/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created by wxMaxima version 0.7.5 ] */

/* [wxMaxima: comment start ]
Problem: Plot the saddle shaped surface z=y^2-x^2.

The first method is simply to type y^2-x^2 in the INPUT box and
then click the Plot 3D button. We modify the x-range and the 
y-range to be [-3,3].
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
wxplot3d(y^2-x^2, [x,-3,3], [y,-3,3])$
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
Note that we can plot the surface in an external window that
allows us to rotate the surface by repeating the previous command
with the wx part removed, i.e. using the plot3d command. Try it by
right clicking the above command and using the Edit Input option. 
After deleting the wx press the keys Ctrl-Enter together.

Our next method is to use the draw package.
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
load(draw);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
wxdraw3d(xaxis = true, yaxis = true, zaxis = true,
         xlabel = "X", ylabel = "Y", zlabel = "Z",
         palette = color, enhanced3d   = true,       
         surface_hide = true,
         explicit(y^2-x^2, x,-3,3, y,-3,3) )$
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
We can make a contour plot with the levels z=-2,-1,0,1,2
using the following:
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
wxdraw3d(xaxis = true, yaxis = true, 
         xlabel = "X", ylabel = "Y", 
         explicit(y^2-x^2,x,-3,3,y,-3,3), 
         contour_levels = {-2,-1,0,1,2}, contour = map ) $
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
The contour plot reveals that the surface goes down if we walk
along the x-axis and goes up if walk along the y-axis.

The next 3d-plot shows both the surface and the contours together.
Use your mouse to rotated the surface (when draw3d is used) to see 
that the above observation is indeed the case.
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
wxdraw3d(xaxis = true, yaxis = true, zaxis = true,
         xlabel = "X", ylabel = "Y", zlabel = "Z",
         palette = color, enhanced3d = true, 
         surface_hide = true,
         explicit(y^2-x^2,x,-3,3,y,-3,3), 
         contour_levels = {-2,-1,0,1,2}, contour = both ) $
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
draw3d(xaxis = true, yaxis = true, zaxis = true,
         xlabel = "X", ylabel = "Y", zlabel = "Z",
         palette = color, enhanced3d = true, 
         surface_hide = true,
         explicit(y^2-x^2,x,-3,3,y,-3,3), 
         contour_levels = {-2,-1,0,1,2}, contour = both ) $
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
The last 3d-plot is an animation showing how the contours
change from hyperbola opening out in the x-direction to
hyperbolas opening out in the y-direction.

In the graph below click your mouse in the plot window to 
select the plot and then use the slider bar on the top tool 
bar to change the contour.
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
with_slider_draw3d(t, makelist(.2*i,i,-10,10),
         xaxis = true, yaxis = true, zaxis = true,
         xlabel = "X", ylabel = "Y", zlabel = "Z",
         palette = color, enhanced3d = true, 
         surface_hide = true,
         explicit(y^2-x^2,x,-3,3,y,-3,3), 
         contour_levels = {t}, contour = both ) $
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]

   [wxMaxima: comment end   ] */

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