How to change the center point of a irregularl shape/object in illutsrator CS5

Lets say I have a square, rectangle or circle. By default I get the center point of those which are positioned exactly in the middle. It is so because the binding box is same as the shape. It can be viewed by the Attributes Panel and clicking "Show Center".

Now I have other shapes which are irregular. If I look at the center point, it is positioned in the middle but the middle is relative to the bounding box of that shape. How would I go about selecting and editing the center point in such a way that it sits exactly in the center, horizontal and vertical relative to the shape and not the bounding box.

In the below image, on the top there is a square, a rectangle and a circle. The center point is exactly in the center.

Below that there is a chicken, cow and fish. The center point are not in the middle.

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The center point is always in the center of the object. It is not associated with the bounding box. You can turn off the Bounding box and retain the center point.

The object's (shape's) outer width and outer height are used to draw the center point as well as its bounding box. What you see is the exact center of your shapes. Moving it would place it off-center.

With symmetrical shapes, such as the rectangles and circle, it appears to be centered more. However it's just as centered in the irregular shapes of the chicken, cow, and fish. The difference is that every associated path in the irregular shapes is not an equal distance from the center of the shape as it is in the symmetrical shapes.

To illustrate more... see the attached image. It clearly shows the center point is in equidistant from either side. Green rectangle is merely a copy of the red rectangle.

However, all of this is irrelevant since you can not edit or alter the center point beyond showing and hiding it.

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I don't get it. When you say the center is not associated with the bouding box, does it mean the center point is always relative to the bouding box and not the co-ordinates of the shape? –  Jawad Mar 29 '12 at 17:53
Both the center point and the bounding box are relative to the shape. It may appear as though the bounding box and center point are associated, but they are not. They both simply use the same reference for drawing. Simply put.. those center points ARE centered based on the outer paths of the shape. –  Scott Mar 29 '12 at 17:54
Right. Thank you very much. –  Jawad Mar 29 '12 at 18:03