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The ExtendDynamic command extends a curve by its natural extension to a boundary or point.
Commandline options  

Select a boundary to extend the curve to. 

Type 
NaturalLines, polylines, and polycurves with a line at the end to extend are extended by line. Arcs and polycurves with arc at the end to extend are extended by same radius arc. Other curves are extended smooth. ArcMakes an arc extension tangent to the original curve. Arc optionsCenterExtends a curve with an arc by picking the arc's center and endpoint. Center steps
LineMakes a line extension tangent to the original curve. SmoothMakes a smooth curve extension curvature continuous with the original curve. 
ToPoint 
Extends a curve smoothly by picking the curve's endpoint. 
Undo 
Reverses the last action. 
Rhinoceros 6 © 20102020 Robert McNeel & Associates. 21Feb2020