Alter shapes with path operations

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Merge Paths options
Using the Repeater to replicate shapes

Path operations are similar to effects. These live operations act nondestructively on a shape’s path to create a modified path that other shape operations (such as fills and strokes) can apply to. The original path is not modified. Because path operations are live, you can modify or remove them at any time. Path operations apply to all paths above them in the same group; as with all shape attributes, you can reorder path operations by dragging, cutting, copying, and pasting in the Timeline panel.

In the Composition panel or Timeline panel, select the shape group into which to add the path operation.
Choose a path operation from the Add menu in the Tools panel or the Timeline panel:
Merge Paths

Combines paths into a compound path. (See Merge Paths options.)
Offset Paths

Expands or contracts a shape by offsetting the path from the original path. For a closed path, a positive Amount value expands the shape; a negative Amount value contracts it. The Line Join property specifies the appearance of the path where offset path segments come together. A bevel join is a squared-off connection. A miter join is a pointed connection. The miter limit determines the conditions under which a beveled join is used instead of a miter join. If the miter limit is 4, then when the length of the point reaches four times the stroke weight, a bevel join is used instead. A miter limit of 1 causes a bevel join.
Pucker & Bloat

Pulls the vertices of a path outward while curving the segments inward (Pucker), or pulls the vertices inward while curving the segments outward (Bloat).
Repeater

Creates multiple copies of a shape, applying a specified transformation to each copy. (See Using the Repeater to replicate shapes.)
Round Corners

Rounds corners of paths. Higher Radius values cause greater roundness.
Trim Paths

Animate the Start, End, and Offset properties to trim a path to create results similar to results achieved with the Write-on effect and the Write On setting for paint strokes. If the Trim Paths path operation is below multiple paths in a group, then you can choose to have the paths trimmed simultaneously or treated as a compound path and trimmed individually.
Aharon Rabinowitz provides a video tutorial on the Creative COW website that shows how to use the Trim Paths operation to animate a dashed line following a path on a map.

Twist

Rotates a path more sharply in the center than at the edges. Entering a positive value twists clockwise; entering a negative value twists counterclockwise.
Wiggle Paths

Randomizes (wiggles) a path by converting it into a series of jagged peaks and valleys of various sizes. The distortion is auto-animated, meaning that it changes over time without the need to set any keyframes or add expressions.
Several properties for this path operation behave the same as properties of the same name for the Wiggly selector for text animation. (See Wiggly selector properties.) The Correlation property specifies the amount of similarity between the movement of a vertex and that of its neighbors; smaller values create more jagged results, as the position of a vertex depends less on the position of its neighbors. The Correlation property is similar to Correlation for the Wiggly selector, except that the Wiggle Paths version specifies the correlation between neighboring vertices instead of neighboring characters. Set the maximum length for segment paths using an absolute or relative size. Set the density of jagged edges (Detail) and choose between soft edges (Smooth) or sharp edges (Corner).
Animate the Size property to fade the wiggling up or down. To smoothly accelerate or decelerate the wiggling, set Wiggles/Second to a constant value of 0, and animate the Temporal Phase property.

Wiggle Transform

Randomizes (wiggles) any combination of the position, anchor point, scale, and rotation transformations for a path. Indicate the desired magnitude of the wiggle for each of these transformations by setting a value in the Transform property group that is contained in the Wiggle Transform property group. The wiggled transformations are auto-animated, meaning that they change over time without the need to set any keyframes or add expressions. The Wiggle Transform operation is especially useful following a Repeater operation, because it allows you to randomize the transformations of each repeated shape separately. (See Using the Repeater to replicate shapes.)
Several properties for this path operation behave the same as properties of the same name for the Wiggly selector for text animation. (See Wiggly selector properties.) The Correlation property specifies the amount of similarity between the wiggled transformations of a repeated shape and its neighbor within a set of repeated shapes. Correlation is only relevant if a Repeater operation precedes the Wiggle Transform operation. When Correlation is 100%, all repeated items are transformed in the same way; when Correlation is 0%, all repeated items are transformed independently.

When randomizing repeated shapes keep the following in mind: If the Wiggle Transform path operation precedes (is above) the Repeater path operation, then all of the repeated shapes will be wiggled (randomized) in the same way. If the Repeater path operation precedes (is above) the Wiggle Transform path operation, then each of the repeated shapes will be wiggled (randomized) independently.
Chris Meyer provides a video tutorial on the ProVideo Coalition website that shows how to use the Wiggle Transform path operation. This tutorial explains why you must use multiple instances of the Wiggle Transform path operation if you want to wiggle multiple properties independently.

Zig Zag

Converts a path into a series of jagged peaks and valleys of uniform size. Set the length between peaks and valleys using an absolute or relative size. Set the number of ridges per path segment, and choose between wavy edges (Smooth) or jagged edges (Corner).

Merge Paths options

The Merge Paths path operation takes all of the paths above it in the same group as input. The output is a single path that combines the input paths. The input paths are still visible in the Timeline panel, but they are essentially removed from the rendering of the shape layer, so they don’t appear in the Composition panel. A fill and stroke are added after the Merge Paths property group in the Timeline panel if a fill and stroke are not already present; otherwise, the output path wouldn’t be visible.

Merge Paths options

A.: Add for all shapes
B.: Subtract for squares
C.: Intersect for squares
D.: Exclude Intersections for squares

Aharon Rabinowitz provides a video tutorial on the Creative COW website that shows how to combine multiple paths into a single compound shape using the Merge Paths path operation.

The Merge Paths path operation has the following options, each of which performs different calculations to determine the output path:

Merge: Merges all input paths into a single compound path. This option is the default used for shapes created from text characters made up of multiple paths, like the letter e, when using the Create Shapes From Text command.
Add: Creates a path that encompasses the union of the areas of the input paths.
Subtract: Creates a path that encompasses only the areas defined by the topmost path, subtracting the area defined by underlying paths.
Intersect: Creates a path that encompasses only the areas defined by intersections between all input paths.
Exclude Intersections: Creates a path that is the union of the areas defined by all input paths, minus the areas defined by intersections between all input paths.

Using the Repeater to replicate shapes

The Repeater path operation creates virtual copies of all paths, strokes, and fills above it in the same group. The virtual copies are not represented by separate entries in the Timeline panel, but they are rendered in the Composition panel. Each copy is transformed according to its order in the set of copies and the values of the properties in the Transform property group for that instance of the Repeater.

Original shape (upper-left), one instance of the Repeater operation applied (upper-right), and two instances of the Repeater operation applied (lower-right)

If the original shape is numbered 0, the next copy is numbered 1, and so on, then the result of the Repeater is to apply each transformation in the Transform property group n times to copy number n.

Consider the example of the Repeater applied to a shape with the Copies value set to 10 and the Position property in the Transform property group for the Repeater set to (0.0, 8.0). The original shape remains in its original position, (0.0, 0.0). The first copy appears at (0.0, 8.0), the second copy appears at (0.0, 16.0), the third copy appears at (0.0, 24.0), and so on until the ninth copy at (0.0, 72.0), for a total of ten shapes.

You can apply multiple instances of the Repeater within the same group. In other words, you can repeat the Repeater. Using multiple instances of the Repeater is an easy way to create a grid of virtual copies of a single shape: just set the Position property for one instance of the Repeater to modify the horizontal values, and another instance to modify vertical values.

The Offset property value is used to offset the transformations by a specific number of copies. For example, if the Copies value is 10 and the Offset value is 3, then the original shape is transformed by 3 times the amount specified in the Transform property group, and the last copy is transformed by 12 times the amount specified in the Transform property group.

Animating the Offset property is a good way to easily create interesting results.

The Composite option determines whether copies are rendered above (in front of) or below (behind) the copies that precede them.

Use the Start Opacity value to set the opacity of the original shape, and the End Opacity value to set the opacity for the last copy. Opacity values for copies in between are interpolated.

If you place the Repeater after a path, above the fill and stroke property groups for a shape, then the set of virtual copies is filled or stroked as a compound path. If you leave the Repeater below the fill and stroke, then each copy is filled and stroked individually. The difference is most apparent with gradient fills and strokes.

Add a Wiggle Transform path operation after a Repeater operation to randomize (wiggle) the position, scale, anchor point, or rotation of the repeated copies within an instance of the Repeater. If the Wiggle Transform path operation precedes (is above) the Repeater path operation, then all of the repeated shapes will be wiggled (randomized) in the same way. If the Repeater path operation precedes (is above) the Wiggle Transform path operation, then each of the repeated shapes will be wiggled (randomized) independently.

Eran Stern provides a video tutorial on the Creative COW website that shows how to use the Repeater operation.

Chris Zwar provides an example project on his website that uses the Card Dance effect and a shape layer with the Repeater operation to simulate a halftone color separation for any image or video.