Changeset 7889:3670aecb098e

Timestamp:

12/23/07 23:34:29 (5 years ago)

Author:

William Stein <wstein@…>

Branch:

default

Message:

Add 3d parametric plots (implemented currently in terms of line segments); lots of other misc touch up.

Location:

sage/plot

Files:

• plot.py (modified) (6 diffs)
• plot3d/base.pyx (modified) (2 diffs)
• plot3d/index_face_set.pyx (modified) (1 diff)
• plot3d/shapes.pyx (modified) (2 diffs)

sage/plot/plot.py

@@ -2283 +2283 @@
         plot(X, ...)
         
-    where X is a SAGE object that either is callable and returns
-    numbers that can be coerced to floats, or has a plot method
-    that returns a GraphicPrimitive object.
+    where X is a Sage object (or list of Sage objects) that either is
+    callable and returns numbers that can be coerced to floats, or has
+    a plot method that returns a GraphicPrimitive object.
     
     Type plot.options for a dictionary of the default
@@ -2352 +2352 @@
         sage: P.show()   # render
         
+    We plot several functions together by passing a list
+    of functions as input:
+       sage: show(plot([sin(n*x) for n in [1..4]], 0, pi))
+
+
+    The function $\sin(1/x)$ wiggles wildtly near $0$, so the
+    first plot below won't look perfect.  Sage adapts to this
+    and plots extra points near the origin.
+       sage: show(plot(sin(1/x), -1, 1))
+
+    The \code{plot_points} option, you can increase the number
+    of sample points, to obtain a more accurate plot. 
+       sage: show(plot(sin(1/x), -1, 1, plot_points=1000))
+
+    The actual sample points are slightly randomized, so the above
+    plots may look slightly different each time you draw them.
+
     Use \code{show(plot(sin, 0,10))} or \code{plot(sin,0,10).show()}
     to show the corresponding graphics object.
-    
+
     We draw the graph of an elliptic curve as the union
     of graphs of 2 functions.
@@ -2419 +2436 @@
         #and will plotted as (f(x), g(x)) for all x in the given range
         if parametric:
-            f,g = funcs
+            if len(funcs) == 3:
+                # 3d
+                from plot3d.shapes import parametric_plot_3d
+                return parametric_plot_3d(funcs, xmin, xmax, polar=polar, label=label, show=show, **kwds)
+            elif len(funcs) == 2:
+                # 2d
+                f,g = funcs
+            else:
+                raise ValueError, "parametric plots only implemented in 2 and 3 dimensions."
+            
         #or we have only a single function to be plotted:
         else:
@@ -2542 +2568 @@
 ########## misc functions ###################
 
-def parametric_plot((f,g), tmin, tmax, show=None, **kwargs):
+def parametric_plot(funcs, tmin, tmax, show=None, **kwargs):
     """
     parametric_plot takes two functions as a list or a tuple and make
@@ -2549 +2575 @@
 
     INPUT:
-        (f,g) -- tuple of functions
+        funcs -- 2 or 3-tuple of functions
         tmin -- start value of t
         tmax -- end value of t
@@ -2558 +2584 @@
 
     EXAMPLE:
+    We draw a 2d parametric plot:
         sage: t = var('t')
         sage: G = parametric_plot( (sin(t), sin(2*t)), 0, 2*pi, rgbcolor=hue(0.6) )
         sage: G.show()
+
+    We draw a 3d parametric plot:
+        sage: show(parametric_plot( (5*cos(x), 5*sin(x), x), -12, 12, plot_points=150, color="red"))    
     """
     if show is None:
         show = SHOW_DEFAULT
-    return plot((f,g), tmin, tmax, parametric=True, show=show, **kwargs)            
+    return plot(funcs, tmin, tmax, parametric=True, show=show, **kwargs)            
 
 def polar_plot(funcs, xmin, xmax, show=None, **kwargs):

sage/plot/plot3d/base.pyx

@@ -243 +243 @@
             import sage.misc.viewer
             viewer_app = sage.misc.viewer.browser()
+
         if DOCTEST_MODE or viewer=='java3d':
             f = open(filename+".obj", "w")
@@ -264 +265 @@
         if ext is None:
             raise ValueError, "Unknown 3d plot type: %s" % viewer
+
         if not DOCTEST_MODE and not EMBEDDED_MODE:
             if verbosity:

sage/plot/plot3d/index_face_set.pyx

@@ -178 +178 @@
     """
 
-    def __new__(self, faces, point_list=None, enclosde=False, **kwds):
+    def __new__(self, faces, point_list=None, enclosed=False, **kwds):
         self.vs = <point_c *>NULL
         self.face_indices = <int *>NULL

sage/plot/plot3d/shapes.pyx

@@ -50 +50 @@
 from sage.modules.free_module_element import vector
 
-from base import Graphics3dGroup
+from sage.misc.all import srange
+
+from base import Graphics3dGroup, Graphics3d
 
 
 class Box(IndexFaceSet):
+    """
+
+    EXAMPLES:
+    A square black box:
+        sage: show(Box([1,1,1]))
+
+    A red rectangular box. 
+        sage: show(Box([2,3,4], color="red"))
+
+    A stack of boxes:
+        sage: show(sum([Box([2,3,1], color="red").translate((0,0,6*i)) for i in [0..3]]))
+
+    A sinusoidal stack of multicolored boxes:
+        sage: B = sum([Box([2,4,1/4], color=(i/4,i/5,1)).translate((sin(i),0,5-i)) for i in [0..20]])
+        sage: show(B, figsize=6)    
+    """
     
     def __init__(self, *size, **kwds):
@@ -334 +352 @@
 
 
+def parametric_plot_3d(funcs, tmin, tmax, plot_points=50, show=None, thickness=0.2, polar=False, **kwargs):
+
+    if polar:
+        raise NotImplementedError, "3d parametric polar plots not implemented"
+
+    f,g,h = funcs
+
+    # normalize number of points to an integer
+    plot_points = int(plot_points)
+    if plot_points <= 1:
+        plot_points = 1
+
+    
+    v = srange(tmin, tmax, (tmax-tmin)/plot_points, include_endpoint=True)
+    t0 = v[0]
+    P =  (f(t0), g(t0), h(t0))
+    G = 0
+    for i in range(1, len(v)):
+        t1 = v[i]
+        Q = (f(t1), g(t1), h(t1))
+        G += LineSegment(P, Q, **kwargs)
+        P = Q
+
+    if show:
+        G.show(**kwargs)
+    
+    return G
+