The Shape Analysis of DTB-like and DT B-spline-like Curves

Abstract

In the field of computer-aided design and related applications, the free curve with parameters shows its strong function. But an excellent curve with parameters need to eliminate unnecessary cusps and inflection points, so shape analysis is needed for some specific curves. We have already shown many excellent properties of the DTB-like curves and DT B-spline-like curves. Thus the shape features like convexity, loops, inflection points, and cusps of the DTB-like curves, and DT B-spline-like curves are further discussed in this paper. And the necessary and sufficient conditions for the existence of shape features of the corresponding DTB-like curves and DT B-spline-like curves are given. And the shape features distribution all be generalized into tables and diagrams, which are useful for industrial design. In addition, the effect of shape parameters on the shape features diagram and its adjustment ability to the shape of corresponding curves are analyzed, respectively. The work in this paper enables users to determine how to set parameter values so that the generated curve could be a global convex or local convex curve, has a required inflection point, or eliminate the unnecessary one, and could be adjusted to another aimed shape.