Computer Aided Geometric Design

Lines of curvature are important intrinsic characteristics of a curved surface used in a wide variety of geometric analysis and processing. Although their differential attributes have been examined in detail, their global geometric distribution and ...

From the rational functions defining a rational plane curve it is possible to construct two bivariate polynomials that can be seen as univariate polynomials in the parameter value. In this paper several relevant properties of the subresultant sequence ...

We introduce a non-uniform subdivision algorithm that partitions the neighborhood of an extraordinary point in the ratio @s:1-@s, where @s@?(0,1). We call @s the speed of the non-uniform subdivision and verify C^1 continuity of the limit surface. For @s=...

We provide a technique to detect the singularities of rational planar curves and to compute the correct order of each singularity including the infinitely near singularities without resorting to blow ups. Our approach employs the given parametrization ...

We construct closed trigonometric curves in a Bezier-like fashion. A closed control polygon defines the curves, and the control points exert a push-pull effect on the curve. The representation of circles and derived curves turns out to be surprisingly ...

In this paper, we study a necessary and sufficient condition for a planar quartic Bezier curve to possess a Pythagorean-hodograph (PH). Based on the definition of PH curve and complex representation of planar curve, we deduce geometric conditions in ...

A given polynomial of degree less than or equal to n naturally ''blossoms'' into a function of n variables called its blossom. Considered as a polynomial function of degree less than or equal to (n+1) it ''blossoms'' into a ''new'' blossom which is now ...