Regularity and Convexity of NURBS Curves

Determining regularity and convexity of NURBS curves is necessary in computer aided geometric design. In this paper, the problems above are converted to the questions related to polynomials. Then based on properties of algebraic equations and isolation theorem of roots, a simple and practical method for determining those geometric properties of NURBS curves is put forward. Compared with traditional method it will save us much computation

Regularity of Bézier Curves

Regularity is one of important properties of curves in computer aided design. In this paper, we convert the problem of determining regularity of Bézier curves to that of detecting existence of zero points of polynomials. Based on the properties of algebraic equations and isolation theorem of roots, a simple and practical method is presented. Regularity of Bézier curves and number of singular points can be determined by easier computation.