Showing 3D intersection of surface and plane clear

[julian]

I\'m trying to show my students how to find minima of functions of two variables.  Take a simple example: z=x^2+y^2.  Then draw the plane y=a.  By turning the graph, I can see "inside" the bowl, and thereby see that there\'s a minimum along the intersection.  But what I really want to be able to do is to make the surface fairly transparent, so that the intersection of the surface and the plane is very clear.

Any suggestions as to how I might go about doing this?  (The curve I am actually interested in is more evil than this.)

Many thanks!

Julian

[Simon]

Hi Julian,

For the example you\'ve given:
1. Enter Equation > y = a > OK
2. Enter Equation > z = x

[julian]

No, it didn\'t really help, unfortunately.  I had already tried that, but from the "outside" of the graph, it is still very hard to see where the intersection is - it is still obscured, or so it seems.  Of course, looking down from above, everything is clear, but that doesn\'t necessarily help that much.

So, for example, if I have z=x[sup]2[/sup]+y[sup]2[/sup] even with transparency 100%, and then y=1, I can\'t see the plane through the paraboloid.

I am using Autograph 3.11; perhaps this is something which has been improved in version 3.20?

Many thanks,

Julian

[Simon]

In order to see the plane through the surface you need to create the plane first.  This applies for all objects.

Basically to get 3D transparency to work perfectly we would need to sort all the objects on the page everytime anything changed, e.g. rotating the view, dragging a point, etc.  This makes things very sluggish.  Therefore we choose to plot things in the order they were created.  Unfortunately for 3D transparency this means that objects created after the transparent object are not seen through it.  

Sorry for the confusion!

Simon