert command or (b) ffmpeg is installed. See the web sites of ImageMagick and FFmpeg for more details. By default, this produces the gif using convert if it is present. If this can’t find convert or if use_ffmpeg is True, then it uses ffmpeg instead.
INPUT:
If savefile is not specified: in notebook mode, display the animation; otherwise, save it to a default file name.
EXAMPLES:
sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)],
....: xmin=0, xmax=2*pi, ymin=-1, ymax=1, figsize=[2,1])
sage: td = tmp_dir()
sage: a.gif() # not tested
sage: a.gif(savefile=td + 'my_animation.gif', delay=35, iterations=3) # optional -- ImageMagick
sage: with open(td + 'my_animation.gif', 'rb') as f: print '\x21\xf9\x04\x08\x23\x00' in f.read() # optional -- ImageMagick
True
sage: a.gif(savefile=td + 'my_animation.gif', show_path=True) # optional -- ImageMagick
Animation saved to .../my_animation.gif.
sage: a.gif(savefile=td + 'my_animation_2.gif', show_path=True, use_ffmpeg=True) # optional -- ffmpeg
Animation saved to .../my_animation_2.gif.
Note
If neither ffmpeg nor ImageMagick is installed, you will get an error message like this:
Error: Neither ImageMagick nor ffmpeg appears to be installed. Saving an
animation to a GIF file or displaying an animation requires one of these
packages, so please install one of them and try again.
See www.imagemagick.org and www.ffmpeg.org for more information.
Return a sage.plot.graphics.GraphicsArray with plots of the frames of this animation, using the given number of columns. The frames must be acceptable inputs for sage.plot.graphics.GraphicsArray.
EXAMPLES:
sage: E = EllipticCurve('37a')
sage: v = [E.change_ring(GF(p)).plot(pointsize=30) for p in [97, 101, 103, 107]]
sage: a = animate(v, xmin=0, ymin=0, axes=False)
sage: a # optional -- ImageMagick
Animation with 4 frames
sage: a.show() # optional -- ImageMagick
Modify the default arrangement of array:
sage: g = a.graphics_array(); print g
Graphics Array of size 2 x 3
sage: g.show(figsize=[6,3]) # not tested
Specify different arrangement of array and save it with a given file name:
sage: g = a.graphics_array(ncols=2); print g
Graphics Array of size 2 x 2
sage: f = tmp_filename(ext='.png')
sage: g.save(f)
Frames can be specified as a generator too; it is internally converted to a list:
sage: t = var('t')
sage: b = animate((plot(sin(c*pi*t)) for c in sxrange(1,2,.2)))
sage: g = b.graphics_array()
sage: g
Graphics Array of size 2 x 3
Given a frame which has no save_image() method, make a graphics object and save it as an image with the given filename. By default, this is sage.plot.plot.plot(). To make animations of other objects, override this method in a subclass.
EXAMPLES:
sage: from sage.plot.animate import Animation
sage: class MyAnimation(Animation):
....: def make_image(self, frame, filename, **kwds):
....: P = parametric_plot(frame[0], frame[1], **frame[2])
....: P.save_image(filename,**kwds)
sage: t = var('t')
sage: x = lambda t: cos(t)
sage: y = lambda n,t: sin(t)/n
sage: B = MyAnimation([([x(t), y(i+1,t)],(t,0,1), {'color':Color((1,0,i/4)), 'aspect_ratio':1, 'ymax':1}) for i in range(4)])
sage: d = B.png(); v = os.listdir(d); v.sort(); v # long time
['00000000.png', '00000001.png', '00000002.png', '00000003.png']
sage: B.show() # not tested
sage: class MyAnimation(Animation):
....: def make_image(self, frame, filename, **kwds):
....: G = frame.plot()
....: G.set_axes_range(floor(G.xmin()),ceil(G.xmax()),floor(G.ymin()),ceil(G.ymax()))
....: G.save_image(filename, **kwds)
sage: B = MyAnimation([graphs.CompleteGraph(n) for n in range(7,11)], figsize=5)
sage: d = B.png()
sage: v = os.listdir(d); v.sort(); v
['00000000.png', '00000001.png', '00000002.png', '00000003.png']
sage: B.show() # not tested
Render PNG images of the frames in this animation, saving them in dir. Return the absolute path to that directory. If the frames have been previously rendered and dir is None, just return the directory in which they are stored.
When dir is other than None, force re-rendering of frames.
INPUT:
EXAMPLES:
sage: a = animate([plot(x^2 + n) for n in range(4)], ymin=0, ymax=4)
sage: d = a.png(); v = os.listdir(d); v.sort(); v # long time
['00000000.png', '00000001.png', '00000002.png', '00000003.png']
Save this animation.
INPUT:
If filename is None, then in notebook mode, display the animation; otherwise, save the animation to a GIF file. If filename ends in ‘.sobj’, save to an sobj file. Otherwise, try to determine the format from the filename extension (‘.mpg’, ‘.gif’, ‘.avi’, etc.). If the format cannot be determined, default to GIF.
For GIF files, either ffmpeg or the ImageMagick suite must be installed. For other movie formats, ffmpeg must be installed. An sobj file can be saved with no extra software installed.
EXAMPLES:
sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)],
....: xmin=0, xmax=2*pi, ymin=-1, ymax=1, figsize=[2,1])
sage: td = tmp_dir()
sage: a.save() # not tested
sage: a.save(td + 'wave.gif') # optional -- ImageMagick
sage: a.save(td + 'wave.gif', show_path=True) # optional -- ImageMagick
Animation saved to file .../wave.gif.
sage: a.save(td + 'wave.avi', show_path=True) # optional -- ffmpeg
Animation saved to file .../wave.avi.
sage: a.save(td + 'wave0.sobj')
sage: a.save(td + 'wave1.sobj', show_path=True)
Animation saved to file .../wave1.sobj.
TESTS:
Ensure that we can pass delay and iteration count to the saved GIF image (see trac ticket #18176):
sage: a.save(td + 'wave.gif') # optional -- ImageMagick
sage: with open(td + 'wave.gif', 'rb') as f: print '!\xf9\x04\x08\x14\x00' in f.read() # optional -- ImageMagick
True
sage: with open(td + 'wave.gif', 'rb') as f: print '!\xff\x0bNETSCAPE2.0\x03\x01\x00\x00\x00' in f.read() # optional -- ImageMagick
True
sage: a.save(td + 'wave.gif', delay=35) # optional -- ImageMagick
sage: with open(td + 'wave.gif', 'rb') as f: print '!\xf9\x04\x08\x14\x00' in f.read() # optional -- ImageMagick
False
sage: with open(td + 'wave.gif', 'rb') as f: print '!\xf9\x04\x08\x23\x00' in f.read() # optional -- ImageMagick
True
sage: a.save(td + 'wave.gif', iterations=3) # optional -- ImageMagick
sage: with open(td + 'wave.gif', 'rb') as f: print '!\xff\x0bNETSCAPE2.0\x03\x01\x00\x00\x00' in f.read() # optional -- ImageMagick
False
sage: with open(td + 'wave.gif', 'rb') as f: print '!\xff\x0bNETSCAPE2.0\x03\x01\x03\x00\x00' in f.read() # optional -- ImageMagick
True
Show this animation immediately.
This method attempts to display the graphics immediately, without waiting for the currently running code (if any) to return to the command line. Be careful, calling it from within a loop will potentially launch a large number of external viewer programs.
INPUT:
OUTPUT:
This method does not return anything. Use save() if you want to save the figure as an image.
Note
Currently this is done using an animated gif, though this could change in the future. This requires that either ffmpeg or the ImageMagick suite (in particular, the convert command) is installed.
See also the ffmpeg() method.
EXAMPLES:
sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)],
....: xmin=0, xmax=2*pi, figsize=[2,1])
sage: a.show() # optional -- ImageMagick
The preceding will loop the animation forever. If you want to show only three iterations instead:
sage: a.show(iterations=3) # optional -- ImageMagick
To put a half-second delay between frames:
sage: a.show(delay=50) # optional -- ImageMagick
Note
If you don’t have ffmpeg or ImageMagick installed, you will get an error message like this:
Error: Neither ImageMagick nor ffmpeg appears to be installed. Saving an
animation to a GIF file or displaying an animation requires one of these
packages, so please install one of them and try again.
See www.imagemagick.org and www.ffmpeg.org for more information.
Animate a list of frames by creating a sage.plot.animate.Animation object.
EXAMPLES:
sage: t = var('t')
sage: a = animate((cos(c*pi*t) for c in sxrange(1,2,.2)))
sage: a.show() # optional -- ImageMagick
See also sage.plot.animate for more examples.