The modification of a knot of a B-spline curve of order k generates a family of B-spline curves. We show that an envelope of this family is a B-spline curve defined by the same control polygon, and its order is k −m, where m is the multiplicity of the modified knot. Moreover, their arbitrary order derivatives differ only in a multiplier.  2003 Elsevier Science B.V. All rights reserved.

We propose the evolution of curves in direction of their unit normal using a combined implicit and explicit spline representation according to a given velocity field. In the implicit case we evolve a level set function for segmentation and geometry reconstruction in 2D images. The level set approach allows for topological changes of the evolving curves. The evolution of the explicit B-spline cu...

Cranial implants, especially custom made are complex, important and necessary in craniofacial fracture restoration surgery. However, the classical procedure of manual design implant is time consuming complicated. Different computer-based techniques proposed by different researchers, including CAD/CAM, mirroring, reference skull, thin plate spline radial basis functions have been used for crania...

Beta-spline is built on G continuity which guarantees smoothness of generated curves and surfaces using it. This curve is preferred to be used in object design rather than reconstruction. This study however, employs the Beta-spline in reconstructing a 3dimensional G image of the Stanford Rabbit. The original data consists of multi-slice binary images of the rabbit. The result is then compared w...