Changeset 7903:439e75ca1c61

Timestamp:

01/01/08 02:24:35 (5 years ago)

Author:

William Stein <wstein@…>

Branch:

default

Message:

3d plotting -- more work on parametric plotting.

Location:

sage

Files:

• plot/plot3d/parametric_plot3d.py (modified) (5 diffs)
• rings/polynomial/polynomial_element.pyx (modified) (1 diff)
• server/notebook/cell.py (modified) (1 diff)
• server/notebook/js.py (modified) (2 diffs)

sage/plot/plot3d/parametric_plot3d.py

@@ -45 +45 @@
     We demonstrate each of the four ways to call this function.
 
-    1. A space curve defined by three functions of 1 variable:
-        sage: show(parametric_plot3d( (sin, cos, lambda u: u/10), (0, 20)))
-
-    Note above the lambda function, which creates a callable Python function
-    that sends u to u/10.
-
-    2. Next we draw the same plot as above, but using symbolic functions:
-        sage: var('u')
-        sage: show(parametric_plot3d( (sin(u), cos(u), u/10), (u, 0, 20)))
-
-    3. We draw a parametric surface using 3 Python functions (defined using
-       lambda):
+        1. A space curve defined by three functions of 1 variable:
+            sage: show(parametric_plot3d( (sin, cos, lambda u: u/10), (0, 20)))
+
+        Note above the lambda function, which creates a callable Python function
+        that sends u to u/10.
+
+        2. Next we draw the same plot as above, but using symbolic functions:
+            sage: var('u')
+            sage: show(parametric_plot3d( (sin(u), cos(u), u/10), (u, 0, 20)))
+
+        3. We draw a parametric surface using 3 Python functions (defined using
+           lambda):
+            sage: f = (lambda u,v: cos(u), lambda u,v: sin(u)+cos(v), lambda u,v: sin(v))
+            sage: show(parametric_plot3d(f, (0, 2*pi), (-pi, pi)))                 
+
+        4. The same surface, but where the defining functions are symbolic:
+            sage: var('u,v')
+            sage: show(parametric_plot3d((cos(u), sin(u) + cos(v), sin(v)), (u, 0, 2*pi), (v, -pi, pi)))
+
+    We call the space curve function but with polynomials instead of
+    symbolic variables.
+
+        sage: R.<t> = RDF[]
+        sage: show(parametric_plot3d( (t, t^2, t^3), (t, 0, 3) ) )
         
-    
-    4. The same surface, but where the defining functions are symbolic:
-        sage: var('u,v')
-        sage: show(parametric_plot3d((cos(u), sin(u) + cos(v), sin(v)), (u, 0, 2*pi), (v, -pi, pi)))
+    Next we plot the same curve, but because we use (0, 3) instead of (t, 0, 3),
+    each polynomial is viewed as a callable function of one variable:
+
+        sage: show(parametric_plot3d( (t, t^2, t^3), (0, 3) ) )
+
+    We do a plot but mix a symbolic input, and an integer:
+        sage: var('t')
+        sage: show(parametric_plot3d( (1, sin(t), cos(t)), (t, 0, 3) ) )
+
+    We plot two interlinked tori:
+        sage: f1 = (4+(3+cos(v))*sin(u), 4+(3+cos(v))*cos(u), 4+sin(v))
+        sage: f2 = (8+(3+cos(v))*cos(u), 3+sin(v), 4+(3+cos(v))*sin(u))
+        sage: p1 = parametric_plot3d(f1, (u,0,2*pi), (v,0,2*pi), texture="red")
+        sage: p2 = parametric_plot3d(f2, (u,0,2*pi), (v,0,2*pi), texture="blue")
+        sage: show(p1 + p2)    
     """
     # TODO:
@@ -102 +125 @@
     fail = 0
     
-    f_x, f_y, f_z = f
     if u is None:
+        f_x, f_y, f_z = f
         for t in vals:
             try:
@@ -110 +133 @@
                 fail += 1
     else:
+        f_x, f_y, f_z = [ensure_subs(m) for m in f]
         for t in vals:
             try:
-                w.append((float(f_x.substitute({u:t})), float(f_y.substitute({u:t})),
-                          float(f_z.substitute({u:t}))))
+                w.append((float(f_x.subs({u:t})), float(f_y.subs({u:t})),
+                          float(f_z.subs({u:t}))))
             except TypeError:
                 fail += 1
+                
     if fail > 0:
         print "WARNING: Failed to evaluate parametric plot at %s points"%fail
@@ -136 +161 @@
         if v is None:
             raise ValueError, "both ranges must specify a variable or neither must"
-        f0, f1, f2 = f
+        f0, f1, f2 = [ensure_subs(w) for w in f]
         def f_x(uu,vv):
-            return float(f0.substitute({u:uu, v:vv}))
+            return float(f0.subs({u:uu, v:vv}))
         def f_y(uu,vv):
-            return float(f1.substitute({u:uu, v:vv}))
+            return float(f1.subs({u:uu, v:vv}))
         def f_z(uu,vv):
-            return float(f2.substitute({u:uu, v:vv}))
+            return float(f2.subs({u:uu, v:vv}))
 
     def g(x,y):
@@ -191 +216 @@
         v.append(b)
     return v
+
+
+def ensure_subs(f):
+    if not hasattr(f, 'subs'):
+        from sage.calculus.all import SR
+        return SR(f)
+    return f

sage/rings/polynomial/polynomial_element.pyx

@@ -260 +260 @@
             sage: f.subs(5)
             127
-        """
+            sage: f.subs({x:2})
+            7
+            sage: f.subs({})
+            x^3 + x - 3            
+            sage: f.subs({'x':2})
+            Traceback (most recent call last):
+            ...
+            TypeError: keys do not match self's parent
+        """
+        if len(x) == 1 and isinstance(x[0], dict):
+            g = self.parent().gen()
+            if x[0].has_key(g):
+                return self(x[0][g])
+            elif len(x[0]) > 0:
+                raise TypeError, "keys do not match self's parent"
+            return self
         return self.__call__(*x, **kwds)
         

sage/server/notebook/cell.py

@@ -601 +601 @@
                 else:
                     size = 200
-                popup  = """<br><a href="javascript:jmol_popup('%s');">Enlarge 3d View</a>"""%url
+                popup  = """<br><a href="javascript:jmol_popup('%s');">Enlarge</a>"""%url
                 script = '<script>jmol_applet(%s, "%s");</script>%s' % (size, url, popup)
                 images.append(script)

sage/server/notebook/js.py

@@ -46 +46 @@
 
 function jmol_popup(url) {
-    win = window.open ("", url, "width=400,height=400,resizable=1");
+    win = window.open ("", "jmol viewer", "width=400,height=400,resizable=1,statusbar=0");
+    win.document.body.innerHTML = "";
+    win.document.title = "Sage 3d Viewer";
+    win.document.writeln("<h1 align=center>Sage 3d Viewer</h1>");
     jmolSetDocument(win.document);
     jmolApplet("100%", "script" + url);
+    win.focus(); 
 }
     """
@@ -821 +825 @@
     window.open ("/history", 
       "", "menubar=1,scrollbars=1,width=800,height=600, toolbar=1,resizable=1");
-
 }