Hi all,
I’m trying to create a rational Bézier curve (actually an approximation of one). To do so, you need to create a normal/ordinary Bézier curve (in space) and apply an perspective projection to it. That means that each point of the curve is projected towards the origin.
Between the normal Bézier curve and the origin one adds a plane, so that the Bézier curve is actually projected onto this plane (this projection onto the plane is your rational Bézier curve).
So far so good, but I got a few short questions:

How to create a vertex at the intersection of a line and a plane? Is there a readytouse function for this, or is it possible to create a vertex on a line, and slide it (along this line) to a certain height (zvalue)? That would be all right since I know the planes zvalue.

How to create a vertex at the origin? The way I do it now seems a little cumbersome – creating a circle (with 3 sides) in the plane z=0, deleting two vertices and moving the third one to the origin.

Can I make my plane a little translucent (in the editing mode)? I set some material properties, but without result.

When I first select a vertex, and then Shiftselect another, is there a shortcut to unselect this last vertex (except for Shiftclicking it again)? The Ctrl + Numpad Minus deselects all – is it possible to configure this somehow? The thing is, I’m looking for a fast way to draw all those lines you see in the figure above.

Is it possible to display the actual control polygon of a Bézier curve? For me that would be more useful than these handles that show up.