Wavelets based quantitative design of B-spline curves

• The concept of reference index of modeling is proposed.
• A new modeling algorithm is put forth for B-spline curves.
• The objective shape is evaluated quantitatively by the new approach.
• The effectiveness of the new algorithm is verified by some examples.

In order to achieve a better control of deformations and a more accurate modeling, this paper first introduces a new concept called “reference index of modeling (RIOM)” by wavelet technology. Next, according to RIOM, a quantitative modeling algorithm of B-spline curves is presented. Compared with the traditional modeling methods, the present algorithm employs the RIOM as the objective function and the objective shape can be evaluated quantitatively by the value of the RIOM based objective function. Meanwhile, the new algorithm can preserve the overall shapes during the deformation. Several examples are given to demonstrate the effectiveness of this approach.