Sharpen > Sharpen Polygons (available after Sharpen > Extend Tangent Lines) creates a suggested edge that is defined by the intersection of tangent lines from the previous step, allows that suggested edge to be smoothed, then extends the polygon mesh up to the suggested edge to form a sharp edge.
When the dialog opens, immediately press Update Grid to see the initial suggestion of a sharp edge. If necessary, adjust the parameters and press Update Grid again. Press Sharpen Polygons to reconstruct the polygon mesh to match the suggested sharp edge, then Done.
The controls are:
Edit group - specifies a method of inserting control points on the length of the selected suggested edge. To select a suggested edge for editing, click it in the Viewing Area. To cause two or more contiguous suggested edges to behave as one, select one suggested edge then shift-click one or more contiguous suggested edges.
Control Point Layout dropdown (Constant or Tolerance Based) - specifies the method of inserting control points onto the suggested sharp edge.
Constant - allows an evenly spaced number of control points to be specified (in the Control Points field).
Tolerance Based - inserts more control points in areas of high curvature and fewer control points on straight area of the suggested sharp edge, and
Control Points field (when Control Point Layout is Constant) - specifies the exact number of evenly spaced control points on the selected suggested edge.
Tolerance field (when Control Point Layout is Tolerance Based) - specifies the greatest distance that a suggested sharp edge is allowed to stray from its control points when the Tension is turned up.
Tension field - specifies a degree of elasticity between the endpoints of the selected sharp edge(s). Higher tension creates a smoother edge that strays from the control points (and the original geometry).
Apply to All button - applies the Control Point Layout and its parameters to all suggested edges on the object, not just the selected suggested edge.
Update Grid button - applies the Control Point Layout to the selected suggested edge. The result is a framework on which additional polygons will be constructed when you press Sharpen Polygons.
Sharpen Polygons button - reconstructs the polygon mesh to cover the framework and thus sharpen the edge(s).
Done button - saves the sharpened polygon object to the Model Manager and closes the dialog.
Cancel button - terminates the dialog without saving the sharpened polygon object.
Next >> button (appears only when this function is called through the Polygons > Sharpening Wizard) - no function, because this is the last step of the Wizard.