Basic objects such as Sphere, Box, Cone, etc.¶

AUTHORS:

Robert Bradshaw 2007-02: initial version
Robert Bradshaw 2007-08: obj/tachyon rendering, much updating
Robert Bradshaw 2007-08: cythonization

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import *
sage: S = Sphere(.5, color='yellow')
sage: S += Cone(.5, .5, color='red').translate(0,0,.3)
sage: S += Sphere(.1, color='white').translate(.45,-.1,.15)
sage: S += Sphere(.05, color='black').translate(.51,-.1,.17)
sage: S += Sphere(.1, color='white').translate(.45, .1,.15)
sage: S += Sphere(.05, color='black').translate(.51, .1,.17)
sage: S += Sphere(.1, color='yellow').translate(.5, 0, -.2)
sage: S.show()
sage: S.scale(1,1,2).show()

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import *
>>> S = Sphere(RealNumber('.5'), color='yellow')
>>> S += Cone(RealNumber('.5'), RealNumber('.5'), color='red').translate(Integer(0),Integer(0),RealNumber('.3'))
>>> S += Sphere(RealNumber('.1'), color='white').translate(RealNumber('.45'),-RealNumber('.1'),RealNumber('.15'))
>>> S += Sphere(RealNumber('.05'), color='black').translate(RealNumber('.51'),-RealNumber('.1'),RealNumber('.17'))
>>> S += Sphere(RealNumber('.1'), color='white').translate(RealNumber('.45'), RealNumber('.1'),RealNumber('.15'))
>>> S += Sphere(RealNumber('.05'), color='black').translate(RealNumber('.51'), RealNumber('.1'),RealNumber('.17'))
>>> S += Sphere(RealNumber('.1'), color='yellow').translate(RealNumber('.5'), Integer(0), -RealNumber('.2'))
>>> S.show()
>>> S.scale(Integer(1),Integer(1),Integer(2)).show()

Sage

sage: from sage.plot.plot3d.shapes import *
sage: Torus(.7, .2, color=(0,.3,0)).show()

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import *
>>> Torus(RealNumber('.7'), RealNumber('.2'), color=(Integer(0),RealNumber('.3'),Integer(0))).show()

class sage.plot.plot3d.shapes.Box(*size, **kwds)[source]¶

Bases: IndexFaceSet

Return a box.

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Box

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Box

A square black box:

Sage

sage: show(Box([1,1,1]), color='black')

Python

>>> from sage.all import *
>>> show(Box([Integer(1),Integer(1),Integer(1)]), color='black')

A red rectangular box:

Sage

sage: show(Box([2,3,4], color='red'))

Python

>>> from sage.all import *
>>> show(Box([Integer(2),Integer(3),Integer(4)], color='red'))

A stack of boxes:

Sage

sage: show(sum(Box([2,3,1], color='red').translate((0,0,6*i))
....:          for i in [0..3]))

Python

>>> from sage.all import *
>>> show(sum(Box([Integer(2),Integer(3),Integer(1)], color='red').translate((Integer(0),Integer(0),Integer(6)*i))
...          for i in (ellipsis_range(Integer(0),Ellipsis,Integer(3)))))

A sinusoidal stack of multicolored boxes:

Sage

sage: B = sum(Box([2,4,1/4],                                                    # needs sage.symbolic
....:             color=(i/4,i/5,1)).translate((sin(i),0,5-i))
....:         for i in [0..20])
sage: show(B, figsize=6)                                                        # needs sage.symbolic

Python

>>> from sage.all import *
>>> B = sum(Box([Integer(2),Integer(4),Integer(1)/Integer(4)],                                                    # needs sage.symbolic
...             color=(i/Integer(4),i/Integer(5),Integer(1))).translate((sin(i),Integer(0),Integer(5)-i))
...         for i in (ellipsis_range(Integer(0),Ellipsis,Integer(20))))
>>> show(B, figsize=Integer(6))                                                        # needs sage.symbolic

bounding_box()[source]¶

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Box
sage: Box([1,2,3]).bounding_box()
((-1.0, -2.0, -3.0), (1.0, 2.0, 3.0))

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Box
>>> Box([Integer(1),Integer(2),Integer(3)]).bounding_box()
((-1.0, -2.0, -3.0), (1.0, 2.0, 3.0))

x3d_geometry()[source]¶

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Box
sage: Box([1,2,1/4]).x3d_geometry()
"<Box size='1.0 2.0 0.25'/>"

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Box
>>> Box([Integer(1),Integer(2),Integer(1)/Integer(4)]).x3d_geometry()
"<Box size='1.0 2.0 0.25'/>"

sage.plot.plot3d.shapes.ColorCube(size, colors, opacity=1, **kwds)[source]¶

Return a cube with given size and sides with given colors.

INPUT:

size – 3-tuple of sizes (same as for box and frame)
colors – list of either 3 or 6 colors
opacity – (default: 1) opacity of cube sides
**kwds – passed to the face constructor

OUTPUT: a 3d graphics object

EXAMPLES:

A color cube with translucent sides:

Sage

sage: from sage.plot.plot3d.shapes import ColorCube
sage: c = ColorCube([1,2,3], ['red', 'blue', 'green', 'black', 'white', 'orange'], opacity=0.5)
sage: c.show()

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import ColorCube
>>> c = ColorCube([Integer(1),Integer(2),Integer(3)], ['red', 'blue', 'green', 'black', 'white', 'orange'], opacity=RealNumber('0.5'))
>>> c.show()

Sage

sage: list(c.texture_set())[0].opacity
0.5

Python

>>> from sage.all import *
>>> list(c.texture_set())[Integer(0)].opacity
0.5

If you omit the last 3 colors then the first three are repeated (with repeated colors on opposing faces):

Sage

sage: c = ColorCube([0.5,0.5,0.5], ['red', 'blue', 'green'])

Python

>>> from sage.all import *
>>> c = ColorCube([RealNumber('0.5'),RealNumber('0.5'),RealNumber('0.5')], ['red', 'blue', 'green'])

class sage.plot.plot3d.shapes.Cone[source]¶

Bases: ParametricSurface

A cone, with base in the xy-plane pointing up the z-axis.

INPUT:

radius – positive real number
height – positive real number
closed – whether or not to include the base (default: True)
**kwds – passed to the ParametricSurface constructor

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Cone
sage: c = Cone(3/2, 1, color='red')
sage: c += Cone(1, 2, color='yellow').translate(3, 0, 0)
sage: c.show(aspect_ratio=1)

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Cone
>>> c = Cone(Integer(3)/Integer(2), Integer(1), color='red')
>>> c += Cone(Integer(1), Integer(2), color='yellow').translate(Integer(3), Integer(0), Integer(0))
>>> c.show(aspect_ratio=Integer(1))

We may omit the base:

Sage

sage: Cone(1, 1, closed=False)
Graphics3d Object

Python

>>> from sage.all import *
>>> Cone(Integer(1), Integer(1), closed=False)
Graphics3d Object

A spiky plot of the sine function:

Sage

sage: sum(Cone(.1, sin(n), color='yellow').translate(n, sin(n), 0)              # needs sage.symbolic
....:     for n in [0..10, step=.1])
Graphics3d Object

Python

>>> from sage.all import *
>>> sum(Cone(RealNumber('.1'), sin(n), color='yellow').translate(n, sin(n), Integer(0))              # needs sage.symbolic
...     for n in (ellipsis_range(Integer(0),Ellipsis,Integer(10), step=RealNumber('.1'))))
Graphics3d Object

A Christmas tree:

Sage

sage: T = sum(Cone(exp(-n/5), 4/3*exp(-n/5),                                    # needs sage.symbolic
....:              color=(0, .5, 0)).translate(0, 0, -3*exp(-n/5))
....:         for n in [1..7])
sage: T += Cone(1/8, 1, color='brown').translate(0, 0, -3)                      # needs sage.symbolic
sage: T.show(aspect_ratio=1, frame=False)                                       # needs sage.symbolic

Python

>>> from sage.all import *
>>> T = sum(Cone(exp(-n/Integer(5)), Integer(4)/Integer(3)*exp(-n/Integer(5)),                                    # needs sage.symbolic
...              color=(Integer(0), RealNumber('.5'), Integer(0))).translate(Integer(0), Integer(0), -Integer(3)*exp(-n/Integer(5)))
...         for n in (ellipsis_range(Integer(1),Ellipsis,Integer(7))))
>>> T += Cone(Integer(1)/Integer(8), Integer(1), color='brown').translate(Integer(0), Integer(0), -Integer(3))                      # needs sage.symbolic
>>> T.show(aspect_ratio=Integer(1), frame=False)                                       # needs sage.symbolic

get_grid(ds)[source]¶

Return the grid on which to evaluate this parametric surface.

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Cone
sage: Cone(1, 3, closed=True).get_grid(100)
([1, 0, -1], [0.0, 1.2566..., 2.5132..., 3.7699..., 5.0265..., 0.0])
sage: Cone(1, 3, closed=False).get_grid(100)
([1, 0], [0.0, 1.2566..., 2.5132..., 3.7699..., 5.0265..., 0.0])
sage: len(Cone(1, 3).get_grid(.001)[1])
38

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Cone
>>> Cone(Integer(1), Integer(3), closed=True).get_grid(Integer(100))
([1, 0, -1], [0.0, 1.2566..., 2.5132..., 3.7699..., 5.0265..., 0.0])
>>> Cone(Integer(1), Integer(3), closed=False).get_grid(Integer(100))
([1, 0], [0.0, 1.2566..., 2.5132..., 3.7699..., 5.0265..., 0.0])
>>> len(Cone(Integer(1), Integer(3)).get_grid(RealNumber('.001'))[Integer(1)])
38

x3d_geometry()[source]¶

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Cone
sage: Cone(1, 3).x3d_geometry()
"<Cone bottomRadius='1.0' height='3.0'/>"

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Cone
>>> Cone(Integer(1), Integer(3)).x3d_geometry()
"<Cone bottomRadius='1.0' height='3.0'/>"

class sage.plot.plot3d.shapes.Cylinder[source]¶

Bases: ParametricSurface

A cone, with base in the xy-plane pointing up the z-axis.

INPUT:

radius – positive real number
height – positive real number
closed – whether or not to include the ends (default: True)
**kwds – passed to the ParametricSurface constructor

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Cylinder
sage: c = Cylinder(3/2, 1, color='red')
sage: c += Cylinder(1, 2, color='yellow').translate(3, 0, 0)
sage: c.show(aspect_ratio=1)

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Cylinder
>>> c = Cylinder(Integer(3)/Integer(2), Integer(1), color='red')
>>> c += Cylinder(Integer(1), Integer(2), color='yellow').translate(Integer(3), Integer(0), Integer(0))
>>> c.show(aspect_ratio=Integer(1))

We may omit the base:

Sage

sage: Cylinder(1, 1, closed=False)
Graphics3d Object

Python

>>> from sage.all import *
>>> Cylinder(Integer(1), Integer(1), closed=False)
Graphics3d Object

Some gears:

Sage

sage: # needs sage.symbolic
sage: G = Cylinder(1, .5) + Cylinder(.25, 3).translate(0, 0, -3)
sage: G += sum(Cylinder(.2, 1).translate(cos(2*pi*n/9), sin(2*pi*n/9), 0)
....:          for n in [1..9])
sage: G += G.translate(2.3, 0, -.5)
sage: G += G.translate(3.5, 2, -1)
sage: G.show(aspect_ratio=1, frame=False)

Python

>>> from sage.all import *
>>> # needs sage.symbolic
>>> G = Cylinder(Integer(1), RealNumber('.5')) + Cylinder(RealNumber('.25'), Integer(3)).translate(Integer(0), Integer(0), -Integer(3))
>>> G += sum(Cylinder(RealNumber('.2'), Integer(1)).translate(cos(Integer(2)*pi*n/Integer(9)), sin(Integer(2)*pi*n/Integer(9)), Integer(0))
...          for n in (ellipsis_range(Integer(1),Ellipsis,Integer(9))))
>>> G += G.translate(RealNumber('2.3'), Integer(0), -RealNumber('.5'))
>>> G += G.translate(RealNumber('3.5'), Integer(2), -Integer(1))
>>> G.show(aspect_ratio=Integer(1), frame=False)

bounding_box()[source]¶

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Cylinder
sage: Cylinder(1, 2).bounding_box()
((-1.0, -1.0, 0), (1.0, 1.0, 2.0))

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Cylinder
>>> Cylinder(Integer(1), Integer(2)).bounding_box()
((-1.0, -1.0, 0), (1.0, 1.0, 2.0))

get_endpoints(transform=None)[source]¶

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Cylinder
sage: from sage.plot.plot3d.transform import Transformation
sage: Cylinder(1, 5).get_endpoints()
((0, 0, 0), (0, 0, 5.0))
sage: Cylinder(1, 5).get_endpoints(Transformation(trans=(1,2,3),
....:                                             scale=(2,2,2)))
((1.0, 2.0, 3.0), (1.0, 2.0, 13.0))

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Cylinder
>>> from sage.plot.plot3d.transform import Transformation
>>> Cylinder(Integer(1), Integer(5)).get_endpoints()
((0, 0, 0), (0, 0, 5.0))
>>> Cylinder(Integer(1), Integer(5)).get_endpoints(Transformation(trans=(Integer(1),Integer(2),Integer(3)),
...                                             scale=(Integer(2),Integer(2),Integer(2))))
((1.0, 2.0, 3.0), (1.0, 2.0, 13.0))

get_grid(ds)[source]¶

Return the grid on which to evaluate this parametric surface.

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Cylinder
sage: Cylinder(1, 3, closed=True).get_grid(100)
([2, 1, -1, -2], [0.0, 1.2566..., 2.5132..., 3.7699..., 5.0265..., 0.0])
sage: Cylinder(1, 3, closed=False).get_grid(100)
([1, -1], [0.0, 1.2566..., 2.5132..., 3.7699..., 5.0265..., 0.0])
sage: len(Cylinder(1, 3).get_grid(.001)[1])
38

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Cylinder
>>> Cylinder(Integer(1), Integer(3), closed=True).get_grid(Integer(100))
([2, 1, -1, -2], [0.0, 1.2566..., 2.5132..., 3.7699..., 5.0265..., 0.0])
>>> Cylinder(Integer(1), Integer(3), closed=False).get_grid(Integer(100))
([1, -1], [0.0, 1.2566..., 2.5132..., 3.7699..., 5.0265..., 0.0])
>>> len(Cylinder(Integer(1), Integer(3)).get_grid(RealNumber('.001'))[Integer(1)])
38

get_radius(transform=None)[source]¶

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Cylinder
sage: from sage.plot.plot3d.transform import Transformation
sage: Cylinder(3, 1).get_radius()
3.0
sage: Cylinder(3, 1).get_radius(Transformation(trans=(1,2,3),
....:                                          scale=(2,2,2)))
6.0

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Cylinder
>>> from sage.plot.plot3d.transform import Transformation
>>> Cylinder(Integer(3), Integer(1)).get_radius()
3.0
>>> Cylinder(Integer(3), Integer(1)).get_radius(Transformation(trans=(Integer(1),Integer(2),Integer(3)),
...                                          scale=(Integer(2),Integer(2),Integer(2))))
6.0

jmol_repr(render_params)[source]¶

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Cylinder

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Cylinder

For thin cylinders, lines are used:

Sage

sage: C = Cylinder(.1, 4)
sage: C.jmol_repr(C.default_render_params())
['\ndraw line_1 width 0.1 {0 0 0} {0 0 4.0}\ncolor $line_1  [102,102,255]\n']

Python

>>> from sage.all import *
>>> C = Cylinder(RealNumber('.1'), Integer(4))
>>> C.jmol_repr(C.default_render_params())
['\ndraw line_1 width 0.1 {0 0 0} {0 0 4.0}\ncolor $line_1  [102,102,255]\n']

For anything larger, we use a pmesh:

Sage

sage: C = Cylinder(3, 1, closed=False)
sage: C.jmol_repr(C.testing_render_params())
['pmesh obj_1 "obj_1.pmesh"\ncolor pmesh  [102,102,255]']

Python

>>> from sage.all import *
>>> C = Cylinder(Integer(3), Integer(1), closed=False)
>>> C.jmol_repr(C.testing_render_params())
['pmesh obj_1 "obj_1.pmesh"\ncolor pmesh  [102,102,255]']

tachyon_repr(render_params)[source]¶

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Cylinder
sage: C = Cylinder(1/2, 4, closed=False)
sage: C.tachyon_repr(C.default_render_params())
'FCylinder\n   Base 0 0 0\n   Apex 0 0 4.0\n   Rad 0.5\n   texture...     '
sage: C = Cylinder(1, 2)
sage: C.tachyon_repr(C.default_render_params())
    ['Ring Center 0 0 0 Normal 0 0 1 Inner 0 Outer 1.0 texture...',
     'FCylinder\n   Base 0 0 0\n   Apex 0 0 2.0\n   Rad 1.0\n   texture...     ',
     'Ring Center 0 0 2.0 Normal 0 0 1 Inner 0 Outer 1.0 texture...']

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Cylinder
>>> C = Cylinder(Integer(1)/Integer(2), Integer(4), closed=False)
>>> C.tachyon_repr(C.default_render_params())
'FCylinder\n   Base 0 0 0\n   Apex 0 0 4.0\n   Rad 0.5\n   texture...     '
>>> C = Cylinder(Integer(1), Integer(2))
>>> C.tachyon_repr(C.default_render_params())
    ['Ring Center 0 0 0 Normal 0 0 1 Inner 0 Outer 1.0 texture...',
     'FCylinder\n   Base 0 0 0\n   Apex 0 0 2.0\n   Rad 1.0\n   texture...     ',
     'Ring Center 0 0 2.0 Normal 0 0 1 Inner 0 Outer 1.0 texture...']

x3d_geometry()[source]¶

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Cylinder
sage: Cylinder(1, 2).x3d_geometry()
"<Cylinder radius='1.0' height='2.0'/>"

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Cylinder
>>> Cylinder(Integer(1), Integer(2)).x3d_geometry()
"<Cylinder radius='1.0' height='2.0'/>"

sage.plot.plot3d.shapes.LineSegment(start, end, thickness=1, radius=None, **kwds)[source]¶

Create a line segment, which is drawn as a cylinder from start to end with radius radius.

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import LineSegment, Sphere
sage: P = (0,0,0.1)
sage: Q = (0.5,0.6,0.7)
sage: S = Sphere(.2, color='red').translate(P)
sage: S += Sphere(.2, color='blue').translate(Q)
sage: S += LineSegment(P, Q, .05, color='black')
sage: S.show()

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import LineSegment, Sphere
>>> P = (Integer(0),Integer(0),RealNumber('0.1'))
>>> Q = (RealNumber('0.5'),RealNumber('0.6'),RealNumber('0.7'))
>>> S = Sphere(RealNumber('.2'), color='red').translate(P)
>>> S += Sphere(RealNumber('.2'), color='blue').translate(Q)
>>> S += LineSegment(P, Q, RealNumber('.05'), color='black')
>>> S.show()

Sage

sage: S = Sphere(.1, color='red').translate(P)
sage: S += Sphere(.1, color='blue').translate(Q)
sage: S += LineSegment(P, Q, .15, color='black')
sage: S.show()

Python

>>> from sage.all import *
>>> S = Sphere(RealNumber('.1'), color='red').translate(P)
>>> S += Sphere(RealNumber('.1'), color='blue').translate(Q)
>>> S += LineSegment(P, Q, RealNumber('.15'), color='black')
>>> S.show()

AUTHOR:

Robert Bradshaw

class sage.plot.plot3d.shapes.Sphere[source]¶

Bases: ParametricSurface

This class represents a sphere centered at the origin.

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Sphere
sage: Sphere(3)
Graphics3d Object

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Sphere
>>> Sphere(Integer(3))
Graphics3d Object

Plot with aspect_ratio=1 to see it unsquashed:

Sage

sage: S = Sphere(3, color='blue') + Sphere(2, color='red').translate(0,3,0)
sage: S.show(aspect_ratio=1)

Python

>>> from sage.all import *
>>> S = Sphere(Integer(3), color='blue') + Sphere(Integer(2), color='red').translate(Integer(0),Integer(3),Integer(0))
>>> S.show(aspect_ratio=Integer(1))

Scale to get an ellipsoid:

Sage

sage: S = Sphere(1).scale(1,2,1/2)
sage: S.show(aspect_ratio=1)

Python

>>> from sage.all import *
>>> S = Sphere(Integer(1)).scale(Integer(1),Integer(2),Integer(1)/Integer(2))
>>> S.show(aspect_ratio=Integer(1))

bounding_box()[source]¶

Return the bounding box that contains this sphere.

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Sphere
sage: Sphere(3).bounding_box()
((-3.0, -3.0, -3.0), (3.0, 3.0, 3.0))

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Sphere
>>> Sphere(Integer(3)).bounding_box()
((-3.0, -3.0, -3.0), (3.0, 3.0, 3.0))

get_grid(ds)[source]¶

Return the range of variables to be evaluated on to render as a parametric surface.

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Sphere
sage: Sphere(1).get_grid(100)
([-10.0, ..., 10.0],
 [0.0, ..., 3.141592653589793, ..., 0.0])

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Sphere
>>> Sphere(Integer(1)).get_grid(Integer(100))
([-10.0, ..., 10.0],
 [0.0, ..., 3.141592653589793, ..., 0.0])

jmol_repr(render_params)[source]¶

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Sphere

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Sphere

Jmol has native code for handling spheres:

Sage

sage: S = Sphere(2)
sage: S.jmol_repr(S.default_render_params())
['isosurface sphere_1  center {0 0 0} sphere 2.0\ncolor isosurface  [102,102,255]']
sage: S.translate(10, 100, 1000).jmol_repr(S.default_render_params())
[['isosurface sphere_1  center {10.0 100.0 1000.0} sphere 2.0\ncolor isosurface  [102,102,255]']]

Python

>>> from sage.all import *
>>> S = Sphere(Integer(2))
>>> S.jmol_repr(S.default_render_params())
['isosurface sphere_1  center {0 0 0} sphere 2.0\ncolor isosurface  [102,102,255]']
>>> S.translate(Integer(10), Integer(100), Integer(1000)).jmol_repr(S.default_render_params())
[['isosurface sphere_1  center {10.0 100.0 1000.0} sphere 2.0\ncolor isosurface  [102,102,255]']]

It cannot natively handle ellipsoids:

Sage

sage: Sphere(1).scale(2, 3, 4).jmol_repr(S.testing_render_params())
[['pmesh obj_2 "obj_2.pmesh"\ncolor pmesh  [102,102,255]']]

Python

>>> from sage.all import *
>>> Sphere(Integer(1)).scale(Integer(2), Integer(3), Integer(4)).jmol_repr(S.testing_render_params())
[['pmesh obj_2 "obj_2.pmesh"\ncolor pmesh  [102,102,255]']]

Small spheres need extra hints to render well:

Sage

sage: Sphere(.01).jmol_repr(S.default_render_params())
['isosurface sphere_1 resolution 100 center {0 0 0} sphere 0.01\ncolor isosurface  [102,102,255]']

Python

>>> from sage.all import *
>>> Sphere(RealNumber('.01')).jmol_repr(S.default_render_params())
['isosurface sphere_1 resolution 100 center {0 0 0} sphere 0.01\ncolor isosurface  [102,102,255]']

tachyon_repr(render_params)[source]¶

Tachyon can natively handle spheres. Ellipsoids rendering is done as a parametric surface.

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Sphere
sage: S = Sphere(2)
sage: S.tachyon_repr(S.default_render_params())
'Sphere center 0 0 0 Rad 2.0 texture...'
sage: S.translate(1, 2, 3).scale(3).tachyon_repr(S.default_render_params())
[['Sphere center 3.0 6.0 9.0 Rad 6.0 texture...']]
sage: S.scale(1,1/2,1/4).tachyon_repr(S.default_render_params())
[['TRI V0 0 0 -0.5 V1 0.308116 0.0271646 -0.493844 V2 0.312869 0 -0.493844',
  'texture...',
   ...
  'TRI V0 0.308116 -0.0271646 0.493844 V1 0.312869 0 0.493844 V2 0 0 0.5',
  'texture...']]

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Sphere
>>> S = Sphere(Integer(2))
>>> S.tachyon_repr(S.default_render_params())
'Sphere center 0 0 0 Rad 2.0 texture...'
>>> S.translate(Integer(1), Integer(2), Integer(3)).scale(Integer(3)).tachyon_repr(S.default_render_params())
[['Sphere center 3.0 6.0 9.0 Rad 6.0 texture...']]
>>> S.scale(Integer(1),Integer(1)/Integer(2),Integer(1)/Integer(4)).tachyon_repr(S.default_render_params())
[['TRI V0 0 0 -0.5 V1 0.308116 0.0271646 -0.493844 V2 0.312869 0 -0.493844',
  'texture...',
   ...
  'TRI V0 0.308116 -0.0271646 0.493844 V1 0.312869 0 0.493844 V2 0 0 0.5',
  'texture...']]

x3d_geometry()[source]¶

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Sphere
sage: Sphere(12).x3d_geometry()
"<Sphere radius='12.0'/>"

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Sphere
>>> Sphere(Integer(12)).x3d_geometry()
"<Sphere radius='12.0'/>"

class sage.plot.plot3d.shapes.Text(string, **kwds)[source]¶

Bases: PrimitiveObject

A text label attached to a point in 3d space. It always starts at the origin, translate it to move it elsewhere.

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Text
sage: Text("Just a lonely label.")
Graphics3d Object

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Text
>>> Text("Just a lonely label.")
Graphics3d Object

Sage

sage: pts = [(RealField(10)^3).random_element() for k in range(20)]
sage: sum(Text(str(P)).translate(P) for P in pts)
Graphics3d Object

Python

>>> from sage.all import *
>>> pts = [(RealField(Integer(10))**Integer(3)).random_element() for k in range(Integer(20))]
>>> sum(Text(str(P)).translate(P) for P in pts)
Graphics3d Object

bounding_box()[source]¶

Text labels have no extent:

Sage

sage: from sage.plot.plot3d.shapes import Text
sage: Text("Hi").bounding_box()
((0, 0, 0), (0, 0, 0))

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Text
>>> Text("Hi").bounding_box()
((0, 0, 0), (0, 0, 0))

jmol_repr(render_params)[source]¶

Labels in jmol must be attached to atoms.

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Text
sage: T = Text("Hi")
sage: T.jmol_repr(T.testing_render_params())
['select atomno = 1', 'color atom  [102,102,255]', 'label "Hi"']
sage: T = Text("Hi").translate(-1, 0, 0) + Text("Bye").translate(1, 0, 0)
sage: T.jmol_repr(T.testing_render_params())
[[['select atomno = 1', 'color atom  [102,102,255]', 'label "Hi"']],
 [['select atomno = 2', 'color atom  [102,102,255]', 'label "Bye"']]]

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Text
>>> T = Text("Hi")
>>> T.jmol_repr(T.testing_render_params())
['select atomno = 1', 'color atom  [102,102,255]', 'label "Hi"']
>>> T = Text("Hi").translate(-Integer(1), Integer(0), Integer(0)) + Text("Bye").translate(Integer(1), Integer(0), Integer(0))
>>> T.jmol_repr(T.testing_render_params())
[[['select atomno = 1', 'color atom  [102,102,255]', 'label "Hi"']],
 [['select atomno = 2', 'color atom  [102,102,255]', 'label "Bye"']]]

obj_repr(render_params)[source]¶

The obj file format does not support text strings:

Sage

sage: from sage.plot.plot3d.shapes import Text
sage: Text("Hi").obj_repr(None)
''

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Text
>>> Text("Hi").obj_repr(None)
''

tachyon_repr(render_params)[source]¶

Strings are not yet supported in Tachyon, so we ignore them for now:

Sage

sage: from sage.plot.plot3d.shapes import Text
sage: Text("Hi").tachyon_repr(None)
''

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Text
>>> Text("Hi").tachyon_repr(None)
''

threejs_repr(render_params)[source]¶

Return representation of the text suitable for plotting in three.js.

EXAMPLES:

Sage

sage: T = text3d("Hi", (1, 2, 3), color='red', fontfamily='serif',
....:            fontweight='bold', fontstyle='italic', fontsize=20,
....:            opacity=0.5)
sage: T.threejs_repr(T.default_render_params())
[('text',
  {'color': '#ff0000',
   'fontFamily': ['serif'],
   'fontSize': 20.0,
   'fontStyle': 'italic',
   'fontWeight': 'bold',
   'opacity': 0.5,
   'text': 'Hi',
   'x': 1.0,
   'y': 2.0,
   'z': 3.0})]

Python

>>> from sage.all import *
>>> T = text3d("Hi", (Integer(1), Integer(2), Integer(3)), color='red', fontfamily='serif',
...            fontweight='bold', fontstyle='italic', fontsize=Integer(20),
...            opacity=RealNumber('0.5'))
>>> T.threejs_repr(T.default_render_params())
[('text',
  {'color': '#ff0000',
   'fontFamily': ['serif'],
   'fontSize': 20.0,
   'fontStyle': 'italic',
   'fontWeight': 'bold',
   'opacity': 0.5,
   'text': 'Hi',
   'x': 1.0,
   'y': 2.0,
   'z': 3.0})]

x3d_geometry()[source]¶

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Text
sage: Text("Hi").x3d_geometry()
"<Text string='Hi' solid='true'/>"

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Text
>>> Text("Hi").x3d_geometry()
"<Text string='Hi' solid='true'/>"

class sage.plot.plot3d.shapes.Torus[source]¶

Bases: ParametricSurface

INPUT:

R – (default: 1) outer radius
r – (default: .3) inner radius

OUTPUT: a 3d torus

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Torus
sage: Torus(1, .2).show(aspect_ratio=1)

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Torus
>>> Torus(Integer(1), RealNumber('.2')).show(aspect_ratio=Integer(1))

Sage

sage: Torus(1, .7, color='red').show(aspect_ratio=1)

Python

>>> from sage.all import *
>>> Torus(Integer(1), RealNumber('.7'), color='red').show(aspect_ratio=Integer(1))

A rubberband ball:

Sage

sage: show(sum(Torus(1, .03, color=(1, t/30.0, 0)).rotate((1,1,1), t)
....:          for t in range(30)))

Python

>>> from sage.all import *
>>> show(sum(Torus(Integer(1), RealNumber('.03'), color=(Integer(1), t/RealNumber('30.0'), Integer(0))).rotate((Integer(1),Integer(1),Integer(1)), t)
...          for t in range(Integer(30))))

Mmm… doughnuts:

Sage

sage: D = Torus(1, .4, color=(.5, .3, .2))
sage: D += Torus(1, .3, color='yellow').translate(0, 0, .15)
sage: G = sum(D.translate(RDF.random_element(-.2, .2),
....:                     RDF.random_element(-.2, .2),
....:                     .8*t)
....:         for t in range(10))
sage: G.show(aspect_ratio=1, frame=False)

Python

>>> from sage.all import *
>>> D = Torus(Integer(1), RealNumber('.4'), color=(RealNumber('.5'), RealNumber('.3'), RealNumber('.2')))
>>> D += Torus(Integer(1), RealNumber('.3'), color='yellow').translate(Integer(0), Integer(0), RealNumber('.15'))
>>> G = sum(D.translate(RDF.random_element(-RealNumber('.2'), RealNumber('.2')),
...                     RDF.random_element(-RealNumber('.2'), RealNumber('.2')),
...                     RealNumber('.8')*t)
...         for t in range(Integer(10)))
>>> G.show(aspect_ratio=Integer(1), frame=False)

get_grid(ds)[source]¶

Return the range of variables to be evaluated on to render as a parametric surface.

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import Torus
sage: Torus(2, 1).get_grid(100)
([0.0, -1.047..., -3.141592653589793, ..., 0.0],
 [0.0, 1.047..., 3.141592653589793, ..., 0.0])

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import Torus
>>> Torus(Integer(2), Integer(1)).get_grid(Integer(100))
([0.0, -1.047..., -3.141592653589793, ..., 0.0],
 [0.0, 1.047..., 3.141592653589793, ..., 0.0])

sage.plot.plot3d.shapes.arrow3d(start, end, width=1, radius=None, head_radius=None, head_len=None, **kwds)[source]¶

Create a 3d arrow.

INPUT:

start – (x,y,z) point; the starting point of the arrow
end – (x,y,z) point; the end point
width – (default: 1) how wide the arrow is
radius – (default: width/50.0) the radius of the arrow
head_radius – (default: 3*radius) radius of arrow head
head_len – (default: 3*head_radius) len of arrow head

EXAMPLES:

The default arrow:

Sage

sage: arrow3d((0,0,0), (1,1,1), 1)
Graphics3d Object

Python

>>> from sage.all import *
>>> arrow3d((Integer(0),Integer(0),Integer(0)), (Integer(1),Integer(1),Integer(1)), Integer(1))
Graphics3d Object

A fat arrow:

Sage

sage: arrow3d((0,0,0), (1,1,1), radius=0.1)
Graphics3d Object

Python

>>> from sage.all import *
>>> arrow3d((Integer(0),Integer(0),Integer(0)), (Integer(1),Integer(1),Integer(1)), radius=RealNumber('0.1'))
Graphics3d Object

A green arrow:

Sage

sage: arrow3d((0,0,0), (1,1,1), color='green')
Graphics3d Object

Python

>>> from sage.all import *
>>> arrow3d((Integer(0),Integer(0),Integer(0)), (Integer(1),Integer(1),Integer(1)), color='green')
Graphics3d Object

A fat arrow head:

Sage

sage: arrow3d((2,1,0), (1,1,1), color='green', head_radius=0.3,
....:         aspect_ratio=[1,1,1])
Graphics3d Object

Python

>>> from sage.all import *
>>> arrow3d((Integer(2),Integer(1),Integer(0)), (Integer(1),Integer(1),Integer(1)), color='green', head_radius=RealNumber('0.3'),
...         aspect_ratio=[Integer(1),Integer(1),Integer(1)])
Graphics3d Object

Many arrows arranged in a circle (flying spears?):

Sage

sage: sum(arrow3d((cos(t),sin(t),0), (cos(t),sin(t),1))                         # needs sage.symbolic
....:     for t in [0,0.3,..,2*pi])
Graphics3d Object

Python

>>> from sage.all import *
>>> sum(arrow3d((cos(t),sin(t),Integer(0)), (cos(t),sin(t),Integer(1)))                         # needs sage.symbolic
...     for t in (ellipsis_range(Integer(0),RealNumber('0.3'),Ellipsis,Integer(2)*pi)))
Graphics3d Object

Change the width of the arrow. (Note: for an arrow that scales with zoom, please consider the line3d() function with the option arrow_head=True):

Sage

sage: arrow3d((0,0,0), (1,1,1), width=1)
Graphics3d Object

Python

>>> from sage.all import *
>>> arrow3d((Integer(0),Integer(0),Integer(0)), (Integer(1),Integer(1),Integer(1)), width=Integer(1))
Graphics3d Object

sage.plot.plot3d.shapes.validate_frame_size(size)[source]¶

Check that the input is an iterable of length 3 with all elements nonnegative and coercible to floats.

EXAMPLES:

Sage

sage: from sage.plot.plot3d.shapes import validate_frame_size
sage: validate_frame_size([3,2,1])
[3.0, 2.0, 1.0]

Python

>>> from sage.all import *
>>> from sage.plot.plot3d.shapes import validate_frame_size
>>> validate_frame_size([Integer(3),Integer(2),Integer(1)])
[3.0, 2.0, 1.0]