See Online Help regarding the Free Distort tool.
This is what you refer to? http://help.adobe.com/en_US/Illustrator/
Doesn't solve the problem of the resetting bouding box each time the
mouse is released.
No Doubt about it if you have a clean vector art them bring it into Photoshop s a shape layer or Path if you wish and use the Transform tool as the Distort option. Drag the corners to match the perspective lines on the Illustration and tweak it.
This is a live trace s it is not real accurate but it shows what you can get in ten seconds in Photoshop. I t would be great if Illustrator had a perspective feature but as that feature request has been around for as long as AI exists I would not hold my breath on it and in this case I am not sure such a feature would help but a real distortion tool would.
There is one in Illustrator that can do this but as it has no live preview on the artboard it makes things more difficult rather than easier.
In Photoshop this is simple the path from photoshop can then be pasted into Illustrator and filled with a color as I did.
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Doesn't solve the problem of the resetting bouding box
I never said it did. But the distortion of your image can be matched with the tool (I know, because I did it), although not in a single move. Use both the so-called "perspective" keyboard modifiers and the skew modifiers.
Yes, several moves are required, and you just have to deal with the tool's horrible bounding box behavior. But your specific expample is quite simple and can be easily matched.
That's it! I never thought of it to use photoshop to do the trick.
It was not the most hardest thing to do in illustrator indeed, but it felt like i was doing something wrong with that weird bounding box behavior.
The photoshop way is the more intuitive and accurate.
You're welcome and of course your assessment of this feature in Illustrator hits the head on the nail. It is not intuitive in Illustrator and the feature needs lots of work.