# HG changeset patch # User Oscar Gerardo Lazo Arjona geometricamente@hotmail.com # Date 1266175612 21600 # Node ID ca8d6a70cdff2182cb602b55b72cf9191acb6e72 # Parent 21efb0b3fc474972b5c7f617d99173536a3d79d0 SD diff -r 21efb0b3fc47 -r ca8d6a70cdff sage/plot/plot3d/all.py --- a/sage/plot/plot3d/all.py Thu Dec 24 09:44:02 2009 -0800 +++ b/sage/plot/plot3d/all.py Sun Feb 14 13:26:52 2010 -0600 @@ -1,6 +1,6 @@ - from plot3d import plot3d from parametric_plot3d import parametric_plot3d +from revolution_plot3d import revolution_plot3d from plot_field3d import plot_vector_field3d from implicit_plot3d import implicit_plot3d from list_plot3d import list_plot3d diff -r 21efb0b3fc47 -r ca8d6a70cdff sage/plot/plot3d/revolution_plot3d.py --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/sage/plot/plot3d/revolution_plot3d.py Sun Feb 14 13:26:52 2010 -0600 @@ -0,0 +1,171 @@ +#***************************************************************************** +# Copyright (C) 2010 Oscar Gerardo Lazo Arjona algebraicamente@gmail.com +# +# Distributed under the terms of the GNU General Public License (GPL) +# +# This code is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +# General Public License for more details. +# +# The full text of the GPL is available at: +# +# http://www.gnu.org/licenses/ +#***************************************************************************** + +from sage.plot.plot3d.parametric_plot3d import parametric_plot3d +def revolution_plot3d(curve,trange,phirange=None,parallel_axis='z',axis=(0,0),print_vector=False,show_curve=False,**kwds): + ''' + Return a plot of a revolved curve. + + There are three ways to call this function: + + - ``revolution_plot3d(f,trange)`` where `f` is a function located in the `x z` plane. + + - ``revolution_plot3d((f_x,f_z),trange)`` where `(f_x,f_z)` is a parametric curve on the `x z` plane. + + - ``revolution_plot3d((f_x,f_y,f_z),trange)`` where `(f_x,f_y,f_z)` can be any parametric curve. + + INPUT: + + - ``curve`` - A curve to be revolved, specified as a function, a 2-tuple or a 3-tuple. + + - ``trange`` - A 3-tuple `(t,t_{\min},t_{\max})` where t is the independent variable of the curve. + + - ``phirange`` - A 2-tuple of the form `(\phi_{\min},\phi_{\max})`, (default `(0,\pi)`) that specifies the angle in which the curve is to be revolved. + + - ``parallel_axis`` - A string (Either 'x', 'y', or 'z'), (default 'z') that specifies the coordinate axis parallel to the revolution axis. + + - ``axis`` - A 2-tuple that specifies the position of the revolution axis (default `(0,0)`). If parallel is: + + - 'z' - then axis is the point in which the revolution axis intersects the `x y` plane. + + - 'x' - then axis is the point in which the revolution axis intersects the `y z` plane. + + - 'y' - then axis is the point in which the revolution axis intersects the `x z` plane. + + - ``print_vector`` - If True, the parametrization of the surface of revolution will be printed (default False). + + - ``show_curve`` - If True, the curve will be displayed (default False). + + + EXAMPLES: + + Let's revolve a simple function around different axes:: + + sage: var('u') + sage: f=u^2 + sage: revolution_plot3d(f,(u,0,2),show_curve=True,opacity=0.7).show(aspect_ratio=(1,1,1)) + + If we move slightly the axis, we get a goblet-like surface:: + + sage: revolution_plot3d(f,(u,0,2),axis=(1,0.2),show_curve=True,opacity=0.5).show(aspect_ratio=(1,1,1)) + + A common problem in calculus books, find the volume within the following revolution solid:: + + sage: line=u + sage: parabola=u^2 + sage: sur1=revolution_plot3d(line,(u,0,1),opacity=0.5,rgbcolor=(1,0.5,0),show_curve=True,parallel_axis='x') + sage: sur2=revolution_plot3d(parabola,(u,0,1),opacity=0.5,rgbcolor=(0,1,0),show_curve=True,parallel_axis='x') + sage: (sur1+sur2).show() + + + Now let's revolve a parametrically defined circle. We can play with the topology of the surface by changing the axis, an axis in `(0,0)` (as the previous one) will produce a sphere-like surface:: + + sage: var('u') + sage: circle=(cos(u),sin(u)) + sage: revolution_plot3d(circle,(u,0,2*pi),axis=(0,0),show_curve=True,opacity=0.5).show(aspect_ratio=(1,1,1)) + + An axis on `(0,y)` will produce a cylinder-like surface:: + + sage: revolution_plot3d(circle,(u,0,2*pi),axis=(0,2),show_curve=True,opacity=0.5).show(aspect_ratio=(1,1,1)) + + And any other axis will produce a torus-like surface:: + + sage: revolution_plot3d(circle,(u,0,2*pi),axis=(2,0),show_curve=True,opacity=0.5).show(aspect_ratio=(1,1,1)) + + Now, we can get another goblet-like surface by revolving a curve in 3d:: + + sage: var('u') + sage: curve=(u,cos(4*u),u^2) + sage: revolution_plot3d(curve,(u,0,2),show_curve=True,parallel_axis='z',axis=(1,.2),opacity=0.5).show(aspect_ratio=(1,1,1)) + + A curvy curve with only a quarter turn:: + + sage: var('u') + sage: curve=(sin(3*u),.8*cos(4*u),cos(u)) + sage: revolution_plot3d(curve,(u,0,pi),(0,pi/2),show_curve=True,parallel_axis='z',opacity=0.5).show(aspect_ratio=(1,1,1),frame=False) + ''' + from sage.symbolic.ring import var + from sage.symbolic.constants import pi + from sage.functions.other import sqrt + from sage.functions.trig import sin + from sage.functions.trig import cos + from sage.functions.trig import atan2 + + + if parallel_axis not in ['x','y','z']: + raise ValueError, "parallel_axis must be either 'x', 'y', or 'z'." + + vart=trange[0] + + + if str(vart)=='phi': + phi=var('fi') + else: + phi=var('phi') + + + if phirange is None:#this if-else provides a phirange + phirange=(phi,0,2*pi) + elif len(phirange)==3: + phi=phirange[0] + pass + else: + print 'ta' + phirange=(phi,phirange[0],phirange[1]) + + if isinstance(curve,tuple) or isinstance(curve,list): + #this if-else provides a vector v to be plotted + #if curve is a tuple or a list of length 2, it is interpreted as a parametric curve + #in the x-z plane. + #if it is of length 3 it is interpreted as a parametric curve in 3d space + + if len(curve) ==2: + x=curve[0] + y=0 + z=curve[1] + elif len(curve)==3: + x=curve[0] + y=curve[1] + z=curve[2] + else: + x=vart + y=0 + z=curve + + if parallel_axis=='z': + x0=axis[0] + y0=axis[1] + phase=atan2((y-y0),(x-x0)) + R=sqrt((x-x0)**2+(y-y0)**2) + v=(R*cos(phi+phase)+x0,R*sin(phi+phase)+y0,z) + elif parallel_axis=='x': + y0=axis[0] + z0=axis[1] + phase=atan2((z-z0),(y-y0)) + R=sqrt((y-y0)**2+(z-z0)**2) + v=(x,R*cos(phi+phase)+y0,R*sin(phi+phase)+z0) + elif parallel_axis=='y': + x0=axis[0] + z0=axis[1] + phase=atan2((z-z0),(x-x0)) + R=sqrt((x-x0)**2+(z-z0)**2) + v=(R*cos(phi+phase)+x0,y,R*sin(phi+phase)+z0) + + if print_vector: + print v + if show_curve: + curveplot=parametric_plot3d((x,y,z),trange,thickness=2,rgbcolor=(1,0,0)) + return parametric_plot3d(v,trange,phirange,**kwds)+curveplot + return parametric_plot3d(v,trange,phirange,**kwds)