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We propose a specialized form of the curved-knot B-spline surface of Hayes [1982] that we call regular curved- knot spline surface. Unlike the original formulation where the knots of the first parametric coordinate can evolve arbitrarily with respect to the second coordinate, our formulation designs the knot functions as special curves that guarantee a monotonic blending of the knots corresponding to opposite surface boundaries. Furthermore, we demonstrate that local derivatives on the boundary can be described as an ordinary B-spline surface. The latter property allows for constructing smooth transitions between B-spline boundaries with different knot vectors. [ABSTRACT FROM AUTHOR]

Abstract: The envelope of a one-parameter set of spheres with radii and centers is a canal surface with as the spine curve and as the radii function. This concept is a generalization of the classical notion of an offset of a plane curve. In this paper, we firstly survey the principle geometric features of canal surfaces. In particular, a sufficient condition for canal surfaces without local self-intersection is presented. Moreover, a simple expression for the area and Gaussian curvature of canal surfaces are given. We also consider the implicit equation of canal surfaces with the degree of presented. By using the degree of , a low boundary of the degree of parameterizations representations of canal surfaces is presented. [Copyright &y& Elsevier]

Abstract: Dynamic partial differential equation (PDE) parametric curves which can be expressed as a coupled system of two hyperbolic equations are developed. In curve design, dynamic PDE parametric curves can be modified intuitively and are more flexible than ordinary differential equation (ODE) curves. The calculation of dynamic PDE parametric curves must recur to numerical methods and a three-level finite difference scheme is proposed. Approximation and stability properties for the scheme are proved and convergence property is derived. An example of interpolating PDE curves is presented as an application of dynamic PDE parametric curves. [Copyright &y& Elsevier]

Curves on surfaces play an important role in computer-aided geometric design. Because of the considerably high degree of exact curves on surfaces, approximation algorithms are preferred in CAD systems. To approximate the exact curve with a reasonably low degree curve which also lies completely on the -spline surface, an algorithm is presented in this paper. The Hausdorff distance between the approximate curve and the exact curve is controlled under the user-specified distance tolerance. The approximate curve is continuous, where is the user-specified angle tolerance. Examples are given to show the performance of our algorithm. [Copyright &y& Elsevier]

Abstract: By Bezout''s theorem, three quadric surfaces have at most eight isolated intersections although they may have infinitely many intersections. In this paper, we present an efficient and robust algorithm, to obtain the isolated and the connected components of, or to determine the number of isolated real intersections of, three quadric surfaces by reducing the problem to computing the real intersections of two planar curves obtained by Levin''s method. [Copyright &y& Elsevier]