You may know that Average can find the center of an object. This is done by averaging both axes.
You may not have thought about using Average on selected points. The Average function does exactly the same thing on points within a path as it does on the entire path. It finds the average of the point positions and moves all of the points to that plane. If you choose Both for the average Axis you end up with a point instead of a plane. Just use the Direct Selection tool to select the points you want to adjust.
Let’s say for example you created some artwork and reflected it to merge the two into a symmetrical design. When brought together, some points do not line up perfectly. This slight misalignment would leave a gap in your artwork. You could just move one of the points to the other so that they are registered but that ruins the symmetrical nature of the design. You could try to guess where the middle between the points is and move them both there. At best it is still a guess and it is more work than it should be. Average can do this for you automatically.
Direct Select the points you want to merge and click Object > Path > Average (Alt/Opt + Ctrl/CMD + J). When the dialog box pops up select Both and click OK. Illustrator finds the exact center between the two points and moves them there.
Depending on your art you may choose to join the points into the same path. When you join paths at points in perfect registration, Illustrator removes the unnecessary point. If they are not in exactly the same spot the extra point gets left on the path. When extra points are not in perfect registration and they are on a corner they can cause another problem. This can cause misshapen corners on your art.
Moving one or both points so that they are in exactly the same position fixes this problem. This can be tedious if you have many corners like this. Sometimes you want the points to move to the exact middle of their current position. It would be challenging to attempt this manually. After using average (both) you see the intended shape.
Both points are in perfect registration and no longer cause the skewed corner. At this point you can select the point and delete it if you like. Since the points are in exactly the same spot the corner won’t move. The points have different handle positions so the shape of a curve adjacent to the point may change. If you concerned about the shape changing then just leave the points where they are.
Another use for Average is making lines horizontal or vertical. This is sometimes useful when editing artwork which was vectorized with Live Trace. When you choose Horizontal the line is made horizontal. With Vertical the line is made vertical.
This table shows several shapes and the results of horizontal and vertical averaging.
In row 1 you see the shortening of the line as it is pressed into a single plane. In rows 3 through 5 you see that some interesting results are possible when simple shapes are rotated prior to averaging. In row 5 the points were converted to smooth and the handle lengths were scaled longer to approximate a circle. This resulted in a “curvier” shape when averaged.
A horizontal averaging aligns all points in the shape along a horizontal line. A vertical averaging aligns all points I the shape along a vertical line. Some of the results remind me, just a little, of pucker and bloat. There is no adjustment possible with Average but unlike pucker and bloat it can be applied in a single plane. You could select some of the points after averaging and move them apart a little to “un-average” them making a unique shape.
There are untapped creative possibilities using the Average function. It would have to be used in conjunction with other tools but it’s worth taking some tie to explore Average.