Adobe Illustrator CC 2015 - Manual (Page 193)

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Painting
Last updated 6/5/2015
To create a discontinuous width point do the following:
1 Create two width points on a stroke with different stroke widths.
2 Drag one width point on to the other width point to create a discontinuous width point for the stroke.
For discontinuous points, the Width Point Edit dialog box shows both sets of side widths.
The Single Width Only check boxes allow using either incoming or outgoing width leaving a single continuous width
point.
Width tool controls
The following table lists the keyboard modifiers to use while working with the Width tool: