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tachyon.py
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tachyon.py
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r"""
The Tachyon 3D Ray Tracer
Given any 3D graphics object one can compute a raytraced
representation by typing ``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')
One can also directly control Tachyon, which gives a huge amount of
flexibility. For example, here we directly use Tachyon to draw 3
spheres on the coordinate axes. Notice that the result is
gorgeous::
sage: t = Tachyon(xres=500,yres=500, camera_center=(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()
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 (trac #799)
- Marshall Hampton: improved doctests, rings, axis-aligned boxes.
TODO:
- clean up trianglefactory stuff
"""
from tri_plot import Triangle, SmoothTriangle, TriangleFactory, TrianglePlot
from sage.interfaces.tachyon import tachyon_rt
from sage.structure.sage_object import SageObject
from sage.misc.misc import SAGE_TMP
from sage.misc.temporary_file import tmp_filename, graphics_filename
#from sage.ext import fast_tachyon_routines
import os
from math import sqrt
class Tachyon(SageObject):
r"""
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 5)
- ``camera_center`` - (default (-3, 0, 0))
- ``updir`` - (default (0, 0, 1))
- ``look_at`` - (default (0,0,0))
- ``viewdir`` - (default None)
- ``projection`` - (default 'PERSPECTIVE')
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_center=(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()
Another twisted cubic, but with a white background, got by putting
infinite planes around the scene.
::
sage: t = Tachyon(xres=512,yres=512, camera_center=(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')
::
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()
Many random spheres::
sage: t = Tachyon(xres=512,yres=512, camera_center=(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()
Points on an elliptic curve, their height indicated by their height
above the axis::
sage: t = Tachyon(camera_center=(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')
sage: P = E([0,0])
sage: Q = P
sage: n = 100
sage: for i in range(n): # increase 20 for a better plot
....: Q = Q + P
....: t.sphere((Q[1], Q[0], ZZ(i)/n), 0.1, 't%s'%(i%3))
sage: t.show()
A beautiful picture of rational points on a rank 1 elliptic curve.
::
sage: t = Tachyon(xres=1000, yres=800, camera_center=(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')
sage: P = E([0,0])
sage: Q = P
sage: n = 100
sage: for i in range(n):
....: 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, e.g., 10-20 seconds
A beautiful spiral.
::
sage: t = Tachyon(xres=800,yres=800, camera_center=(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,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()
"""
def __init__(self,
xres=350, yres=350,
zoom = 1.0,
antialiasing = False,
aspectratio = 1.0,
raydepth = 8,
camera_center = (-3, 0, 0),
updir = (0, 0, 1),
look_at = (0,0,0),
viewdir = None,
projection = 'PERSPECTIVE'):
r"""
Creates an instance of the Tachyon class.
EXAMPLES::
sage: t = Tachyon()
sage: t._xres
350
"""
self._xres = xres
self._yres = yres
self._zoom = zoom
self._aspectratio = aspectratio
self._antialiasing = antialiasing
self._raydepth = raydepth
self._camera_center = camera_center
self._updir = updir
self._projection = projection
self._objects = []
if viewdir is None:
self._viewdir = [look_at[i] - camera_center[i] for i in range(3)]
else:
self._viewdir = viewdir
def __repr__(self):
r"""
Returns the string representation of the Tachyon object,
which is just the scene string input to tachyon.
EXAMPLES::
sage: q = Tachyon()
sage: q.light((1,1,1), 1,(1,1,1))
sage: q.texture('s')
sage: q.sphere((0,0,0),1,'s')
sage: q.__repr__()[-20:]
' \n end_scene'
"""
return self.str()
def save_image(self, filename=None, *args, **kwds):
r"""
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
:meth:`save` method of self, passing along all arguments and
keywords.
.. Note::
Not all image types are necessarily implemented for all
graphics types. See :meth:`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)
TESTS:
:meth:`save_image` is used for generating animations::
sage: def tw_cubic(t):
....: q = Tachyon()
....: q.light((1,1,11), 1,(1,1,1))
....: q.texture('s')
....: for i in srange(-1,t,0.05):
....: q.sphere((i,i^2-0.5,i^3), 0.1, 's')
....: return q
sage: a = animate([tw_cubic(t) for t in srange(-1,1,.3)])
sage: a
Animation with 7 frames
sage: a.show() # optional -- ImageMagick
"""
self.save(filename, *args, **kwds)
def save(self, filename='sage.png', verbose=0, block=True, extra_opts=''):
r"""
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: 0)
- ``0`` - silent
- ``1`` - some output
- ``2`` - very verbose output
- ``block`` - bool (default: True); if False, run the
rendering command in the background.
- ``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)
sage: os.system('rm ' + tempname)
0
"""
tachyon_rt(self.str(), filename, verbose, block, extra_opts)
def show(self, verbose=0, extra_opts=''):
r"""
Creates a PNG file of the scene.
EXAMPLES::
sage: q = Tachyon()
sage: q.light((-1,-1,10), 1,(1,1,1))
sage: q.texture('s')
sage: q.sphere((0,0,0),1,'s')
sage: q.show(verbose=False)
"""
filename = graphics_filename()
self.save(filename, verbose=verbose, extra_opts=extra_opts)
from sage.doctest import DOCTEST_MODE
from sage.plot.plot import EMBEDDED_MODE
if not DOCTEST_MODE and not EMBEDDED_MODE:
os.system('%s %s 2>/dev/null 1>/dev/null &'%(sage.misc.viewer.png_viewer(), filename))
def _res(self):
r"""
An internal function that writes the tachyon string for the
resolution (x and y size of the image).
EXAMPLES::
sage: t = Tachyon(xres = 300, yres = 700)
sage: t._res()
'\nresolution 300 700\n'
"""
return '\nresolution %s %s\n'%(self._xres, self._yres)
def _camera(self):
r"""
An internal function that writes the tachyon string for the
camera and other rendering information (ray depth, antialiasing).
EXAMPLES::
sage: t = Tachyon(raydepth = 16, zoom = 2, antialiasing = True)
sage: t._camera().split()[3:10]
['aspectratio', '1.0', 'antialiasing', '1', 'raydepth', '16', 'center']
"""
return r"""
camera
zoom %s
aspectratio %s
antialiasing %s
raydepth %s
center %s
viewdir %s
updir %s
end_camera
"""%(float(self._zoom), float(self._aspectratio),
int(self._antialiasing),
int(self._raydepth),
tostr(self._camera_center),
tostr(self._viewdir),
tostr(self._updir))
def str(self):
r"""
Returns the complete tachyon scene file as a string.
EXAMPLES::
sage: t = Tachyon(xres=500,yres=500, camera_center=(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.str().find('PLASTIC')
567
"""
return r"""
begin_scene
%s
%s
%s
end_scene"""%(
self._res(),
self._camera(),
'\n'.join([x.str() for x in self._objects])
)
def light(self, center, radius, color):
r"""
Creates 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 '
"""
self._objects.append(Light(center, radius, color))
def texfunc(self, type=0, center=(0,0,0), rotate=(0,0,0), scale=(1,1,1)):
r"""
INPUT:
- ``type`` - (default: 0)
0. No special texture, plain shading
1. 3D checkerboard function, like a rubik's cube
2. Grit Texture, randomized surface color
3. 3D marble texture, uses object's base color
4. 3D wood texture, light and dark brown, not very good yet
5. 3D gradient noise function (can't remember what it looks
like)
6. Don't remember
7. Cylindrical Image Map, requires ppm filename (don't know
how to specify name in sage?!)
8. Spherical Image Map, requires ppm filename (don't know
how to specify name in sage?!)
9. Planar Image Map, requires ppm filename (don't know how
to specify name in sage?!)
- ``center`` - (default: (0,0,0))
- ``rotate`` - (default: (0,0,0))
- ``scale`` - (default: (1,1,1))
EXAMPLES: We draw an infinite checkboard::
sage: t = Tachyon(camera_center=(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()
"""
type = int(type)
if type < 0 or type > 9:
raise ValueError("type must be an integer between 0 and 9")
return Texfunc(type,center,rotate,scale).str()
def texture(self, 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=.5, phongtype="PLASTIC"):
r"""
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_center=(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`)
"""
if texfunc and not isinstance(texfunc, Texfunc):
texfunc = self.texfunc(int(texfunc))
self._objects.append(Texture(name, ambient, diffuse,
specular, opacity, color, texfunc,
phong,phongsize,phongtype))
def texture_recolor(self, name, colors):
r"""
Recolors 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, 1)
"""
base_tex = None
names = []
ident = "SAGETEX%d"%len(self._objects) #don't collide with other texture names
for o in self._objects:
if isinstance(o, Texture) and o._name == name:
base_tex = o
break
if base_tex is None:
base_tex = Texture(name)
for i in range(len(colors)):
n = "%s_%d"%(ident,i)
self._objects.append(base_tex.recolor(n, colors[i]))
names.append(n)
return names
def sphere(self, center, radius, texture):
r"""
Creates 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 '
"""
self._objects.append(Sphere(center, radius, texture))
def ring(self, center, normal, inner, outer, texture):
r"""
Creates 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]
"""
self._objects.append(Ring(center, normal, inner, outer, texture))
def cylinder(self, center, axis, radius, texture):
r"""
Creates 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')
"""
self._objects.append(Cylinder(center, axis, radius, texture))
def plane(self, center, normal, texture):
r"""
Creates an infinite plane with the given center and normal.
EXAMPLES::
sage: t = Tachyon()
sage: t.plane((0,0,0),(1,1,1),'s')
sage: t.str()[338:380]
'plane center 0.0 0.0 0.0 normal 1.0 1.0'
"""
self._objects.append(Plane(center, normal, texture))
def axis_aligned_box(self, min_p, max_p, texture):
r"""
Creates 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')
"""
self._objects.append(Axis_aligned_box(min_p, max_p, texture))
def fcylinder(self, base, apex, radius, texture):
r"""
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
doesn't 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())
423
"""
self._objects.append(FCylinder(base, apex, radius, texture))
def triangle(self, vertex_1, vertex_2, vertex_3, texture):
r"""
Creates 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]
[1, 2, 3] [4, 5, 6] [7, 8, 10] s
"""
self._objects.append(TachyonTriangle(vertex_1,vertex_2,vertex_3,texture))
def smooth_triangle(self, vertex_1, vertex_2, vertex_3, normal_1, normal_2, normal_3, texture):
r"""
Creates 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]
[0, 0, 0] [0, 0, 1] [0, 1, 0] s [0, 1, 1] [-1, 1, 2] [3, 0, 0]
"""
self._objects.append(TachyonSmoothTriangle(vertex_1, vertex_2, vertex_3, normal_1, normal_2, normal_3, texture))
def fractal_landscape(self, res, scale, center, texture):
r"""
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
"""
self._objects.append(FractalLandscape(res, scale, center, texture))
def plot(self, f, xmin_xmax, ymin_ymax, texture, grad_f=None,
max_bend=.7, max_depth=5, initial_depth=3, num_colors=None):
r"""
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_center=(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, num_colors=60) # increase min_depth for better picture
sage: t.show()
Plotting with Smooth Triangles (requires explicit gradient
function)::
sage: t = Tachyon(xres=512,yres=512, camera_center=(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, grad_f = g) # increase min_depth for better picture
sage: t.show()
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.
"""
(xmin, xmax) = xmin_xmax
(ymin, ymax) = ymin_ymax
factory = TachyonTriangleFactory(self,texture)
plot = TrianglePlot(factory, f, (xmin, xmax), (ymin, ymax), g = grad_f,
min_depth=initial_depth, max_depth=max_depth, max_bend=max_bend, num_colors = num_colors)
self._objects.append(plot)
def parametric_plot(self, f, t_0, t_f, tex, r=.1, cylinders = True, min_depth=4, max_depth=8, e_rel = .01, e_abs = .01):
r"""
Plots 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_center=(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)
"""
self._objects.append(ParametricPlot(f, t_0, t_f, tex, r=r, cylinders=cylinders,min_depth=min_depth,max_depth=max_depth,e_rel=.01,e_abs=.01))
#Doesn't seem to be used:
# def collect(self, objects):
# """
# Add a set of objects to the scene from a collection.
#
# EXAMPLES::
#
# sage: t = Tachyon()
# sage: t.texture('s')
# sage: for i in range(10): t.sphere((0,0,i),i,'s')
# """
# self._objects.extend(objects)
class Light:
r"""
Represents 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, 1, 1)
"""
def __init__(self, center, radius, color):
r"""
Stores the center, radius and color.
EXAMPLES::
sage: from sage.plot.plot3d.tachyon import Light
sage: q = Light((1,1,1),1,(1,1,1))
sage: q._color
(1, 1, 1)
"""
self._center = center
self._radius = radius
self._color = color
def str(self):
r"""
Returns 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: q._radius
1
"""
return r"""
light center %s
rad %s
color %s
"""%(tostr(self._center), float(self._radius),
tostr(self._color))
class Texfunc:
def __init__(self, type=0,center=(0,0,0), rotate=(0,0,0), scale=(1,1,1)):
r"""
Creates a texture function.
EXAMPLES::
sage: from sage.plot.plot3d.tachyon import Texfunc
sage: t = Texfunc()
sage: t._type
0
"""
self._type = type
self._center = center
self._rotate = rotate
self._scale = scale
def str(self):
r"""
Returns the scene string for this texture function.
EXAMPLES::
sage: from sage.plot.plot3d.tachyon import Texfunc
sage: t = Texfunc()
sage: t.str()
'0 center 0.0 0.0 0.0 rotate 0.0 0.0 0.0 scale 1.0 1.0 1.0 '
"""
if type == 0:
return "0"
return r"""%d center %s rotate %s scale %s"""%(self._type,
tostr(self._center),
tostr(self._rotate),
tostr(self._scale))
class Texture:
def __init__(self, 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"):
r"""
Stores 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']
"""
self._name = name
self._ambient = ambient
self._diffuse = diffuse
self._specular = specular
self._opacity = opacity
self._color = color
self._texfunc = texfunc
self._phong = phong
self._phongsize = phongsize
self._phongtype = phongtype
def recolor(self, name, color):
r"""
Returns 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 '
"""
return Texture(name, self._ambient, self._diffuse, self._specular, self._opacity,
color, self._texfunc, self._phong, self._phongsize, self._phongtype)
def str(self):
r"""
Returns 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']
"""
return r"""
texdef %s ambient %s diffuse %s specular %s opacity %s
phong %s %s phong_size %s
color %s texfunc %s
"""%(self._name,
self._ambient,
self._diffuse,
self._specular,
self._opacity,
self._phongtype,
self._phong,
self._phongsize,
tostr(self._color),
self._texfunc)
class Sphere:
r"""
A class for creating spheres in tachyon.
"""
def __init__(self, center, radius, texture):
r"""
Stores the center, radius, and texture information in a class.
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._radius
1
"""
self._center = center
self._radius = radius
self._texture = texture
def str(self):
r"""
Returns 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 '
"""
return r"""
sphere center %s rad %s %s
"""%(tostr(self._center), float(self._radius), self._texture)
class Ring:
r"""
An annulus of zero thickness.
"""
def __init__(self, center, normal, inner, outer, texture):
r"""
Creates a ring with the given center, normal, inner radius,
outer radius, and texture.
EXAMPLES::
sage: from sage.plot.plot3d.tachyon import Ring
sage: r = Ring((1,1,1), (1,1,0), 1.0, 2.0, 's')
sage: r._center
(1, 1, 1)
"""
self._center = center
self._normal = normal
self._inner = inner
self._outer = outer