Ticket #1833: trac-1833.patch

sage/plot/plot3d/all.py

@@ -1 +1 @@
 
-from plot3d            import plot3d, plot3d_adaptive
+from plot3d            import plot3d
 from parametric_plot3d import parametric_plot3d
 from list_plot3d       import list_plot3d
 

sage/plot/plot3d/parametric_plot3d.py

@@ -30 +30 @@
     INPUT:
         f -- a 3-tuple of functions or expressions
         urange -- a 2-tuple (u_min, u_max) or a 3-tuple (u, u_min, u_max)
-        vrange -- (optional -- only used for surfaces) a 2-tuple (u_min, u_max)
-                  or a 3-tuple (u, u_min, u_max)        
+        vrange -- (optional -- only used for surfaces) a 2-tuple (v_min, v_max)
+                  or a 3-tuple (v, v_min, v_max)        
         plot_points -- (default: "automatic", which is 75 for curves and
                        [15,15] for surfaces) initial number of sample
                        points in each parameter; an integer for a curve,
@@ -179 +179 @@
     u, vals = var_and_list_of_values(urange, plot_points)
     w = []
     fail = 0
-    
+
+    if u is None:
+        try:
+            f, u, v = adapt_if_symbolic(f)
+        except TypeError:
+            pass
+
     if u is None:
         f_x, f_y, f_z = f
         for t in vals:
@@ -212 +218 @@
     u, u_vals = var_and_list_of_values(urange, int(points0))
     v, v_vals = var_and_list_of_values(vrange, int(points1))
 
+    if u is None and v is None:
+        try:
+            f, u, v = adapt_if_symbolic(f)
+        except TypeError:
+            pass
+            
     if u is None:
         if not v is None:
             raise ValueError, "both ranges must specify a variable or neither must"
@@ -233 +245 @@
         return (float(f_x(x,y)), float(f_y(x,y)), float(f_z(x,y)))
 
     return ParametricSurface(g, (u_vals, v_vals), **kwds)
+
+
+
+def adapt_if_symbolic(f):
+    """
+    If f is symbolic find the variables u, v to substitute into f.
+    Otherwise raise a TypeError.
+
+    This function is used internally by the plot commands for
+    efficiency reasons only.
+    """
+    from sage.calculus.calculus import is_SymbolicExpression, SR
+    if sum([is_SymbolicExpression(a) for a in f]) > 0:
+        g = [SR(a) for a in f]
+        vars = list(set(sum([list(a.variables()) for a in g], [])))
+        vars.sort()
+        if len(vars) > 0:
+            u = vars[0]
+            if len(vars) > 1:
+                v = vars[1]
+            else:
+                v = None
+            return g, u, v
+        else:
+            g = [lambda x: float(a) for a in g]
+            return g, None, None
+        

sage/plot/plot3d/plot3d.py

@@ -1 +1 @@
 r"""
 Plotting Functions.
 
-EXAMPLES: 
+EXAMPLES:
     sage: def f(x,y):
     ...       return math.sin(y*y+x*x)/math.sqrt(x*x+y*y+.0001)
     ...
-    sage: P = plot3d_adaptive(f,(-3,3),(-3,3), color=rainbow(60, 'rgbtuple'), max_bend=.1, max_depth=15)
+    sage: P = plot3d(f,(-3,3),(-3,3), adaptive=True, color=rainbow(60, 'rgbtuple'), max_bend=.1, max_depth=15)
     sage: P.show()
 
     sage: def f(x,y):
     ...       return math.exp(x/5)*math.sin(y)
     ...
-    sage: P = plot3d_adaptive(f,(-5,5),(-5,5), color=['red','yellow'])
+    sage: P = plot3d(f,(-5,5),(-5,5), adaptive=True, color=['red','yellow'])
     sage: from sage.plot.plot3d.plot3d import axes
     sage: S = P + axes(6, color='black')
     sage: S.show()
@@ -26 +26 @@
     sage: S += sphere((.45, .1,.15),size=.1, color='white') + sphere((.51, .1,.17), size=.05, color='black')
     sage: S += sphere((.5,0,-.2),size=.1, color='yellow')
     sage: def f(x,y): return math.exp(x/5)*math.cos(y)
-    sage: P = plot3d_adaptive(f,(-5,5),(-5,5), ['red','yellow'], max_depth=10)
+    sage: P = plot3d(f,(-5,5),(-5,5), adaptive=True, color=['red','yellow'], max_depth=10)
     sage: cape_man = P.scale(.2) + S.translate(1,0,0)
-    sage: cape_man
+    sage: cape_man.show(aspect_ratio=[1,1,1])
 
 AUTHOR:
     -- Tom Boothby: adaptive refinement triangles
@@ -71 +71 @@
         return [a,b,c]
 
 import parametric_plot3d
-def plot3d(f, urange, vrange, **kwds):
+def plot3d(f, urange, vrange, adaptive=False, **kwds):
     """
+    INPUT:
+        f -- a symbolic expression or function of 2 variables
+        urange -- a 2-tuple (u_min, u_max) or a 3-tuple (u, u_min, u_max)
+        vrange -- a 2-tuple (v_min, v_max) or a 3-tuple (v, v_min, v_max)
+        adaptive -- (default: False) whether to use adaptive refinement
+                    to draw the plot (slower, but may look better)
+    
     EXAMPLES:
     We plot a 3d function defined as a Python function:
         sage: plot3d(lambda x, y: x^2 + y^2, (-2,2), (-2,2))
+
+    We plot the same 3d function but using adaptive refinement:
+        sage: plot3d(lambda x, y: x^2 + y^2, (-2,2), (-2,2), adaptive=True)
+
+    Adaptive refinement but with more points:
+        sage: plot3d(lambda x, y: x^2 + y^2, (-2,2), (-2,2), adaptive=True, initial_depth=5)
 
     We plot some 3d symbolic functions:
         sage: x, y = var('x,y')
@@ -84 +97 @@
 
     Two wobby translucent planes:
         sage: x,y = var('x,y')
-        sage: P = plot3d(x+y+sin(x*y), (x,-10,10),(y,-10,10), opacity=0.87)
+        sage: P = plot3d(x+y+sin(x*y), (x,-10,10),(y,-10,10), opacity=0.87, color='blue')
         sage: Q = plot3d(x-2*y-cos(x*y),(x,-10,10),(y,-10,10),opacity=0.3,color='red')
         sage: P + Q
 
@@ -95 +108 @@
         sage: L + P + Q
     """
     if len(urange) == 2:
-        w = (lambda u,v: u, lambda u,v: v, f)
+        from parametric_plot3d import adapt_if_symbolic
+        try:
+            f, u,v = adapt_if_symbolic((f,1,1))
+            f = f[0]
+            w = (u, v, f)
+            urange = (u, urange[0], urange[1])
+            vrange = (v, vrange[0], vrange[1])            
+        except TypeError:
+            w = (lambda u,v: u, lambda u,v: v, f)
     else:
         u = urange[0]
         v = vrange[0]
         w = (u, v, f)
-    P = parametric_plot3d.parametric_plot3d(w, urange, vrange, **kwds)
+
+    if adaptive:
+        P = plot3d_adaptive(f, urange, vrange, **kwds)
+    else:
+        P = parametric_plot3d.parametric_plot3d(w, urange, vrange, **kwds)
     P.frame_aspect_ratio([1.0,1.0,0.5])
     return P
 
 def plot3d_adaptive(f, x_range, y_range, color="automatic",
                     grad_f=None, 
                     max_bend=.5, max_depth=5, initial_depth=4, num_colors=128, **kwds):
-    """
+    r"""
     Adaptive 3d plotting of a function of two variables.
+
+    This is used internally by the plot3d command when the option
+    \code{adaptive=True} is given.
 
     INPUT:
         f -- a symbolic function or a Python function of 3 variables.
@@ -123 +151 @@
         **kwds -- standard graphics parameters
     
     EXAMPLES:
-    We plot sin(xy):
+    We plot $\sin(xy)$:
+        sage: from sage.plot.plot3d.plot3d import plot3d_adaptive
         sage: x,y=var('x,y'); plot3d_adaptive(sin(x*y), (x,-pi,pi), (y,-pi,pi), initial_depth=5)
 
     """