B-spline curves
interpolation, fitting; energy minimization curve fairing; fair curve on surface; curve with fixed length; parser and convert equations into NURBS curve; curve extracted from mesh boundary, image silhouettes, and free-hand sketching.

Curve faring by energy minimization. When interpolating the six blue sample points, using our curve fairing technique, the new gray curve is better than the original red curve with much more smooth curvature combs of new curve (yellow) than the original one (red).

 
Equation driven curves

 
Fair curve on surface


3D Curve defined by length & end tangency


Smooth curves (pink) can be extracted from mesh boundary.

2D quadratic silhouette curves (e.g. lines, arcs …) in right images are extracted from the left original image.

The freehand sketching tool: quadratic sketch segments as well as freeform spline curves can be recognized and fitted from user free sketches drawn on a tablet.