The extend path plug-in is a powerful tool for Illustrator (from Astute Graphics) to modify open curves without the need to manually extend them using others such as the join to add a spiral etc. The easiest way to show an example of this feature is to show examples from a basic single line segment. It works on open design only (such as a line or curve), it is of no use with a closed design
Double click the icon or press return. You will see many options such as extension mode / radius mode / always use fixed radius / reverse / constrain. They are all super useful features that can be used even with a single line but they can be used to modify many other types of open curves such spirals or arcs or artwork from the curvature. It should be noted that some options require others to be set so the extension mode has to be constant radius and spiral for the radius mode to be of use. You can also reverse the lines via the reverse curvature. The spiral option in the extension mode is wonderful for all kinds of spiral designs.
Set the extension mode to constant radius and use a fixed radius setting of 140 or so. Select a straight line. Apply it at both ends to create a nice curved S like design. Of course, you don't need to use just a straight line but for testing purposes that is often the easiest to start with. You can use a curve perhaps created by the curvature. In the example on the right you can see the curved line in dashes following the same as the settings on the left. You can set a smaller radius and you will see a smaller curve attached to the line.
You can use it with one or multiple curves but they can only be modify one at a time. You do not need to keep selecting the curve. Just hover over the end point for any of the curves you want to change and a little indicator will appear and then the preview path will be displayed. You can also hover over that and repeat the operation creating an even longer line or curve. You can also simply update the radius and change it from 30px to 60px etc You can do this via the dialog but you can change the setting for the radius by using the mouse keys left and right to decrease and increase the radius. You can also use others such as join to connect the various lines.
You can select a basic shape (such as a line) and then go to the appearance panel and add effects. Create a straight line. Go to the effects menu and select the distort / transform and apply a transform with 9 copies and 36 degrees rotation. Select and click on the end point of the 'key' line (no point trying to do it with the duplicates) and apply. Use the mouse keys to increase or decrease the radius (using the constant radius and use fixed radius value)
As it is a live effect (transform) and you can display the options by going to the icon and double clicking that - you can also reverse and change the size and radius to create all kinds of wavy curved lines with the live transformation. The artwork is live so you can still transform and shift and rotate and shear and warp etc. Any changes you make with it will be updated in any copies etc
You can use it to add to a line or a curve and you can also use it to cut away or cut back a line or curve. Go to a curve or line, select it, select either end of the line or curve (or go to the other end after you have modified the first end point). And follow the curve back on itself to remove the design.
Select a curve or straight line etc and then go to the object menu and use the repeat radial command and you will create multiple copies of the artwork. Double click on one of the entries and then you can edit that and any changes made to that one object will be reflected in all the other objected in the repeat. You can also apply it to add to spirals, increase or decrease the curve etc and they will also be updated in all the other parts of the design.
You can apply a width profile (or brush stroke) and then use the tool. Select a line. apply a width profile. use the tool.
There are a few switches or shortcuts while you use such as
V which reverses the curvature direction
M Absolute measurements / percentage
E goes through the extension modes such as single then constant etc
Up / down arrow keys for the spiral constant
left / right arrow keys for scale radius