The Tachyon 3D Ray Tracer#

Given any 3D graphics object M one can compute a raytraced representation by typing M.show(viewer='tachyon'). For example, we draw two translucent spheres that contain a red tube, and render the result using Tachyon.

sage: S = sphere(opacity=0.8, aspect_ratio=[1,1,1])
sage: L = line3d([(0,0,0),(2,0,0)], thickness=10, color='red')
sage: M = S + S.translate((2,0,0)) + L
sage: M.show(viewer='tachyon')

>>> from sage.all import *
>>> S = sphere(opacity=RealNumber('0.8'), aspect_ratio=[Integer(1),Integer(1),Integer(1)])
>>> L = line3d([(Integer(0),Integer(0),Integer(0)),(Integer(2),Integer(0),Integer(0))], thickness=Integer(10), color='red')
>>> M = S + S.translate((Integer(2),Integer(0),Integer(0))) + L
>>> M.show(viewer='tachyon')

A number of options can be given to the show() method and correspondingly to the save() method for saving the generated image to a file:

sage: M.show(viewer='tachyon',
....:    antialiasing=True, raydepth=3,
....:    figsize=[12,8], # the image resolution is 100*figsize
....:    camera_position=[4, 4.4, 1], # a distant camera position combined with
....:    zoom=3, # a large zoom factor will decrease perspective distortion.
....:    updir=(0, -0.1, 1), # the camera is slightly tilted
....:    viewdir=(-2.,-2.,-0.5), # slightly off-center
....:    light_position=(4.0, -3.0, 2.0),
....:   )

>>> from sage.all import *
>>> M.show(viewer='tachyon',
...    antialiasing=True, raydepth=Integer(3),
...    figsize=[Integer(12),Integer(8)], # the image resolution is 100*figsize
...    camera_position=[Integer(4), RealNumber('4.4'), Integer(1)], # a distant camera position combined with
...    zoom=Integer(3), # a large zoom factor will decrease perspective distortion.
...    updir=(Integer(0), -RealNumber('0.1'), Integer(1)), # the camera is slightly tilted
...    viewdir=(-RealNumber('2.'),-RealNumber('2.'),-RealNumber('0.5')), # slightly off-center
...    light_position=(RealNumber('4.0'), -RealNumber('3.0'), RealNumber('2.0')),
...   )

One can also directly control Tachyon by creating a Tachyon object and adding elements of the scene one by one, which gives a huge amount of flexibility. For example, here we directly use Tachyon to draw 3 spheres on the coordinate axes:

sage: t = Tachyon(xres=500, yres=500, camera_position=(2,0,0))
sage: t.light((4,3,2), 0.2, (1,1,1))
sage: t.texture('t2', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(1,0,0))
sage: t.texture('t3', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(0,1,0))
sage: t.texture('t4', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(0,0,1))
sage: t.sphere((0,0.5,0), 0.2, 't2')
sage: t.sphere((0.5,0,0), 0.2, 't3')
sage: t.sphere((0,0,0.5), 0.2, 't4')
sage: t.show()

>>> from sage.all import *
>>> t = Tachyon(xres=Integer(500), yres=Integer(500), camera_position=(Integer(2),Integer(0),Integer(0)))
>>> t.light((Integer(4),Integer(3),Integer(2)), RealNumber('0.2'), (Integer(1),Integer(1),Integer(1)))
>>> t.texture('t2', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.5'), opacity=RealNumber('1.0'), color=(Integer(1),Integer(0),Integer(0)))
>>> t.texture('t3', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.5'), opacity=RealNumber('1.0'), color=(Integer(0),Integer(1),Integer(0)))
>>> t.texture('t4', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.5'), opacity=RealNumber('1.0'), color=(Integer(0),Integer(0),Integer(1)))
>>> t.sphere((Integer(0),RealNumber('0.5'),Integer(0)), RealNumber('0.2'), 't2')
>>> t.sphere((RealNumber('0.5'),Integer(0),Integer(0)), RealNumber('0.2'), 't3')
>>> t.sphere((Integer(0),Integer(0),RealNumber('0.5')), RealNumber('0.2'), 't4')
>>> t.show()

For scenes with many reflections it is helpful to increase the raydepth option, and turn on antialiasing. The following scene is an extreme case with many reflections between four cotangent spheres:

sage: t = Tachyon(camera_position=(0,-4,1), xres=800, yres=600, raydepth=12,
....:             aspectratio=.75, antialiasing=4)
sage: t.light((0.02,0.012,0.001), 0.01, (1,0,0))
sage: t.light((0,0,10), 0.01, (0,0,1))
sage: t.texture('s', color=(.8,1,1), opacity=.9, specular=.95, diffuse=.3, ambient=0.05)
sage: t.texture('p', color=(0,0,1), opacity=1, specular=.2)
sage: t.sphere((-1,-.57735,-0.7071),1,'s')
sage: t.sphere((1,-.57735,-0.7071),1,'s')
sage: t.sphere((0,1.15465,-0.7071),1,'s')
sage: t.sphere((0,0,0.9259),1,'s')
sage: t.plane((0,0,-1.9259),(0,0,1),'p')
sage: t.show() # long time

>>> from sage.all import *
>>> t = Tachyon(camera_position=(Integer(0),-Integer(4),Integer(1)), xres=Integer(800), yres=Integer(600), raydepth=Integer(12),
...             aspectratio=RealNumber('.75'), antialiasing=Integer(4))
>>> t.light((RealNumber('0.02'),RealNumber('0.012'),RealNumber('0.001')), RealNumber('0.01'), (Integer(1),Integer(0),Integer(0)))
>>> t.light((Integer(0),Integer(0),Integer(10)), RealNumber('0.01'), (Integer(0),Integer(0),Integer(1)))
>>> t.texture('s', color=(RealNumber('.8'),Integer(1),Integer(1)), opacity=RealNumber('.9'), specular=RealNumber('.95'), diffuse=RealNumber('.3'), ambient=RealNumber('0.05'))
>>> t.texture('p', color=(Integer(0),Integer(0),Integer(1)), opacity=Integer(1), specular=RealNumber('.2'))
>>> t.sphere((-Integer(1),-RealNumber('.57735'),-RealNumber('0.7071')),Integer(1),'s')
>>> t.sphere((Integer(1),-RealNumber('.57735'),-RealNumber('0.7071')),Integer(1),'s')
>>> t.sphere((Integer(0),RealNumber('1.15465'),-RealNumber('0.7071')),Integer(1),'s')
>>> t.sphere((Integer(0),Integer(0),RealNumber('0.9259')),Integer(1),'s')
>>> t.plane((Integer(0),Integer(0),-RealNumber('1.9259')),(Integer(0),Integer(0),Integer(1)),'p')
>>> t.show() # long time

Different projection options are available. The following examples all use a sphere and cube:

sage: cedges = [[[1, 1, 1], [-1, 1, 1]], [[1, 1, 1], [1, -1, 1]],
....: [[1, 1, 1], [1, 1, -1]], [[-1, 1, 1], [-1, -1, 1]], [[-1, 1, 1],
....: [-1, 1, -1]], [[1, -1, 1], [-1, -1, 1]], [[1, -1, 1], [1, -1, -1]],
....: [[-1, -1, 1], [-1, -1, -1]], [[1, 1, -1], [-1, 1, -1]],
....: [[1, 1, -1], [1, -1, -1]], [[-1, 1, -1], [-1, -1, -1]],
....: [[1, -1, -1], [-1, -1, -1]]]

>>> from sage.all import *
>>> cedges = [[[Integer(1), Integer(1), Integer(1)], [-Integer(1), Integer(1), Integer(1)]], [[Integer(1), Integer(1), Integer(1)], [Integer(1), -Integer(1), Integer(1)]],
... [[Integer(1), Integer(1), Integer(1)], [Integer(1), Integer(1), -Integer(1)]], [[-Integer(1), Integer(1), Integer(1)], [-Integer(1), -Integer(1), Integer(1)]], [[-Integer(1), Integer(1), Integer(1)],
... [-Integer(1), Integer(1), -Integer(1)]], [[Integer(1), -Integer(1), Integer(1)], [-Integer(1), -Integer(1), Integer(1)]], [[Integer(1), -Integer(1), Integer(1)], [Integer(1), -Integer(1), -Integer(1)]],
... [[-Integer(1), -Integer(1), Integer(1)], [-Integer(1), -Integer(1), -Integer(1)]], [[Integer(1), Integer(1), -Integer(1)], [-Integer(1), Integer(1), -Integer(1)]],
... [[Integer(1), Integer(1), -Integer(1)], [Integer(1), -Integer(1), -Integer(1)]], [[-Integer(1), Integer(1), -Integer(1)], [-Integer(1), -Integer(1), -Integer(1)]],
... [[Integer(1), -Integer(1), -Integer(1)], [-Integer(1), -Integer(1), -Integer(1)]]]

The default projection is 'perspective':

sage: t = Tachyon(xres=800, yres=600, camera_position=(-1.5,0.0,0.0), zoom=.2)
sage: t.texture('t1', color=(0,0,1))
sage: for ed in cedges:
....:     t.fcylinder(ed[0], ed[1], .05, 't1')
sage: t.light((-4,-4,4), .1, (1,1,1))
sage: t.show()

>>> from sage.all import *
>>> t = Tachyon(xres=Integer(800), yres=Integer(600), camera_position=(-RealNumber('1.5'),RealNumber('0.0'),RealNumber('0.0')), zoom=RealNumber('.2'))
>>> t.texture('t1', color=(Integer(0),Integer(0),Integer(1)))
>>> for ed in cedges:
...     t.fcylinder(ed[Integer(0)], ed[Integer(1)], RealNumber('.05'), 't1')
>>> t.light((-Integer(4),-Integer(4),Integer(4)), RealNumber('.1'), (Integer(1),Integer(1),Integer(1)))
>>> t.show()

Another option is projection='fisheye', which requires frustum information. The frustum data is (bottom angle, top angle, left angle, right angle):

sage: t = Tachyon(xres=800, yres=600, camera_position=(-1.5,0.0,0.0),
....: projection='fisheye', frustum=(-1.2, 1.2, -1.2, 1.2))
sage: t.texture('t1', color=(0,0,1))
sage: for ed in cedges:
....:     t.fcylinder(ed[0], ed[1], .05, 't1')
sage: t.light((-4,-4,4), .1, (1,1,1))
sage: t.show()

>>> from sage.all import *
>>> t = Tachyon(xres=Integer(800), yres=Integer(600), camera_position=(-RealNumber('1.5'),RealNumber('0.0'),RealNumber('0.0')),
... projection='fisheye', frustum=(-RealNumber('1.2'), RealNumber('1.2'), -RealNumber('1.2'), RealNumber('1.2')))
>>> t.texture('t1', color=(Integer(0),Integer(0),Integer(1)))
>>> for ed in cedges:
...     t.fcylinder(ed[Integer(0)], ed[Integer(1)], RealNumber('.05'), 't1')
>>> t.light((-Integer(4),-Integer(4),Integer(4)), RealNumber('.1'), (Integer(1),Integer(1),Integer(1)))
>>> t.show()

Finally there is the projection='perspective_dof' option.

sage: T = Tachyon(xres=800, antialiasing=4, raydepth=10,
....:             projection='perspective_dof', focallength='1.0', aperture='.0025')
sage: T.light((0,5,7), 1.0, (1,1,1))
sage: T.texture('t1', opacity=1, specular=.3)
sage: T.texture('t2', opacity=1, specular=.3, color=(0,0,1))
sage: T.texture('t3', opacity=1, specular=1, color=(1,.8,1), diffuse=0.2)
sage: T.plane((0,0,-1), (0,0,1), 't3')
sage: ttlist = ['t1', 't2']
sage: tt = 't1'
sage: T.cylinder((0,0,.1), (1,1/3,0), .05, 't3')
sage: for q in srange(-3, 100, .15):
....:     if tt == 't1':
....:         tt = 't2'
....:     else:
....:         tt = 't1'
....:     T.sphere((q, q/3+.3*sin(3*q), .1+.3*cos(3*q)), .1, tt)
sage: T.show()

>>> from sage.all import *
>>> T = Tachyon(xres=Integer(800), antialiasing=Integer(4), raydepth=Integer(10),
...             projection='perspective_dof', focallength='1.0', aperture='.0025')
>>> T.light((Integer(0),Integer(5),Integer(7)), RealNumber('1.0'), (Integer(1),Integer(1),Integer(1)))
>>> T.texture('t1', opacity=Integer(1), specular=RealNumber('.3'))
>>> T.texture('t2', opacity=Integer(1), specular=RealNumber('.3'), color=(Integer(0),Integer(0),Integer(1)))
>>> T.texture('t3', opacity=Integer(1), specular=Integer(1), color=(Integer(1),RealNumber('.8'),Integer(1)), diffuse=RealNumber('0.2'))
>>> T.plane((Integer(0),Integer(0),-Integer(1)), (Integer(0),Integer(0),Integer(1)), 't3')
>>> ttlist = ['t1', 't2']
>>> tt = 't1'
>>> T.cylinder((Integer(0),Integer(0),RealNumber('.1')), (Integer(1),Integer(1)/Integer(3),Integer(0)), RealNumber('.05'), 't3')
>>> for q in srange(-Integer(3), Integer(100), RealNumber('.15')):
...     if tt == 't1':
...         tt = 't2'
...     else:
...         tt = 't1'
...     T.sphere((q, q/Integer(3)+RealNumber('.3')*sin(Integer(3)*q), RealNumber('.1')+RealNumber('.3')*cos(Integer(3)*q)), RealNumber('.1'), tt)
>>> T.show()

Image files in the ppm format can be used to tile planes or cover cylinders or spheres. In this example an image is created and then used to tile the plane:

sage: T = Tachyon(xres=800, yres=600, camera_position=(-2.0,-.1,.3),
....:             projection='fisheye', frustum=(-1.0, 1.0, -1.0, 1.0))
sage: T.texture('t1',color=(0,0,1))
sage: for ed in cedges:
....:     T.fcylinder(ed[0], ed[1], .05, 't1')
sage: T.light((-4,-4,4),.1,(1,1,1))
sage: fname_png = tmp_filename(ext='.png')
sage: fname_ppm = tmp_filename(ext='.ppm')
sage: T.save(fname_png)
sage: from sage.features.imagemagick import Magick
sage: r2 = os.system(Magick().executable+' '+fname_png+' '+fname_ppm)    # optional -- ImageMagick
sage: # optional - imagemagick
sage: T = Tachyon(xres=800, yres=600,
....:             camera_position=(-2.0,-.1,.3),
....:             projection='fisheye',
....:             frustum=(-1.0, 1.0, -1.0, 1.0))
sage: T.texture('t1', color=(1,0,0), specular=.9)
sage: T.texture('p1', color=(1,1,1), opacity=.1,
....:           imagefile=fname_ppm, texfunc=9)
sage: T.sphere((0,0,0), .5, 't1')
sage: T.plane((0,0,-1), (0,0,1), 'p1')
sage: T.light((-4,-4,4), .1, (1,1,1))
sage: T.show()

>>> from sage.all import *
>>> T = Tachyon(xres=Integer(800), yres=Integer(600), camera_position=(-RealNumber('2.0'),-RealNumber('.1'),RealNumber('.3')),
...             projection='fisheye', frustum=(-RealNumber('1.0'), RealNumber('1.0'), -RealNumber('1.0'), RealNumber('1.0')))
>>> T.texture('t1',color=(Integer(0),Integer(0),Integer(1)))
>>> for ed in cedges:
...     T.fcylinder(ed[Integer(0)], ed[Integer(1)], RealNumber('.05'), 't1')
>>> T.light((-Integer(4),-Integer(4),Integer(4)),RealNumber('.1'),(Integer(1),Integer(1),Integer(1)))
>>> fname_png = tmp_filename(ext='.png')
>>> fname_ppm = tmp_filename(ext='.ppm')
>>> T.save(fname_png)
>>> from sage.features.imagemagick import Magick
>>> r2 = os.system(Magick().executable+' '+fname_png+' '+fname_ppm)    # optional -- ImageMagick
>>> # optional - imagemagick
>>> T = Tachyon(xres=Integer(800), yres=Integer(600),
...             camera_position=(-RealNumber('2.0'),-RealNumber('.1'),RealNumber('.3')),
...             projection='fisheye',
...             frustum=(-RealNumber('1.0'), RealNumber('1.0'), -RealNumber('1.0'), RealNumber('1.0')))
>>> T.texture('t1', color=(Integer(1),Integer(0),Integer(0)), specular=RealNumber('.9'))
>>> T.texture('p1', color=(Integer(1),Integer(1),Integer(1)), opacity=RealNumber('.1'),
...           imagefile=fname_ppm, texfunc=Integer(9))
>>> T.sphere((Integer(0),Integer(0),Integer(0)), RealNumber('.5'), 't1')
>>> T.plane((Integer(0),Integer(0),-Integer(1)), (Integer(0),Integer(0),Integer(1)), 'p1')
>>> T.light((-Integer(4),-Integer(4),Integer(4)), RealNumber('.1'), (Integer(1),Integer(1),Integer(1)))
>>> T.show()

AUTHOR:

  • John E. Stone (johns@megapixel.com): wrote tachyon ray tracer

  • William Stein: sage-tachyon interface

  • Joshua Kantor: 3d function plotting

  • Tom Boothby: 3d function plotting n’stuff

  • Leif Hille: key idea for bugfix for texfunc issue (Issue #799)

  • Marshall Hampton: improved doctests, rings, axis-aligned boxes.

  • Paul Graham: Respect global verbosity settings (Issue #16228)

Todo

  • clean up trianglefactory stuff

class sage.plot.plot3d.tachyon.Axis_aligned_box(min_p, max_p, texture)[source]#

Bases: object

Box with axis-aligned edges with the given min and max coordinates.

str()[source]#

Return the scene string of the axis-aligned box.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import Axis_aligned_box
sage: aab = Axis_aligned_box((0,0,0),(1,1,1),'s')
sage: aab.str()
'\n        box min  0.0 0.0 0.0  max  1.0 1.0 1.0  s\n        '

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import Axis_aligned_box
>>> aab = Axis_aligned_box((Integer(0),Integer(0),Integer(0)),(Integer(1),Integer(1),Integer(1)),'s')
>>> aab.str()
'\n        box min  0.0 0.0 0.0  max  1.0 1.0 1.0  s\n        '
class sage.plot.plot3d.tachyon.Cylinder(center, axis, radius, texture)[source]#

Bases: object

An infinite cylinder.

str()[source]#

Return the scene string of the cylinder.

EXAMPLES:

sage: t = Tachyon()
sage: from sage.plot.plot3d.tachyon import Cylinder
sage: c = Cylinder((0,0,0),(1,1,1),.1,'s')
sage: c.str()
'\n        cylinder center  0.0 0.0 0.0  axis  1.0 1.0 1.0  rad 0.1 s\n        '

>>> from sage.all import *
>>> t = Tachyon()
>>> from sage.plot.plot3d.tachyon import Cylinder
>>> c = Cylinder((Integer(0),Integer(0),Integer(0)),(Integer(1),Integer(1),Integer(1)),RealNumber('.1'),'s')
>>> c.str()
'\n        cylinder center  0.0 0.0 0.0  axis  1.0 1.0 1.0  rad 0.1 s\n        '
class sage.plot.plot3d.tachyon.FCylinder(base, apex, radius, texture)[source]#

Bases: object

A finite cylinder.

str()[source]#

Return the scene string of the finite cylinder.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import FCylinder
sage: fc = FCylinder((0,0,0),(1,1,1),.1,'s')
sage: fc.str()
'\n        fcylinder base  0.0 0.0 0.0  apex  1.0 1.0 1.0  rad 0.1 s\n        '

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import FCylinder
>>> fc = FCylinder((Integer(0),Integer(0),Integer(0)),(Integer(1),Integer(1),Integer(1)),RealNumber('.1'),'s')
>>> fc.str()
'\n        fcylinder base  0.0 0.0 0.0  apex  1.0 1.0 1.0  rad 0.1 s\n        '
class sage.plot.plot3d.tachyon.FractalLandscape(res, scale, center, texture)[source]#

Bases: object

Axis-aligned fractal landscape.

Does not seem very useful at the moment, but perhaps will be improved in the future.

str()[source]#

Return the scene string of the fractal landscape.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import FractalLandscape
sage: fl = FractalLandscape([20,20],[30,30],[1,2,3],'s')
sage: fl.str()
'\n        scape res  20 20  scale  30 30  center  1.0 2.0 3.0  s\n        '

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import FractalLandscape
>>> fl = FractalLandscape([Integer(20),Integer(20)],[Integer(30),Integer(30)],[Integer(1),Integer(2),Integer(3)],'s')
>>> fl.str()
'\n        scape res  20 20  scale  30 30  center  1.0 2.0 3.0  s\n        '
class sage.plot.plot3d.tachyon.Light(center, radius, color)[source]#

Bases: object

Represent lighting objects.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import Light
sage: q = Light((1,1,1), 1, (1,1,1))
sage: q._center
(1.0, 1.0, 1.0)

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import Light
>>> q = Light((Integer(1),Integer(1),Integer(1)), Integer(1), (Integer(1),Integer(1),Integer(1)))
>>> q._center
(1.0, 1.0, 1.0)
str()[source]#

Return the tachyon string defining the light source.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import Light
sage: q = Light((1,1,1), 1, (1,1,1))
sage: print(q.str())
        light center  1.0 1.0 1.0
              rad 1.0
              color  1.0 1.0 1.0

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import Light
>>> q = Light((Integer(1),Integer(1),Integer(1)), Integer(1), (Integer(1),Integer(1),Integer(1)))
>>> print(q.str())
        light center  1.0 1.0 1.0
              rad 1.0
              color  1.0 1.0 1.0
class sage.plot.plot3d.tachyon.ParametricPlot(f, t_0, t_f, tex, r=0.1, cylinders=True, min_depth=4, max_depth=8, e_rel=0.01, e_abs=0.01)[source]#

Bases: object

Parametric plotting routines.

str()[source]#

Return the tachyon string representation of the parameterized curve.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import ParametricPlot
sage: f = lambda t: (t,t^2,t^3)
sage: q = ParametricPlot(f,0,1,'s')
sage: q.str()[9:69]
'sphere center  0.0 0.0 0.0  rad 0.1 s\n        \n        fcyli'

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import ParametricPlot
>>> f = lambda t: (t,t**Integer(2),t**Integer(3))
>>> q = ParametricPlot(f,Integer(0),Integer(1),'s')
>>> q.str()[Integer(9):Integer(69)]
'sphere center  0.0 0.0 0.0  rad 0.1 s\n        \n        fcyli'
tol(est, val)[source]#

Check relative, then absolute tolerance.

If both fail, return False.

This is a zero-safe error checker.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import ParametricPlot
sage: f = lambda t: (t,t^2,t^3)
sage: q = ParametricPlot(f,0,1,'s')
sage: q.tol([0,0,0],[1,0,0])
False
sage: q.tol([0,0,0],[.0001,0,0])
True

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import ParametricPlot
>>> f = lambda t: (t,t**Integer(2),t**Integer(3))
>>> q = ParametricPlot(f,Integer(0),Integer(1),'s')
>>> q.tol([Integer(0),Integer(0),Integer(0)],[Integer(1),Integer(0),Integer(0)])
False
>>> q.tol([Integer(0),Integer(0),Integer(0)],[RealNumber('.0001'),Integer(0),Integer(0)])
True
class sage.plot.plot3d.tachyon.Plane(center, normal, texture)[source]#

Bases: object

An infinite plane.

str()[source]#

Return the scene string of the plane.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import Plane
sage: p = Plane((1,2,3),(1,2,4),'s')
sage: p.str()
'\n        plane center  1.0 2.0 3.0  normal  1.0 2.0 4.0  s\n        '

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import Plane
>>> p = Plane((Integer(1),Integer(2),Integer(3)),(Integer(1),Integer(2),Integer(4)),'s')
>>> p.str()
'\n        plane center  1.0 2.0 3.0  normal  1.0 2.0 4.0  s\n        '
class sage.plot.plot3d.tachyon.Ring(center, normal, inner, outer, texture)[source]#

Bases: object

An annulus of zero thickness.

str()[source]#

Return the scene string of the ring.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import Ring
sage: r = Ring((0,0,0), (1,1,0), 1.0, 2.0, 's')
sage: r.str()
'\n        ring center  0.0 0.0 0.0  normal  1.0 1.0 0.0  inner 1.0 outer 2.0 s\n        '

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import Ring
>>> r = Ring((Integer(0),Integer(0),Integer(0)), (Integer(1),Integer(1),Integer(0)), RealNumber('1.0'), RealNumber('2.0'), 's')
>>> r.str()
'\n        ring center  0.0 0.0 0.0  normal  1.0 1.0 0.0  inner 1.0 outer 2.0 s\n        '
class sage.plot.plot3d.tachyon.Sphere(center, radius, texture)[source]#

Bases: object

A class for creating spheres in tachyon.

str()[source]#

Return the scene string for the sphere.

EXAMPLES:

sage: t = Tachyon()
sage: from sage.plot.plot3d.tachyon import Sphere
sage: t.texture('r', color=(.8,0,0), ambient = .1)
sage: s = Sphere((1,1,1), 1, 'r')
sage: s.str()
'\n        sphere center  1.0 1.0 1.0  rad 1.0 r\n        '

>>> from sage.all import *
>>> t = Tachyon()
>>> from sage.plot.plot3d.tachyon import Sphere
>>> t.texture('r', color=(RealNumber('.8'),Integer(0),Integer(0)), ambient = RealNumber('.1'))
>>> s = Sphere((Integer(1),Integer(1),Integer(1)), Integer(1), 'r')
>>> s.str()
'\n        sphere center  1.0 1.0 1.0  rad 1.0 r\n        '
class sage.plot.plot3d.tachyon.Tachyon(xres=350, yres=350, zoom=1.0, antialiasing=False, aspectratio=1.0, raydepth=8, camera_position=None, camera_center=None, updir=[0, 0, 1], look_at=[0, 0, 0], viewdir=None, projection='PERSPECTIVE', focallength='', aperture='', frustum='')[source]#

Bases: WithEqualityById, SageObject

Create a scene the can be rendered using the Tachyon ray tracer.

INPUT:

  • xres – (default 350)

  • yres – (default 350)

  • zoom – (default 1.0)

  • antialiasing – (default False)

  • aspectratio – (default 1.0)

  • raydepth – (default 8)

  • camera_position – (default (-3, 0, 0))

  • updir – (default (0, 0, 1))

  • look_at – (default (0,0,0))

  • viewdir – (default None), otherwise list of three numbers

  • projection – 'PERSPECTIVE' (default), 'perspective_dof' or 'fisheye'.

  • frustum – (default ''), otherwise list of four numbers. Only used with projection='fisheye'.

  • focallength – (default ‘’), otherwise a number. Only used with projection='perspective_dof'.

  • aperture – (default ‘’), otherwise a number. Only used with projection='perspective_dof'.

OUTPUT: A Tachyon 3d scene.

Note that the coordinates are by default such that \(z\) is up, positive \(y\) is to the {left} and \(x\) is toward you. This is not oriented according to the right hand rule.

EXAMPLES: Spheres along the twisted cubic.

sage: t = Tachyon(xres=512,yres=512, camera_position=(3,0.3,0))
sage: t.light((4,3,2), 0.2, (1,1,1))
sage: t.texture('t0', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(1.0,0,0))
sage: t.texture('t1', ambient=0.1, diffuse=0.9, specular=0.3, opacity=1.0, color=(0,1.0,0))
sage: t.texture('t2', ambient=0.2, diffuse=0.7, specular=0.5, opacity=0.7, color=(0,0,1.0))
sage: k=0
sage: for i in srange(-1,1,0.05):
....:    k += 1
....:    t.sphere((i,i^2-0.5,i^3), 0.1, 't%s'%(k%3))
sage: t.show()

>>> from sage.all import *
>>> t = Tachyon(xres=Integer(512),yres=Integer(512), camera_position=(Integer(3),RealNumber('0.3'),Integer(0)))
>>> t.light((Integer(4),Integer(3),Integer(2)), RealNumber('0.2'), (Integer(1),Integer(1),Integer(1)))
>>> t.texture('t0', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.5'), opacity=RealNumber('1.0'), color=(RealNumber('1.0'),Integer(0),Integer(0)))
>>> t.texture('t1', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.3'), opacity=RealNumber('1.0'), color=(Integer(0),RealNumber('1.0'),Integer(0)))
>>> t.texture('t2', ambient=RealNumber('0.2'), diffuse=RealNumber('0.7'), specular=RealNumber('0.5'), opacity=RealNumber('0.7'), color=(Integer(0),Integer(0),RealNumber('1.0')))
>>> k=Integer(0)
>>> for i in srange(-Integer(1),Integer(1),RealNumber('0.05')):
...    k += Integer(1)
...    t.sphere((i,i**Integer(2)-RealNumber('0.5'),i**Integer(3)), RealNumber('0.1'), 't%s'%(k%Integer(3)))
>>> t.show()

Another twisted cubic, but with a white background, got by putting infinite planes around the scene.

sage: t = Tachyon(xres=512,yres=512, camera_position=(3,0.3,0), raydepth=8)
sage: t.light((4,3,2), 0.2, (1,1,1))
sage: t.texture('t0', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(1.0,0,0))
sage: t.texture('t1', ambient=0.1, diffuse=0.9, specular=0.3, opacity=1.0, color=(0,1.0,0))
sage: t.texture('t2', ambient=0.2,diffuse=0.7, specular=0.5, opacity=0.7, color=(0,0,1.0))
sage: t.texture('white', color=(1,1,1))
sage: t.plane((0,0,-1), (0,0,1), 'white')
sage: t.plane((0,-20,0), (0,1,0), 'white')
sage: t.plane((-20,0,0), (1,0,0), 'white')

>>> from sage.all import *
>>> t = Tachyon(xres=Integer(512),yres=Integer(512), camera_position=(Integer(3),RealNumber('0.3'),Integer(0)), raydepth=Integer(8))
>>> t.light((Integer(4),Integer(3),Integer(2)), RealNumber('0.2'), (Integer(1),Integer(1),Integer(1)))
>>> t.texture('t0', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.5'), opacity=RealNumber('1.0'), color=(RealNumber('1.0'),Integer(0),Integer(0)))
>>> t.texture('t1', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.3'), opacity=RealNumber('1.0'), color=(Integer(0),RealNumber('1.0'),Integer(0)))
>>> t.texture('t2', ambient=RealNumber('0.2'),diffuse=RealNumber('0.7'), specular=RealNumber('0.5'), opacity=RealNumber('0.7'), color=(Integer(0),Integer(0),RealNumber('1.0')))
>>> t.texture('white', color=(Integer(1),Integer(1),Integer(1)))
>>> t.plane((Integer(0),Integer(0),-Integer(1)), (Integer(0),Integer(0),Integer(1)), 'white')
>>> t.plane((Integer(0),-Integer(20),Integer(0)), (Integer(0),Integer(1),Integer(0)), 'white')
>>> t.plane((-Integer(20),Integer(0),Integer(0)), (Integer(1),Integer(0),Integer(0)), 'white')

sage: k=0
sage: for i in srange(-1,1,0.05):
....:    k += 1
....:    t.sphere((i,i^2 - 0.5,i^3), 0.1, 't%s'%(k%3))
....:    t.cylinder((0,0,0), (0,0,1), 0.05,'t1')
sage: t.show()

>>> from sage.all import *
>>> k=Integer(0)
>>> for i in srange(-Integer(1),Integer(1),RealNumber('0.05')):
...    k += Integer(1)
...    t.sphere((i,i**Integer(2) - RealNumber('0.5'),i**Integer(3)), RealNumber('0.1'), 't%s'%(k%Integer(3)))
...    t.cylinder((Integer(0),Integer(0),Integer(0)), (Integer(0),Integer(0),Integer(1)), RealNumber('0.05'),'t1')
>>> t.show()

Many random spheres:

sage: t = Tachyon(xres=512,yres=512, camera_position=(2,0.5,0.5), look_at=(0.5,0.5,0.5), raydepth=4)
sage: t.light((4,3,2), 0.2, (1,1,1))
sage: t.texture('t0', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(1.0,0,0))
sage: t.texture('t1', ambient=0.1, diffuse=0.9, specular=0.3, opacity=1.0, color=(0,1.0,0))
sage: t.texture('t2', ambient=0.2, diffuse=0.7, specular=0.5, opacity=0.7, color=(0,0,1.0))
sage: k=0
sage: for i in range(100):
....:    k += 1
....:    t.sphere((random(),random(), random()), random()/10, 't%s'%(k%3))
sage: t.show()

>>> from sage.all import *
>>> t = Tachyon(xres=Integer(512),yres=Integer(512), camera_position=(Integer(2),RealNumber('0.5'),RealNumber('0.5')), look_at=(RealNumber('0.5'),RealNumber('0.5'),RealNumber('0.5')), raydepth=Integer(4))
>>> t.light((Integer(4),Integer(3),Integer(2)), RealNumber('0.2'), (Integer(1),Integer(1),Integer(1)))
>>> t.texture('t0', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.5'), opacity=RealNumber('1.0'), color=(RealNumber('1.0'),Integer(0),Integer(0)))
>>> t.texture('t1', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.3'), opacity=RealNumber('1.0'), color=(Integer(0),RealNumber('1.0'),Integer(0)))
>>> t.texture('t2', ambient=RealNumber('0.2'), diffuse=RealNumber('0.7'), specular=RealNumber('0.5'), opacity=RealNumber('0.7'), color=(Integer(0),Integer(0),RealNumber('1.0')))
>>> k=Integer(0)
>>> for i in range(Integer(100)):
...    k += Integer(1)
...    t.sphere((random(),random(), random()), random()/Integer(10), 't%s'%(k%Integer(3)))
>>> t.show()

Points on an elliptic curve, their height indicated by their height above the axis:

sage: # needs sage.schemes
sage: t = Tachyon(camera_position=(5,2,2), look_at=(0,1,0))
sage: t.light((10,3,2), 0.2, (1,1,1))
sage: t.texture('t0', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(1,0,0))
sage: t.texture('t1', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(0,1,0))
sage: t.texture('t2', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(0,0,1))
sage: E = EllipticCurve('37a')                                                  # needs sage.schemes
sage: P = E([0,0])                                                              # needs sage.schemes
sage: Q = P                                                                     # needs sage.schemes
sage: n = 100
sage: for i in range(n):   # increase 20 for a better plot                      # needs sage.schemes
....:    Q = Q + P
....:    t.sphere((Q[1], Q[0], ZZ(i)/n), 0.1, 't%s'%(i%3))
sage: t.show()                                                                  # needs sage.schemes

>>> from sage.all import *
>>> # needs sage.schemes
>>> t = Tachyon(camera_position=(Integer(5),Integer(2),Integer(2)), look_at=(Integer(0),Integer(1),Integer(0)))
>>> t.light((Integer(10),Integer(3),Integer(2)), RealNumber('0.2'), (Integer(1),Integer(1),Integer(1)))
>>> t.texture('t0', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.5'), opacity=RealNumber('1.0'), color=(Integer(1),Integer(0),Integer(0)))
>>> t.texture('t1', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.5'), opacity=RealNumber('1.0'), color=(Integer(0),Integer(1),Integer(0)))
>>> t.texture('t2', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.5'), opacity=RealNumber('1.0'), color=(Integer(0),Integer(0),Integer(1)))
>>> E = EllipticCurve('37a')                                                  # needs sage.schemes
>>> P = E([Integer(0),Integer(0)])                                                              # needs sage.schemes
>>> Q = P                                                                     # needs sage.schemes
>>> n = Integer(100)
>>> for i in range(n):   # increase 20 for a better plot                      # needs sage.schemes
...    Q = Q + P
...    t.sphere((Q[Integer(1)], Q[Integer(0)], ZZ(i)/n), RealNumber('0.1'), 't%s'%(i%Integer(3)))
>>> t.show()                                                                  # needs sage.schemes

A beautiful picture of rational points on a rank 1 elliptic curve.

sage: # needs sage.schemes
sage: t = Tachyon(xres=1000, yres=800, camera_position=(2,7,4),
....:             look_at=(2,0,0), raydepth=4)
sage: t.light((10,3,2), 1, (1,1,1))
sage: t.light((10,-3,2), 1, (1,1,1))
sage: t.texture('black', color=(0,0,0))
sage: t.texture('red', color=(1,0,0))
sage: t.texture('grey', color=(.9,.9,.9))
sage: t.plane((0,0,0),(0,0,1),'grey')
sage: t.cylinder((0,0,0),(1,0,0),.01,'black')
sage: t.cylinder((0,0,0),(0,1,0),.01,'black')
sage: E = EllipticCurve('37a')                                                  # needs sage.schemes
sage: P = E([0,0])                                                              # needs sage.schemes
sage: Q = P                                                                     # needs sage.schemes
sage: n = 100
sage: for i in range(n):                                                        # needs sage.schemes
....:    Q = Q + P
....:    c = i/n + .1
....:    t.texture('r%s'%i,color=(float(i/n),0,0))
....:    t.sphere((Q[0], -Q[1], .01), .04, 'r%s'%i)
sage: t.show()                          # long time                             # needs sage.schemes

>>> from sage.all import *
>>> # needs sage.schemes
>>> t = Tachyon(xres=Integer(1000), yres=Integer(800), camera_position=(Integer(2),Integer(7),Integer(4)),
...             look_at=(Integer(2),Integer(0),Integer(0)), raydepth=Integer(4))
>>> t.light((Integer(10),Integer(3),Integer(2)), Integer(1), (Integer(1),Integer(1),Integer(1)))
>>> t.light((Integer(10),-Integer(3),Integer(2)), Integer(1), (Integer(1),Integer(1),Integer(1)))
>>> t.texture('black', color=(Integer(0),Integer(0),Integer(0)))
>>> t.texture('red', color=(Integer(1),Integer(0),Integer(0)))
>>> t.texture('grey', color=(RealNumber('.9'),RealNumber('.9'),RealNumber('.9')))
>>> t.plane((Integer(0),Integer(0),Integer(0)),(Integer(0),Integer(0),Integer(1)),'grey')
>>> t.cylinder((Integer(0),Integer(0),Integer(0)),(Integer(1),Integer(0),Integer(0)),RealNumber('.01'),'black')
>>> t.cylinder((Integer(0),Integer(0),Integer(0)),(Integer(0),Integer(1),Integer(0)),RealNumber('.01'),'black')
>>> E = EllipticCurve('37a')                                                  # needs sage.schemes
>>> P = E([Integer(0),Integer(0)])                                                              # needs sage.schemes
>>> Q = P                                                                     # needs sage.schemes
>>> n = Integer(100)
>>> for i in range(n):                                                        # needs sage.schemes
...    Q = Q + P
...    c = i/n + RealNumber('.1')
...    t.texture('r%s'%i,color=(float(i/n),Integer(0),Integer(0)))
...    t.sphere((Q[Integer(0)], -Q[Integer(1)], RealNumber('.01')), RealNumber('.04'), 'r%s'%i)
>>> t.show()                          # long time                             # needs sage.schemes

A beautiful spiral.

sage: t = Tachyon(xres=800, yres=800, camera_position=(2,5,2), look_at=(2.5,0,0))
sage: t.light((0,0,100), 1, (1,1,1))
sage: t.texture('r', ambient=0.1, diffuse=0.9, specular=0.5,
....:           opacity=1.0, color=(1,0,0))
sage: for i in srange(0,50,0.1):
....:    t.sphere((i/10.0,sin(i),cos(i)), 0.05, 'r')
sage: t.texture('white', color=(1,1,1), opacity=1, specular=1, diffuse=1)
sage: t.plane((0,0,-100), (0,0,-100), 'white')
sage: t.show()

>>> from sage.all import *
>>> t = Tachyon(xres=Integer(800), yres=Integer(800), camera_position=(Integer(2),Integer(5),Integer(2)), look_at=(RealNumber('2.5'),Integer(0),Integer(0)))
>>> t.light((Integer(0),Integer(0),Integer(100)), Integer(1), (Integer(1),Integer(1),Integer(1)))
>>> t.texture('r', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.5'),
...           opacity=RealNumber('1.0'), color=(Integer(1),Integer(0),Integer(0)))
>>> for i in srange(Integer(0),Integer(50),RealNumber('0.1')):
...    t.sphere((i/RealNumber('10.0'),sin(i),cos(i)), RealNumber('0.05'), 'r')
>>> t.texture('white', color=(Integer(1),Integer(1),Integer(1)), opacity=Integer(1), specular=Integer(1), diffuse=Integer(1))
>>> t.plane((Integer(0),Integer(0),-Integer(100)), (Integer(0),Integer(0),-Integer(100)), 'white')
>>> t.show()

If the optional parameter viewdir is not set, the camera center should not coincide with the point which is looked at (see Issue #7232):

sage: t = Tachyon(xres=80,yres=80, camera_position=(2,5,2), look_at=(2,5,2))
Traceback (most recent call last):
...
ValueError: camera_position and look_at coincide

>>> from sage.all import *
>>> t = Tachyon(xres=Integer(80),yres=Integer(80), camera_position=(Integer(2),Integer(5),Integer(2)), look_at=(Integer(2),Integer(5),Integer(2)))
Traceback (most recent call last):
...
ValueError: camera_position and look_at coincide

Use of a fisheye lens perspective.

sage: T = Tachyon(xres=800, yres=600, camera_position=(-1.5,-1.5,.3),
....:             projection='fisheye', frustum=(-1.0, 1.0, -1.0, 1.0))
sage: T.texture('t1', color=(0,0,1))
sage: cedges = [[[1, 1, 1], [-1, 1, 1]], [[1, 1, 1], [1, -1, 1]],
....:           [[1, 1, 1], [1, 1, -1]], [[-1, 1, 1], [-1, -1, 1]],
....:           [[-1, 1, 1], [-1, 1, -1]], [[1, -1, 1], [-1, -1, 1]],
....:           [[1, -1, 1], [1, -1, -1]], [[-1, -1, 1], [-1, -1, -1]],
....:           [[1, 1, -1], [-1, 1, -1]], [[1, 1, -1], [1, -1, -1]],
....:           [[-1, 1, -1], [-1, -1, -1]], [[1, -1, -1], [-1, -1, -1]]]
sage: for ed in cedges:
....:     T.fcylinder(ed[0], ed[1], .05, 't1')
sage: T.light((-4,-4,4), .1, (1,1,1))
sage: T.show()

>>> from sage.all import *
>>> T = Tachyon(xres=Integer(800), yres=Integer(600), camera_position=(-RealNumber('1.5'),-RealNumber('1.5'),RealNumber('.3')),
...             projection='fisheye', frustum=(-RealNumber('1.0'), RealNumber('1.0'), -RealNumber('1.0'), RealNumber('1.0')))
>>> T.texture('t1', color=(Integer(0),Integer(0),Integer(1)))
>>> cedges = [[[Integer(1), Integer(1), Integer(1)], [-Integer(1), Integer(1), Integer(1)]], [[Integer(1), Integer(1), Integer(1)], [Integer(1), -Integer(1), Integer(1)]],
...           [[Integer(1), Integer(1), Integer(1)], [Integer(1), Integer(1), -Integer(1)]], [[-Integer(1), Integer(1), Integer(1)], [-Integer(1), -Integer(1), Integer(1)]],
...           [[-Integer(1), Integer(1), Integer(1)], [-Integer(1), Integer(1), -Integer(1)]], [[Integer(1), -Integer(1), Integer(1)], [-Integer(1), -Integer(1), Integer(1)]],
...           [[Integer(1), -Integer(1), Integer(1)], [Integer(1), -Integer(1), -Integer(1)]], [[-Integer(1), -Integer(1), Integer(1)], [-Integer(1), -Integer(1), -Integer(1)]],
...           [[Integer(1), Integer(1), -Integer(1)], [-Integer(1), Integer(1), -Integer(1)]], [[Integer(1), Integer(1), -Integer(1)], [Integer(1), -Integer(1), -Integer(1)]],
...           [[-Integer(1), Integer(1), -Integer(1)], [-Integer(1), -Integer(1), -Integer(1)]], [[Integer(1), -Integer(1), -Integer(1)], [-Integer(1), -Integer(1), -Integer(1)]]]
>>> for ed in cedges:
...     T.fcylinder(ed[Integer(0)], ed[Integer(1)], RealNumber('.05'), 't1')
>>> T.light((-Integer(4),-Integer(4),Integer(4)), RealNumber('.1'), (Integer(1),Integer(1),Integer(1)))
>>> T.show()

Use of the projection='perspective_dof' option. This may not be implemented correctly.

sage: T = Tachyon(xres=800, antialiasing=4, raydepth=10,
....:             projection='perspective_dof', focallength='1.0', aperture='.0025')
sage: T.light((0,5,7), 1.0, (1,1,1))
sage: T.texture('t1', opacity=1, specular=.3)
sage: T.texture('t2', opacity=1, specular=.3, color=(0,0,1))
sage: T.texture('t3', opacity=1, specular=1, color=(1,.8,1), diffuse=0.2)
sage: T.plane((0,0,-1), (0,0,1), 't3')
sage: ttlist = ['t1', 't2']
sage: tt = 't1'
sage: T.cylinder((0,0,.1), (1,1/3,0), .05, 't3')
sage: for q in srange(-3, 100, .15):
....:     if tt == 't1':
....:         tt = 't2'
....:     else:
....:         tt = 't1'
....:     T.sphere((q, q/3+.3*sin(3*q), .1+.3*cos(3*q)), .1, tt)
sage: T.show()

>>> from sage.all import *
>>> T = Tachyon(xres=Integer(800), antialiasing=Integer(4), raydepth=Integer(10),
...             projection='perspective_dof', focallength='1.0', aperture='.0025')
>>> T.light((Integer(0),Integer(5),Integer(7)), RealNumber('1.0'), (Integer(1),Integer(1),Integer(1)))
>>> T.texture('t1', opacity=Integer(1), specular=RealNumber('.3'))
>>> T.texture('t2', opacity=Integer(1), specular=RealNumber('.3'), color=(Integer(0),Integer(0),Integer(1)))
>>> T.texture('t3', opacity=Integer(1), specular=Integer(1), color=(Integer(1),RealNumber('.8'),Integer(1)), diffuse=RealNumber('0.2'))
>>> T.plane((Integer(0),Integer(0),-Integer(1)), (Integer(0),Integer(0),Integer(1)), 't3')
>>> ttlist = ['t1', 't2']
>>> tt = 't1'
>>> T.cylinder((Integer(0),Integer(0),RealNumber('.1')), (Integer(1),Integer(1)/Integer(3),Integer(0)), RealNumber('.05'), 't3')
>>> for q in srange(-Integer(3), Integer(100), RealNumber('.15')):
...     if tt == 't1':
...         tt = 't2'
...     else:
...         tt = 't1'
...     T.sphere((q, q/Integer(3)+RealNumber('.3')*sin(Integer(3)*q), RealNumber('.1')+RealNumber('.3')*cos(Integer(3)*q)), RealNumber('.1'), tt)
>>> T.show()
axis_aligned_box(min_p, max_p, texture)[source]#

Create an axis-aligned box with minimal point min_p and maximum point max_p.

EXAMPLES:

sage: t = Tachyon()
sage: t.axis_aligned_box((0,0,0),(2,2,2),'s')

>>> from sage.all import *
>>> t = Tachyon()
>>> t.axis_aligned_box((Integer(0),Integer(0),Integer(0)),(Integer(2),Integer(2),Integer(2)),'s')
cylinder(center, axis, radius, texture)[source]#

Create the scene information for a infinite cylinder with the given center, axis direction, radius, and texture.

EXAMPLES:

sage: t = Tachyon()
sage: t.texture('c')
sage: t.cylinder((0,0,0),(-1,-1,-1),.1,'c')

>>> from sage.all import *
>>> t = Tachyon()
>>> t.texture('c')
>>> t.cylinder((Integer(0),Integer(0),Integer(0)),(-Integer(1),-Integer(1),-Integer(1)),RealNumber('.1'),'c')
fcylinder(base, apex, radius, texture)[source]#

Finite cylinders are almost the same as infinite ones, but the center and length of the axis determine the extents of the cylinder.

The finite cylinder is also really a shell, it does not have any caps. If you need to close off the ends of the cylinder, use two ring objects, with the inner radius set to 0.0 and the normal set to be the axis of the cylinder. Finite cylinders are built this way to enhance speed.

EXAMPLES:

sage: t = Tachyon()
sage: t.fcylinder((1,1,1),(1,2,3),.01,'s')
sage: len(t.str())
451

>>> from sage.all import *
>>> t = Tachyon()
>>> t.fcylinder((Integer(1),Integer(1),Integer(1)),(Integer(1),Integer(2),Integer(3)),RealNumber('.01'),'s')
>>> len(t.str())
451
fractal_landscape(res, scale, center, texture)[source]#

Axis-aligned fractal landscape.

Not very useful at the moment.

EXAMPLES:

sage: t = Tachyon()
sage: t.texture('s')
sage: t.fractal_landscape([30,30],[80,80],[0,0,0],'s')
sage: len(t._objects)
2

>>> from sage.all import *
>>> t = Tachyon()
>>> t.texture('s')
>>> t.fractal_landscape([Integer(30),Integer(30)],[Integer(80),Integer(80)],[Integer(0),Integer(0),Integer(0)],'s')
>>> len(t._objects)
2
light(center, radius, color)[source]#

Create a light source of the given center, radius, and color.

EXAMPLES:

sage: q = Tachyon()
sage: q.light((1,1,1),1.0,(.2,0,.8))
sage: q.str().split('\n')[17]
'        light center  1.0 1.0 1.0 '

>>> from sage.all import *
>>> q = Tachyon()
>>> q.light((Integer(1),Integer(1),Integer(1)),RealNumber('1.0'),(RealNumber('.2'),Integer(0),RealNumber('.8')))
>>> q.str().split('\n')[Integer(17)]
'        light center  1.0 1.0 1.0 '
parametric_plot(f, t_0, t_f, tex, r=0.1, cylinders=True, min_depth=4, max_depth=8, e_rel=0.01, e_abs=0.01)[source]#

Plot a space curve as a series of spheres and finite cylinders.

Example (twisted cubic)

sage: f = lambda t: (t,t^2,t^3)
sage: t = Tachyon(camera_position=(5,0,4))
sage: t.texture('t')
sage: t.light((-20,-20,40), 0.2, (1,1,1))
sage: t.parametric_plot(f,-5,5,'t',min_depth=6)
sage: t.show(verbose=1)
tachyon ...
Scene contains 482 objects.
...

>>> from sage.all import *
>>> f = lambda t: (t,t**Integer(2),t**Integer(3))
>>> t = Tachyon(camera_position=(Integer(5),Integer(0),Integer(4)))
>>> t.texture('t')
>>> t.light((-Integer(20),-Integer(20),Integer(40)), RealNumber('0.2'), (Integer(1),Integer(1),Integer(1)))
>>> t.parametric_plot(f,-Integer(5),Integer(5),'t',min_depth=Integer(6))
>>> t.show(verbose=Integer(1))
tachyon ...
Scene contains 482 objects.
...
plane(center, normal, texture)[source]#

Create an infinite plane with the given center and normal.

plot(f, xmin_xmax, ymin_ymax, texture, grad_f=None, max_bend=0.7, max_depth=5, initial_depth=3, num_colors=None)[source]#

INPUT:

  • f – Function of two variables, which returns a float (or coercible to a float) (xmin,xmax)

  • (ymin,ymax) – defines the rectangle to plot over texture: Name of texture to be used Optional arguments:

  • grad_f – gradient function. If specified, smooth triangles will be used.

  • max_bend – Cosine of the threshold angle between triangles used to determine whether or not to recurse after the minimum depth

  • max_depth – maximum recursion depth. Maximum triangles plotted = \(2^{2*max_depth}\)

  • initial_depth – minimum recursion depth. No error-tolerance checking is performed below this depth. Minimum triangles plotted: \(2^{2*min_depth}\)

  • num_colors – Number of rainbow bands to color the plot with. Texture supplied will be cloned (with different colors) using the texture_recolor method of the Tachyon object.

Plots a function by constructing a mesh with nonstandard sampling density without gaps. At very high resolutions (depths 10) it becomes very slow. Cython may help. Complexity is approx. \(O(2^{2*maxdepth})\). This algorithm has been optimized for speed, not memory - values from f(x,y) are recycled rather than calling the function multiple times. At high recursion depth, this may cause problems for some machines.

Flat Triangles:

sage: t = Tachyon(xres=512, yres=512, camera_position=(4,-4,3),
....:             viewdir=(-4,4,-3), raydepth=4)
sage: t.light((4.4,-4.4,4.4), 0.2, (1,1,1))
sage: def f(x,y): return float(sin(x*y))
sage: t.texture('t0', ambient=0.1, diffuse=0.9, specular=0.1,
....:           opacity=1.0, color=(1.0,0,0))
sage: t.plot(f, (-4,4), (-4,4), "t0", max_depth=5, initial_depth=3,         # needs sage.symbolic
....:        num_colors=60)  # increase min_depth for better picture
sage: t.show(verbose=1)                                                     # needs sage.symbolic
tachyon ...
Scene contains 2713 objects.
...

>>> from sage.all import *
>>> t = Tachyon(xres=Integer(512), yres=Integer(512), camera_position=(Integer(4),-Integer(4),Integer(3)),
...             viewdir=(-Integer(4),Integer(4),-Integer(3)), raydepth=Integer(4))
>>> t.light((RealNumber('4.4'),-RealNumber('4.4'),RealNumber('4.4')), RealNumber('0.2'), (Integer(1),Integer(1),Integer(1)))
>>> def f(x,y): return float(sin(x*y))
>>> t.texture('t0', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.1'),
...           opacity=RealNumber('1.0'), color=(RealNumber('1.0'),Integer(0),Integer(0)))
>>> t.plot(f, (-Integer(4),Integer(4)), (-Integer(4),Integer(4)), "t0", max_depth=Integer(5), initial_depth=Integer(3),         # needs sage.symbolic
...        num_colors=Integer(60))  # increase min_depth for better picture
>>> t.show(verbose=Integer(1))                                                     # needs sage.symbolic
tachyon ...
Scene contains 2713 objects.
...

Plotting with Smooth Triangles (requires explicit gradient function):

sage: t = Tachyon(xres=512, yres=512, camera_position=(4,-4,3),
....:             viewdir=(-4,4,-3), raydepth=4)
sage: t.light((4.4,-4.4,4.4), 0.2, (1,1,1))
sage: def f(x,y): return float(sin(x*y))
sage: def g(x,y): return (float(y*cos(x*y)), float(x*cos(x*y)), 1)
sage: t.texture('t0', ambient=0.1, diffuse=0.9, specular=0.1,
....:           opacity=1.0, color=(1.0,0,0))
sage: t.plot(f, (-4,4), (-4,4), "t0", max_depth=5, initial_depth=3,         # needs sage.symbolic
....:        grad_f=g)  # increase min_depth for better picture
sage: t.show(verbose=1)                                                     # needs sage.symbolic
tachyon ...
Scene contains 2713 objects.
...

>>> from sage.all import *
>>> t = Tachyon(xres=Integer(512), yres=Integer(512), camera_position=(Integer(4),-Integer(4),Integer(3)),
...             viewdir=(-Integer(4),Integer(4),-Integer(3)), raydepth=Integer(4))
>>> t.light((RealNumber('4.4'),-RealNumber('4.4'),RealNumber('4.4')), RealNumber('0.2'), (Integer(1),Integer(1),Integer(1)))
>>> def f(x,y): return float(sin(x*y))
>>> def g(x,y): return (float(y*cos(x*y)), float(x*cos(x*y)), Integer(1))
>>> t.texture('t0', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.1'),
...           opacity=RealNumber('1.0'), color=(RealNumber('1.0'),Integer(0),Integer(0)))
>>> t.plot(f, (-Integer(4),Integer(4)), (-Integer(4),Integer(4)), "t0", max_depth=Integer(5), initial_depth=Integer(3),         # needs sage.symbolic
...        grad_f=g)  # increase min_depth for better picture
>>> t.show(verbose=Integer(1))                                                     # needs sage.symbolic
tachyon ...
Scene contains 2713 objects.
...

Preconditions: f is a scalar function of two variables, grad_f is None or a triple-valued function of two variables, min_x != max_x, min_y != max_y

sage: f = lambda x,y: x*y
sage: t = Tachyon()
sage: t.plot(f,(2.,2.),(-2.,2.),'')
Traceback (most recent call last):
...
ValueError: plot rectangle is really a line; make sure min_x != max_x and min_y != max_y

>>> from sage.all import *
>>> f = lambda x,y: x*y
>>> t = Tachyon()
>>> t.plot(f,(RealNumber('2.'),RealNumber('2.')),(-RealNumber('2.'),RealNumber('2.')),'')
Traceback (most recent call last):
...
ValueError: plot rectangle is really a line; make sure min_x != max_x and min_y != max_y
ring(center, normal, inner, outer, texture)[source]#

Create the scene information for a ring with the given parameters.

EXAMPLES:

sage: t = Tachyon()
sage: t.ring([0,0,0], [0,0,1], 1.0, 2.0, 's')
sage: t._objects[0]._center
(0.0, 0.0, 0.0)

>>> from sage.all import *
>>> t = Tachyon()
>>> t.ring([Integer(0),Integer(0),Integer(0)], [Integer(0),Integer(0),Integer(1)], RealNumber('1.0'), RealNumber('2.0'), 's')
>>> t._objects[Integer(0)]._center
(0.0, 0.0, 0.0)
save(filename='sage.png', verbose=None, extra_opts='')[source]#

Save rendering of the tachyon scene

INPUT:

  • filename – (default: ‘sage.png’) output filename; the extension of the filename determines the type. Supported types include:

  • tga – 24-bit (uncompressed)

  • bmp – 24-bit Windows BMP (uncompressed)

  • ppm – 24-bit PPM (uncompressed)

  • rgb – 24-bit SGI RGB (uncompressed)

  • png – 24-bit PNG (compressed, lossless)

  • verbose – integer (default: None); if no verbosity setting is supplied, the verbosity level set by sage.misc.verbose.set_verbose is used.

  • 0 – silent

  • 1 – some output

  • 2 – very verbose output

  • extra_opts – passed directly to tachyon command line. Use tachyon_rt.usage() to see some of the possibilities.

EXAMPLES:

sage: q = Tachyon()
sage: q.light((1,1,11), 1,(1,1,1))
sage: q.texture('s')
sage: q.sphere((0,0,0),1,'s')
sage: tempname = tmp_filename()
sage: q.save(tempname)

>>> from sage.all import *
>>> q = Tachyon()
>>> q.light((Integer(1),Integer(1),Integer(11)), Integer(1),(Integer(1),Integer(1),Integer(1)))
>>> q.texture('s')
>>> q.sphere((Integer(0),Integer(0),Integer(0)),Integer(1),'s')
>>> tempname = tmp_filename()
>>> q.save(tempname)
save_image(filename=None, *args, **kwds)[source]#

Save an image representation of self.

The image type is determined by the extension of the filename. For example, this could be .png, .jpg, .gif, .pdf, .svg. Currently this is implemented by calling the save() method of self, passing along all arguments and keywords.

Note

Not all image types are necessarily implemented for all graphics types. See save() for more details.

EXAMPLES:

sage: q = Tachyon()
sage: q.light((1,1,11), 1,(1,1,1))
sage: q.texture('s')
sage: q.sphere((0,-1,1),1,'s')
sage: tempname = tmp_filename()
sage: q.save_image(tempname)

>>> from sage.all import *
>>> q = Tachyon()
>>> q.light((Integer(1),Integer(1),Integer(11)), Integer(1),(Integer(1),Integer(1),Integer(1)))
>>> q.texture('s')
>>> q.sphere((Integer(0),-Integer(1),Integer(1)),Integer(1),'s')
>>> tempname = tmp_filename()
>>> q.save_image(tempname)
show(**kwds)[source]#

Create a PNG file of the scene.

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.

OUTPUT:

This method does not return anything. Use save() if you want to save the figure as an image.

EXAMPLES:

This example demonstrates how the global Sage verbosity setting is used if none is supplied. Firstly, using a global verbosity setting of 0 means no extra technical information is displayed, and we are simply shown the plot.

sage: h = Tachyon(xres=512, yres=512, camera_position=(4,-4,3),
....:             viewdir=(-4,4,-3), raydepth=4)
sage: h.light((4.4,-4.4,4.4), 0.2, (1,1,1))
sage: def f(x,y): return float(sin(x*y))
sage: h.texture('t0', ambient=0.1, diffuse=0.9, specular=0.1,
....:           opacity=1.0, color=(1.0,0,0))
sage: h.plot(f, (-4,4), (-4,4), "t0", max_depth=5, initial_depth=3,         # needs sage.symbolic
....:        num_colors=60)  # increase min_depth for better picture
sage: from sage.misc.verbose import set_verbose, get_verbose
sage: set_verbose(0)
sage: h.show()                                                              # needs sage.symbolic

>>> from sage.all import *
>>> h = Tachyon(xres=Integer(512), yres=Integer(512), camera_position=(Integer(4),-Integer(4),Integer(3)),
...             viewdir=(-Integer(4),Integer(4),-Integer(3)), raydepth=Integer(4))
>>> h.light((RealNumber('4.4'),-RealNumber('4.4'),RealNumber('4.4')), RealNumber('0.2'), (Integer(1),Integer(1),Integer(1)))
>>> def f(x,y): return float(sin(x*y))
>>> h.texture('t0', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.1'),
...           opacity=RealNumber('1.0'), color=(RealNumber('1.0'),Integer(0),Integer(0)))
>>> h.plot(f, (-Integer(4),Integer(4)), (-Integer(4),Integer(4)), "t0", max_depth=Integer(5), initial_depth=Integer(3),         # needs sage.symbolic
...        num_colors=Integer(60))  # increase min_depth for better picture
>>> from sage.misc.verbose import set_verbose, get_verbose
>>> set_verbose(Integer(0))
>>> h.show()                                                              # needs sage.symbolic

This second example, using a “medium” global verbosity setting of 1, displays some extra technical information then displays our graph.

sage: s = Tachyon(xres=512, yres=512, camera_position=(4,-4,3),
....:             viewdir=(-4,4,-3), raydepth=4)
sage: s.light((4.4,-4.4,4.4), 0.2, (1,1,1))
sage: def f(x,y): return float(sin(x*y))
sage: s.texture('t0', ambient=0.1, diffuse=0.9, specular=0.1,
....:           opacity=1.0, color=(1.0,0,0))
sage: s.plot(f, (-4,4), (-4,4), "t0", max_depth=5, initial_depth=3,         # needs sage.symbolic
....:        num_colors=60)  # increase min_depth for better picture
sage: set_verbose(1)
sage: s.show()                                                              # needs sage.symbolic
tachyon ...
Scene contains 2713 objects.
...

>>> from sage.all import *
>>> s = Tachyon(xres=Integer(512), yres=Integer(512), camera_position=(Integer(4),-Integer(4),Integer(3)),
...             viewdir=(-Integer(4),Integer(4),-Integer(3)), raydepth=Integer(4))
>>> s.light((RealNumber('4.4'),-RealNumber('4.4'),RealNumber('4.4')), RealNumber('0.2'), (Integer(1),Integer(1),Integer(1)))
>>> def f(x,y): return float(sin(x*y))
>>> s.texture('t0', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.1'),
...           opacity=RealNumber('1.0'), color=(RealNumber('1.0'),Integer(0),Integer(0)))
>>> s.plot(f, (-Integer(4),Integer(4)), (-Integer(4),Integer(4)), "t0", max_depth=Integer(5), initial_depth=Integer(3),         # needs sage.symbolic
...        num_colors=Integer(60))  # increase min_depth for better picture
>>> set_verbose(Integer(1))
>>> s.show()                                                              # needs sage.symbolic
tachyon ...
Scene contains 2713 objects.
...

The last example shows how you can override the global Sage verbosity setting, my supplying a setting level as an argument. In this case we chose the highest verbosity setting level, 2, so much more extra technical information is shown, along with the plot.

sage: set_verbose(0)
sage: d = Tachyon(xres=512, yres=512, camera_position=(4,-4,3),
....:             viewdir=(-4,4,-3), raydepth=4)
sage: d.light((4.4,-4.4,4.4), 0.2, (1,1,1))
sage: def f(x,y): return float(sin(x*y))
sage: d.texture('t0', ambient=0.1, diffuse=0.9, specular=0.1,
....:           opacity=1.0, color=(1.0,0,0))
sage: d.plot(f,(-4,4),(-4,4),"t0",max_depth=5,initial_depth=3,              # needs sage.symbolic
....:        num_colors=60)  # increase min_depth for better picture
sage: get_verbose()
0
sage: d.show(verbose=2)                                                     # needs sage.symbolic
tachyon ...
Scene contains 2713 objects.
...
Scene contains 1 non-gridded objects
...

>>> from sage.all import *
>>> set_verbose(Integer(0))
>>> d = Tachyon(xres=Integer(512), yres=Integer(512), camera_position=(Integer(4),-Integer(4),Integer(3)),
...             viewdir=(-Integer(4),Integer(4),-Integer(3)), raydepth=Integer(4))
>>> d.light((RealNumber('4.4'),-RealNumber('4.4'),RealNumber('4.4')), RealNumber('0.2'), (Integer(1),Integer(1),Integer(1)))
>>> def f(x,y): return float(sin(x*y))
>>> d.texture('t0', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.1'),
...           opacity=RealNumber('1.0'), color=(RealNumber('1.0'),Integer(0),Integer(0)))
>>> d.plot(f,(-Integer(4),Integer(4)),(-Integer(4),Integer(4)),"t0",max_depth=Integer(5),initial_depth=Integer(3),              # needs sage.symbolic
...        num_colors=Integer(60))  # increase min_depth for better picture
>>> get_verbose()
0
>>> d.show(verbose=Integer(2))                                                     # needs sage.symbolic
tachyon ...
Scene contains 2713 objects.
...
Scene contains 1 non-gridded objects
...
smooth_triangle(vertex_1, vertex_2, vertex_3, normal_1, normal_2, normal_3, texture)[source]#

Create a triangle along with a normal vector for smoothing.

EXAMPLES:

sage: t = Tachyon()
sage: t.light((1,1,1),.1,(1,1,1))
sage: t.texture('s')
sage: t.smooth_triangle([0,0,0],[0,0,1],[0,1,0],[0,1,1],[-1,1,2],[3,0,0],'s')
sage: t._objects[2].get_vertices()
([0, 0, 0], [0, 0, 1], [0, 1, 0])
sage: t._objects[2].get_normals()
([0, 1, 1], [-1, 1, 2], [3, 0, 0])

>>> from sage.all import *
>>> t = Tachyon()
>>> t.light((Integer(1),Integer(1),Integer(1)),RealNumber('.1'),(Integer(1),Integer(1),Integer(1)))
>>> t.texture('s')
>>> t.smooth_triangle([Integer(0),Integer(0),Integer(0)],[Integer(0),Integer(0),Integer(1)],[Integer(0),Integer(1),Integer(0)],[Integer(0),Integer(1),Integer(1)],[-Integer(1),Integer(1),Integer(2)],[Integer(3),Integer(0),Integer(0)],'s')
>>> t._objects[Integer(2)].get_vertices()
([0, 0, 0], [0, 0, 1], [0, 1, 0])
>>> t._objects[Integer(2)].get_normals()
([0, 1, 1], [-1, 1, 2], [3, 0, 0])
sphere(center, radius, texture)[source]#

Create the scene information for a sphere with the given center, radius, and texture.

EXAMPLES:

sage: t = Tachyon()
sage: t.texture('sphere_texture')
sage: t.sphere((1,2,3), .1, 'sphere_texture')
sage: t._objects[1].str()
'\n        sphere center  1.0 2.0 3.0  rad 0.1 sphere_texture\n        '

>>> from sage.all import *
>>> t = Tachyon()
>>> t.texture('sphere_texture')
>>> t.sphere((Integer(1),Integer(2),Integer(3)), RealNumber('.1'), 'sphere_texture')
>>> t._objects[Integer(1)].str()
'\n        sphere center  1.0 2.0 3.0  rad 0.1 sphere_texture\n        '
str()[source]#

Return the complete tachyon scene file as a string.

EXAMPLES:

sage: t = Tachyon(xres=500,yres=500, camera_position=(2,0,0))
sage: t.light((4,3,2), 0.2, (1,1,1))
sage: t.texture('t2', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(1,0,0))
sage: t.texture('t3', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(0,1,0))
sage: t.texture('t4', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(0,0,1))
sage: t.sphere((0,0.5,0), 0.2, 't2')
sage: t.sphere((0.5,0,0), 0.2, 't3')
sage: t.sphere((0,0,0.5), 0.2, 't4')
sage: 'PLASTIC' in t.str()
True

>>> from sage.all import *
>>> t = Tachyon(xres=Integer(500),yres=Integer(500), camera_position=(Integer(2),Integer(0),Integer(0)))
>>> t.light((Integer(4),Integer(3),Integer(2)), RealNumber('0.2'), (Integer(1),Integer(1),Integer(1)))
>>> t.texture('t2', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.5'), opacity=RealNumber('1.0'), color=(Integer(1),Integer(0),Integer(0)))
>>> t.texture('t3', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.5'), opacity=RealNumber('1.0'), color=(Integer(0),Integer(1),Integer(0)))
>>> t.texture('t4', ambient=RealNumber('0.1'), diffuse=RealNumber('0.9'), specular=RealNumber('0.5'), opacity=RealNumber('1.0'), color=(Integer(0),Integer(0),Integer(1)))
>>> t.sphere((Integer(0),RealNumber('0.5'),Integer(0)), RealNumber('0.2'), 't2')
>>> t.sphere((RealNumber('0.5'),Integer(0),Integer(0)), RealNumber('0.2'), 't3')
>>> t.sphere((Integer(0),Integer(0),RealNumber('0.5')), RealNumber('0.2'), 't4')
>>> 'PLASTIC' in t.str()
True
texfunc(type=0, center=(0, 0, 0), rotate=(0, 0, 0), scale=(1, 1, 1), imagefile='')[source]#

INPUT:

  • type – (default: 0)

    1. No special texture, plain shading

    2. 3D checkerboard function, like a rubik’s cube

    3. Grit Texture, randomized surface color

    4. 3D marble texture, uses object’s base color

    5. 3D wood texture, light and dark brown, not very good yet

    6. 3D gradient noise function (can’t remember what it looks like)

    7. Don’t remember

    8. Cylindrical Image Map, requires ppm filename (with path)

    9. Spherical Image Map, requires ppm filename (with path)

    10. Planar Image Map, requires ppm filename (with path)

  • center – (default: (0,0,0))

  • rotate – (default: (0,0,0))

  • scale – (default: (1,1,1))

EXAMPLES: We draw an infinite checkerboard:

sage: t = Tachyon(camera_position=(2,7,4), look_at=(2,0,0))
sage: t.texture('black', color=(0,0,0), texfunc=1)
sage: t.plane((0,0,0),(0,0,1),'black')
sage: t.show()

>>> from sage.all import *
>>> t = Tachyon(camera_position=(Integer(2),Integer(7),Integer(4)), look_at=(Integer(2),Integer(0),Integer(0)))
>>> t.texture('black', color=(Integer(0),Integer(0),Integer(0)), texfunc=Integer(1))
>>> t.plane((Integer(0),Integer(0),Integer(0)),(Integer(0),Integer(0),Integer(1)),'black')
>>> t.show()
texture(name, ambient=0.2, diffuse=0.8, specular=0.0, opacity=1.0, color=(1.0, 0.0, 0.5), texfunc=0, phong=0, phongsize=0.5, phongtype='PLASTIC', imagefile='')[source]#

INPUT:

  • name – string; the name of the texture (to be used later)

  • ambient – (default: 0.2)

  • diffuse – (default: 0.8)

  • specular – (default: 0.0)

  • opacity – (default: 1.0)

  • color – (default: (1.0,0.0,0.5))

  • texfunc – (default: 0); a texture function; this is either the output of self.texfunc, or a number between 0 and 9, inclusive. See the docs for self.texfunc.

  • phong – (default: 0)

  • phongsize – (default: 0.5)

  • phongtype – (default: “PLASTIC”)

EXAMPLES:

We draw a scene with 4 spheres that illustrates various uses of the texture command:

sage: t = Tachyon(camera_position=(2,5,4), look_at=(2,0,0), raydepth=6)
sage: t.light((10,3,4), 1, (1,1,1))
sage: t.texture('mirror', ambient=0.05, diffuse=0.05, specular=.9,
....:           opacity=0.9, color=(.8,.8,.8))
sage: t.texture('grey', color=(.8,.8,.8), texfunc=3)
sage: t.plane((0,0,0),(0,0,1),'grey')
sage: t.sphere((4,-1,1), 1, 'mirror')
sage: t.sphere((0,-1,1), 1, 'mirror')
sage: t.sphere((2,-1,1), 0.5, 'mirror')
sage: t.sphere((2,1,1), 0.5, 'mirror')
sage: show(t)  # known bug (trac #7232)

>>> from sage.all import *
>>> t = Tachyon(camera_position=(Integer(2),Integer(5),Integer(4)), look_at=(Integer(2),Integer(0),Integer(0)), raydepth=Integer(6))
>>> t.light((Integer(10),Integer(3),Integer(4)), Integer(1), (Integer(1),Integer(1),Integer(1)))
>>> t.texture('mirror', ambient=RealNumber('0.05'), diffuse=RealNumber('0.05'), specular=RealNumber('.9'),
...           opacity=RealNumber('0.9'), color=(RealNumber('.8'),RealNumber('.8'),RealNumber('.8')))
>>> t.texture('grey', color=(RealNumber('.8'),RealNumber('.8'),RealNumber('.8')), texfunc=Integer(3))
>>> t.plane((Integer(0),Integer(0),Integer(0)),(Integer(0),Integer(0),Integer(1)),'grey')
>>> t.sphere((Integer(4),-Integer(1),Integer(1)), Integer(1), 'mirror')
>>> t.sphere((Integer(0),-Integer(1),Integer(1)), Integer(1), 'mirror')
>>> t.sphere((Integer(2),-Integer(1),Integer(1)), RealNumber('0.5'), 'mirror')
>>> t.sphere((Integer(2),Integer(1),Integer(1)), RealNumber('0.5'), 'mirror')
>>> show(t)  # known bug (trac #7232)
texture_recolor(name, colors)[source]#

Recolor default textures.

EXAMPLES:

sage: t = Tachyon()
sage: t.texture('s')
sage: q = t.texture_recolor('s',[(0,0,1)])
sage: t._objects[1]._color
(0.0, 0.0, 1.0)

>>> from sage.all import *
>>> t = Tachyon()
>>> t.texture('s')
>>> q = t.texture_recolor('s',[(Integer(0),Integer(0),Integer(1))])
>>> t._objects[Integer(1)]._color
(0.0, 0.0, 1.0)
triangle(vertex_1, vertex_2, vertex_3, texture)[source]#

Create a triangle with the given vertices and texture.

EXAMPLES:

sage: t = Tachyon()
sage: t.texture('s')
sage: t.triangle([1,2,3],[4,5,6],[7,8,10],'s')
sage: t._objects[1].get_vertices()
([1, 2, 3], [4, 5, 6], [7, 8, 10])

>>> from sage.all import *
>>> t = Tachyon()
>>> t.texture('s')
>>> t.triangle([Integer(1),Integer(2),Integer(3)],[Integer(4),Integer(5),Integer(6)],[Integer(7),Integer(8),Integer(10)],'s')
>>> t._objects[Integer(1)].get_vertices()
([1, 2, 3], [4, 5, 6], [7, 8, 10])
class sage.plot.plot3d.tachyon.TachyonSmoothTriangle(a, b, c, da, db, dc, color=0)[source]#

Bases: SmoothTriangle

A triangle along with a normal vector, which is used for smoothing.

str()[source]#

Return the scene string for a smoothed triangle.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import TachyonSmoothTriangle
sage: t = TachyonSmoothTriangle([-1,-1,-1],[0,0,0],[1,2,3],[1,0,0],[0,1,0],[0,0,1])
sage: t.str()
'\n        STRI V0  ...  1.0 0.0 0.0  N1  0.0 1.0 0.0   N2  0.0 0.0 1.0 \n             0\n        '

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import TachyonSmoothTriangle
>>> t = TachyonSmoothTriangle([-Integer(1),-Integer(1),-Integer(1)],[Integer(0),Integer(0),Integer(0)],[Integer(1),Integer(2),Integer(3)],[Integer(1),Integer(0),Integer(0)],[Integer(0),Integer(1),Integer(0)],[Integer(0),Integer(0),Integer(1)])
>>> t.str()
'\n        STRI V0  ...  1.0 0.0 0.0  N1  0.0 1.0 0.0   N2  0.0 0.0 1.0 \n             0\n        '
class sage.plot.plot3d.tachyon.TachyonTriangle(a, b, c, color=0)[source]#

Bases: Triangle

Basic triangle class.

str()[source]#

Return the scene string for a triangle.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import TachyonTriangle
sage: t = TachyonTriangle([-1,-1,-1],[0,0,0],[1,2,3])
sage: t.str()
'\n        TRI V0  -1.0 -1.0 -1.0   V1  0.0 0.0 0.0    V2  1.0 2.0 3.0 \n            0\n        '

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import TachyonTriangle
>>> t = TachyonTriangle([-Integer(1),-Integer(1),-Integer(1)],[Integer(0),Integer(0),Integer(0)],[Integer(1),Integer(2),Integer(3)])
>>> t.str()
'\n        TRI V0  -1.0 -1.0 -1.0   V1  0.0 0.0 0.0    V2  1.0 2.0 3.0 \n            0\n        '
class sage.plot.plot3d.tachyon.TachyonTriangleFactory(tach, tex)[source]#

Bases: TriangleFactory

A class to produce triangles of various rendering types.

get_colors(list)[source]#

Return a list of color labels.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import TachyonTriangleFactory
sage: t = Tachyon()
sage: t.texture('s')
sage: ttf = TachyonTriangleFactory(t, 's')
sage: ttf.get_colors([(1,1,1)])
['SAGETEX1_0']

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import TachyonTriangleFactory
>>> t = Tachyon()
>>> t.texture('s')
>>> ttf = TachyonTriangleFactory(t, 's')
>>> ttf.get_colors([(Integer(1),Integer(1),Integer(1))])
['SAGETEX1_0']
smooth_triangle(a, b, c, da, db, dc, color=None)[source]#

Create a TachyonSmoothTriangle.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import TachyonTriangleFactory
sage: t = Tachyon()
sage: t.texture('s')
sage: ttf = TachyonTriangleFactory(t, 's')
sage: ttfst = ttf.smooth_triangle([0,0,0],[1,0,0],[0,0,1],[1,1,1],[1,2,3],[-1,-1,2])
sage: ttfst.str()
'\n        STRI V0  0.0 0.0 0.0  ...'

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import TachyonTriangleFactory
>>> t = Tachyon()
>>> t.texture('s')
>>> ttf = TachyonTriangleFactory(t, 's')
>>> ttfst = ttf.smooth_triangle([Integer(0),Integer(0),Integer(0)],[Integer(1),Integer(0),Integer(0)],[Integer(0),Integer(0),Integer(1)],[Integer(1),Integer(1),Integer(1)],[Integer(1),Integer(2),Integer(3)],[-Integer(1),-Integer(1),Integer(2)])
>>> ttfst.str()
'\n        STRI V0  0.0 0.0 0.0  ...'
triangle(a, b, c, color=None)[source]#

Create a TachyonTriangle with vertices a, b, and c.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import TachyonTriangleFactory
sage: t = Tachyon()
sage: t.texture('s')
sage: ttf = TachyonTriangleFactory(t, 's')
sage: ttft = ttf.triangle([1,2,3],[3,2,1],[0,2,1])
sage: ttft.str()
'\n        TRI V0  1.0 2.0 3.0   V1  3.0 2.0 1.0    V2  0.0 2.0 1.0 \n            s\n        '

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import TachyonTriangleFactory
>>> t = Tachyon()
>>> t.texture('s')
>>> ttf = TachyonTriangleFactory(t, 's')
>>> ttft = ttf.triangle([Integer(1),Integer(2),Integer(3)],[Integer(3),Integer(2),Integer(1)],[Integer(0),Integer(2),Integer(1)])
>>> ttft.str()
'\n        TRI V0  1.0 2.0 3.0   V1  3.0 2.0 1.0    V2  0.0 2.0 1.0 \n            s\n        '
class sage.plot.plot3d.tachyon.Texfunc(ttype=0, center=(0, 0, 0), rotate=(0, 0, 0), scale=(1, 1, 1), imagefile='')[source]#

Bases: object

Create a texture function.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import Texfunc
sage: t = Texfunc()
sage: t._ttype
0

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import Texfunc
>>> t = Texfunc()
>>> t._ttype
0
str()[source]#

Return the scene string for this texture function.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import Texfunc
sage: t = Texfunc()
sage: t.str()
'0'

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import Texfunc
>>> t = Texfunc()
>>> t.str()
'0'
class sage.plot.plot3d.tachyon.Texture(name, ambient=0.2, diffuse=0.8, specular=0.0, opacity=1.0, color=(1.0, 0.0, 0.5), texfunc=0, phong=0, phongsize=0, phongtype='PLASTIC', imagefile='')[source]#

Bases: object

Store texture information.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import Texture
sage: t = Texture('w')
sage: t.str().split()[2:6]
['ambient', '0.2', 'diffuse', '0.8']

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import Texture
>>> t = Texture('w')
>>> t.str().split()[Integer(2):Integer(6)]
['ambient', '0.2', 'diffuse', '0.8']
recolor(name, color)[source]#

Return a texture with the new given color.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import Texture
sage: t2 = Texture('w')
sage: t2w = t2.recolor('w2', (.1,.2,.3))
sage: t2ws = t2w.str()
sage: color_index = t2ws.find('color')
sage: t2ws[color_index:color_index+20]
'color  0.1 0.2 0.3  '

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import Texture
>>> t2 = Texture('w')
>>> t2w = t2.recolor('w2', (RealNumber('.1'),RealNumber('.2'),RealNumber('.3')))
>>> t2ws = t2w.str()
>>> color_index = t2ws.find('color')
>>> t2ws[color_index:color_index+Integer(20)]
'color  0.1 0.2 0.3  '
str()[source]#

Return the scene string for this texture.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import Texture
sage: t = Texture('w')
sage: t.str().split()[2:6]
['ambient', '0.2', 'diffuse', '0.8']

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import Texture
>>> t = Texture('w')
>>> t.str().split()[Integer(2):Integer(6)]
['ambient', '0.2', 'diffuse', '0.8']
sage.plot.plot3d.tachyon.tostr(s, length=3, out_type=<class 'float'>)[source]#

Convert vector information to a space-separated string.

EXAMPLES:

sage: from sage.plot.plot3d.tachyon import tostr
sage: tostr((1,1,1))
' 1.0 1.0 1.0 '
sage: tostr('2 3 2')
'2 3 2'

>>> from sage.all import *
>>> from sage.plot.plot3d.tachyon import tostr
>>> tostr((Integer(1),Integer(1),Integer(1)))
' 1.0 1.0 1.0 '
>>> tostr('2 3 2')
'2 3 2'