MaplePrimes - answers and comments on Question, plot3d orientation

orientation

gkokovidis — Fri, 01 Feb 2008 05:43:38 Z

Look at the plot3d command below. Once you execute it you will get a plot. If you left click on the plot, the menu bar will change and it will display and angle "theta", and an angle "phi". If you click on the plot and rotate it, those angles will change. You can rotate it and note the angles for a view that you like. Then you can include those angles into your plot3d command. See the second command below. See ?plot3d/details for more help on this. >plot3d(f, x=-2..2, y=-2..1,axes=boxed); >plot3d(f, x=-2..2,y=-2..1,axes=boxed,orientation=[45,46]); Regards, Georgios Kokovidis Dräger Medical

thanks how about exercise 7?

casperyc — Fri, 01 Feb 2008 07:00:21 Z

thanks how about exercise 7?

orientation

gkokovidis — Fri, 01 Feb 2008 08:19:20 Z

>contourplot(f,x=-2..2,y=-2..1,color=red,contours=10);

>contourplot(f,x=-2..2,y=-2..1,color=red,contours=[-1,-7/16,0,3/4]);

Regards,
Georgios Kokovidis
Dräger Medical

contourplot(f,x=-2..2,y=-2..1

casperyc — Fri, 01 Feb 2008 15:46:09 Z

contourplot(f,x=-2..2,y=-2..1,color=red,contours=[-1,-7/16,0,3/4]); can i ask why is this order contours=[-1,-7/16,0,3/4]);? cheers

more contourplot ideas

Doug Meade — Fri, 01 Feb 2008 18:55:29 Z

The contours= option specifies the heights (z) to be drawn on the plot. I do not know why these four curves were selected, but this should not have any connection with the location of the critical points of f. If you wanted to ensure the critical points were highlighted on the contourplot, I would use

contourplot( f, x=-2..2, y=-2..1, color=red, contours=[ f(0,-1), f(3/4,-7/16) ] );

But, I see that you have not defined f as a function, so the function calls would need to be replaced by eval's. Here is how I would approach this problem:

with( plots ):
f:=x^3-3*x*y+2*y^2-3*x+4*y+3:
fx := diff( f, x );
                                  2          
                               3 x  - 3 y - 3
fy := diff( f, y );
                               -3 x + 4 y + 4
cp := solve( [fx=0,fy=0], [x,y] );
                     [                 [    3      -7]]
                     [[x = 0, y = -1], [x = -, y = --]]
                     [                 [    4      16]]


p1 := contourplot( f, x=-2..2, y=-2..1, contours=10 ):
p2 := contourplot( f, x=-2..2, y=-2..1, contours=[seq(eval(f,p),p=cp)], color=pink, grid=[51,51] ):
display( p1,p2 );

The first contoutplot shows the general shape of the function. The second highlights the two level curves that contain the critical points. The grid= option helps to smooth out these curves, but even with grid=[350,350] Maple did not find the single point at (3/4,-7/16). You should also know about the contourplot3d command. The syntax is the same but the output is a 3D plot - the contours are displayed at their height on the surface. This can be useful in some situations. See ?contourplot for information about both commands. Doug

---------------------------------------------------------------------
Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/

thanks that's very

casperyc — Fri, 01 Feb 2008 20:40:53 Z

thanks that's very helpful. Cheers