How can I resize such items without changing the curvature at edges? You know, I don't want the half-circles at the extremes to become half-elipses.
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Hold down the shift key while dragging a corner handle.
Or, the more accurate and flexible method is directly selecting all the vector point anchors for one side (2 corners) and dragging that over, then selecting the other half to drag another side in another direction to achieve the desired dimensions.
You can only do that with the "Direct Selection Tool" which is the second, white, "pointer" button in the Illustrator tools palette. It selects points of a shape instead of the whole shape.
Holding Shift while resizing will constrain proportions and keep the ends as semicircles. If your resized shape is too wide, use
Direct Select (A) to select anchors on one side and then move them to where they need to be.
If you need the edges aligned with other objects, the easiest way is to duplicate your resized object and combine the 2 shapes using overlapping areas.
Step 1: The Initial Resize (to get the correct height without distorting your ends)
Step 2 (Option A): Adjust Width Using Direct Selection (move some anchors)
Step 2 (Option B): Adjust Width Using Compount Shapes (good for aligning with other objects)
I don't know which version of Illustrator you're using, and I also don't recall which version of Illustrator this first arrived in (CS3, maybe?), but the exact answer to your question is: turn on 9-slice scaling for your object.
The instructions for turning this on in CS5 are here in the Illustrator help, but maybe it will help to explain what the heck 9-slice scaling is and why somebody invented it in the first place.
"Why" is easy: it was to solve the exact problem you are running into, where the designer needs to scale an object without affecting the corner radius. 9-Slice Scaling divides the object into three, horizontally and vertically, then protects he four corners while allowing the center and edges to scale up and down. I can't improve on the Fireworks help page that shows all this very clearly.
I was having the same issue, with 'scale stroke and effects' turned as well as turned off. No matter what I tried, holding shift, resizing in different techniques... once I got down to a smaller size, my rounded corners basically became a half circle at the top and bottom of my rectangle. My workaround suggestion is this. Place a very thin stroke around your rectangle once you have the corners how you like them. Convert that stroke to outlines. And then in outline mode (cmd Y), go in with your white arrow tool and delete the outer line.. this seems to create a 'new' shape to the same proportions as your original rectangle, minus the set curvature for the corners... now those curved corners are set it stone and the only way to adjust them is the old fashioned way. I am sure that the the techniques mentioned above are the smart way to do it... but for me, they just were not working. And reading a few threads on this issue, it seems like others are having the same issue... or had the same issue three years ago. Good luck.