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How do I make Illustrator not change the gradient's position and size when I change the path's shape?

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Essentially you don't. Gradient fills are based on the boundaries of the shape they are applied to. If you alter the boundaries, then the gradient position and length will change. It is simply how gradient fills work.

It's a very simple matter to grab the Gradient Tool and move the annotator to where you want it.

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Scott, thank you for the answer! Is it possible to rightly position the gradient using the Gradient Tool then? In other words, can I set certain X and Y of gradient ends? – Sunny Reborn Pony Apr 7 '13 at 19:18
No gradient in Illustrator allows you to set the X and Y specifically. But, using the Gradient Tool you can't manually move the start and end points as well as the size and shape of radial gradients. I'd provide screenshots, but you can't easily take screenshots of the Annotator. – Scott Apr 8 '13 at 2:33

You could do this by using a second path and a clipping mask:

  1. Original shape

    enter image description here

  2. Original shape with the second shape

    enter image description here

  3. Right click to the document with both shapes selected

    enter image description here

  4. The result:

    enter image description here

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Basically I draw a line parallel to the slider and after changing the shape I make the new slider follow that line. Of course you can also use a piece of tape on your screen. To make it myself easier use the following combinations: line ("\"), gradient tool (G) and select object below (cmd+alt+[)

Another way is to use the Info window to show the slider's coordinates. It also shows the slider's height, width, angle and length. Makes me wonder if someone could make use of this to create a guide line

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