A method for approximate NURBS curve compatibility based on multiple curve refitting

This paper presents an approximate method for making a set of NURBS curves of various types compatible. The method is based on refitting input curves simultaneously on a common knot vector while making the refitted curves have parametrically regular transition across curves. It adopts a concept of reducing the number of interior knots of the common knot vector to acquire more compact representation for the resultant curves. It also incorporates energy minimization in the curve refitting process to stabilize the solution of the curve fitting problem and to get smooth curves. The proposed method can be utilized in several construction tasks including surface skinning and surface creation from a mesh of curves. It plays an important role in improving the quality of surfaces and realizing efficient reduction of their control points especially when the parameterization and the compatibility of input curves are not good enough. Some experimental results demonstrate its usefulness and quality.