Date of Award
Master of Science (MS)
Precise curve fitting is an important feature of many computer applications, from statistical analysis cools, co the editors used by font and graphic designers, co the sophisticated computer-aided design/manufacturing environments developed for engineering systems. B-splines are the most widely used curve forms in such applications; composed of piecewise parametric cubic segments, they are notable for their compact representation, computational efficiency and, in particular, the high degree of continuity they enforce between successive curve segments. Such continuity, however, inhibits the freedom with which local, finer resolution editing may be performed on these curves. Refinement is most directly accomplished by inserting knots into the curve, subdividing the curve into a larger number of segments.
Mulciresolution analysis, a form of data analysis based on the use of wavelets, offers a means of determining a unique such subdivision of a given curve. The application of chis process is also reversible so chat curve smooching or knot removal operations may be performed with the same economy as refinement operations. Furthermore, the special computational properties of wavelets guarantee chat such shifts of resolution may be performed in time linear with the size of the curve, suggesting chat editing operations on a curve, at a variety of resolutions, may be done at interactive speeds.
Alberg, Stephen P., "Interactive Multireslution Curve Editing Using" (1999). Open Access Master's Theses. Paper 992.