I want to apply this effect to my artwork, but have no idea how to achieve this.
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Realize in the image above, all work was done by hand. The ears and eyes in each piece vary slightly, indicating manual drawing - not digital copying. The person drew the first.. then traced it, leaving a gap where desired.. then manually filled in the portions of the gap with a pen. Sometimes it is faster to work with a pen and paper than to work within an application.
Digitally... using Illustrator, you can merely select anchor points and move them.
Draw your art... add a line to define where you intend to split the image...
(Quick manual trace of the image, it's not perfect).
Using that line as a guide, intentionally add additional anchor points along paths which cross the guide.
I added one anchor at the line and one anchor slightly to the right of the line.
Two additional anchors because when I move the right anchor, a straight segment will be created between it an the anchor resting on the guide.
From here, you merely select any anchor point which is to the right of the guide... then drag....
(Again, far from perfect in the above, but you should get the idea.)
Image used for educational purpose and I make no claim to ownership or rights to the image. Copyright belongs to the original creator. Unfortunately I can't cite them specifically based upon this question. Google only found http://www.sohu.com/a/130980859_474139 which has the original image
You can get a similar effect by using a mesh warp. Take the following example:
Object → Envelope Distort → Make with Mesh... and set a single row and large number of columns. You essentially need your columns to be narrow enough to only cover the part that needs distorting.
If you want the "cut" at an angle then just rotate your artwork in the opposite direction before applying the mesh and rotate back after the mesh is applied, as I've done here:
Use the Direct Selection Tool to select a bunch of rows and move...
There are a few ways to accomplish what you want. I'll outline what I think are the two simplest.
1- Draw your artwork using the pen tool (p). You need to have continuous lines/shapes. Next create a new layer, draw the line where you would like to have the effect start. Lock that layer. Return to the layer with the artwork, using the pen tool add anchor points (+) along the line where you wanted the effect to occur. Once that is done you are free to use the direct selection tool (a) to select the all the points on the side of the artwork you would like to move.
2 - Draw your artwork using the pen tool (p). You need to have continuous lines/shapes.Next create a new layer, draw the line where you would like to have the effect start. Lock that layer. Now use the cut tool (c) and cut each line/object along the line where you want the effect to start. Note that shapes will do some weird things until you close the shape later. Using the selection tool (v) grab everything on side you want to move, position it where you want. Now pair up endpoints using direct selection tool (a) right click and choose join. It will draw the lines, connect them, and close any shapes you cut through.
Try grouping your design, drawing a line with the pen tool exactly like in your example, then use the Pathfinder tool and click the Divide option and it should give you 2 different shapes where the line was.
You could also try selecting only the anchor points on the area of the design you want to move and use the Direct Selection tool to move those specific anchor points and they should stay connected to the rest of the design and give you that trippy warped effect