You are welcome, Calai, and thank you for sharing.   You can improve the shapes of the new parts 1, 2, and 3, so both Anchor Points are smooth by ClickDragging at both Anchor Points, instead of only Clicking the first Anchor Point, which starts out as a corner and the wrong direction straight towards the other end, and then trying to correct and smooth the first end by ClickDragging the second Anchor Point (obtained at second try for part 3), which then becomes a corner.   If you ClickDrag the first Anchor Point, you can start the new part as a smooth curve with the right direction at the first Anchor Point, and then ClickDrag the second Anchor Point so it is also smooth, in other words work with the two Anchor Points independently to shape the part from both ends.   The key to this is that when you ClickDrag, you are no just dragging out one Handle, but a pair og Handles consisting of the Handle you drag and an exactly opposite mirrored Handle.   When you ClickDrag the first Anchor Point, you can look at the opposite mirrored Handle and ensure that it has the same direction as the existing part, and when you ClickDrag the second Anchor Point, you can just look at the Handle you are dragging out and ensure that it has the same direction as the existing part.   This was what I meant by the above description of the curved part from 1-1) to 1-2), which I have enhanced by the underlined parts (both here and there):   "Then draw the curved part from 1-1) to 1-2): With the Pen Tool Click to snap to 1-1) (Smart Guides say anchor when you are within snapping distance), then ClickDrag down to the left so that the opposite mirrored Handle to the top right follows the direction of the existing curve at 1-1), and so that the Handle length is about one third of the distance to 1-2), Repeat 1. only with 1-2), where you ClickDrag down to the left so that the Handle you are dragging out to the bottom left follows the direction of the existing curve;"Setting the Handle length to about one third of the distance is just a general suggestion to obtain an even curve, and the right lengths, which can be different, depend on the (desired) shape.   If you wish to improve the shape of the part you have just drawn, you can use Ctrl/Cmd+Z to Undo the whole thing and start over. In this way you can avoid changing the existing parts.   Below I have included two sample GIFs, each switching between smooth Anchor Points only and one with a corner at 3-2) where the Cut is.   The first GIF corresponds to a multiple exposure photo showing each part in black with the pair of Handles at each end, and the second GIF shows the final parts in red as the rest. Click to get closer, Click again to get closer still Click to get closer, Click again to get closer still     With the smooth Anchor Points at 3-2), the new part/dash forms a smooth continuation of the right handle, also corresponding to your first screenshot where the dash extends into the rhight handle.   Since the Cut has been moved to a corner, the top right end of the dash is independent of the right handle so a corner there is fine, just as you made it.   ... View more

Calai,   You can do it in a fully accurate way corresponding to my W reply.   But Referring to your screenshot with markings below, you can also do it in a coarser/simplified way as follows, still with unchanged unchanged visible parts of the original path, based on drawing by eye with the Pen Tool, Smart Guides being your friends:   First copy your i dot twice on top of itself and lock and hide the original and the first copy, and work on the second copy;   Then with the Pen Tool Click on the outside and the inside of the top right curve of the i dot path where you wish to cut it to start the dash (Smart Guides say path when you are within snapping distance, and you can move the points back and forth until you are satisfied), and then use ObjectPath>Divide Objects Below;   Now you have cut the path which remains closed with straight segments between the two new Anchor Points; this corresponds to steps 2) - 3) in my W reply;   Then with the Scissors Tool, move the cursor to each of the points, 1-1), 1-2), 2-1), 2.2), 3-1), 3-2) where Smart Guides say anchor when you are within snapping distance, make sure you snap to the bottommost of the two Anchorpoints at 3-1);   Now you have cut up the copy path; this corresponds to step 4) in my W reply;   Then with the (normal) Selection Tool select the handle parts and leave the dash part; this corresponds to step 5) in my W reply;   Then draw the curved part from 1-1) to 1-2): With the Pen Tool Click to snap to 1-1 (Smart Guides say anchor when you are within snapping distance), then ClickDrag down to the left so that the opposite mirrored Handle to the top right follows the direction of the existing curve, and so that the Handle length is about one third of the distance to 1-2), Repeat 1. only with 1-2), where you ClickDrag down to the left so that the Handle you are dragging out to the bottom left follows the direction of the existing curve;   Then draw the curved parts from 2-1) to 2-2) in the same way;   Then draw the curved parts from 3-1) to 3-2) in the same way, make sure that you snap to ;   These three steps correspond to corresponds to steps 6) - 10) in my W reply;   Now you have the dash drawn by eye;   Then switch from Stroke to Fill and give the dash its colour; this corresponds to step 11) in my W reply;   Then Show and Unlock the first copy of the i dot path, and switch from Stroke to (black) Fill; this corresponds to step 12) in my W reply;   Now you can see what it looks like;   Then select both paths and use Minus front (Pathfinder); this also corresponds to step 12) in my W reply.   Click to get closer, Click again to get closer still   Edit: A few bold italic underlined additions have been made. See this reply for explanations: https://community.adobe.com/t5/illustrator-discussions/how-to-cut-a-letter-into-multiple-shapes/m-p/15498504#M452893   ... View more