The Gradient Tool lets you edit existing gradeints on existing shapes. If you want to assign a gradient to a shape, you can pick the shape with this tool, and assign a linear gradient from the "Fill" tab window. Also note that handles displayed will be different depending on which gradient type is being edited; however, any handle displayed reflects the gradient colour at that position.
Linear Gradients
Linear gradients are represented by their start location and end location (the start and end, as well as any optional intermediate colours and opacities can be edited from the "Fill" tab window). You can change either location by clicking with the left mouse button and dragging to the desired new location.
Radial Gradients
Radial gradients are defined by the center and the X and Y radii. You can edit any of the three by dragging a corresponding box. Also note that holding Shift will make both radii the same in length, while holding Control will scale the radii proportionately.
Center-Out Gradients
This type of gradient allows only the center position to be moved by clicking and dragging it to the new desired location.
Center Gradient: Centers the gradient relative to the shape.
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