In this paper odd-order B-spline filters are proposed to reconstruct volumetric data sampled on an optimal Body-Centered Cubic (BCC) grid. To make these filters nearly interpolating, we adapt a previously published framework, which is based on a discrete frequency-domain prefiltering. It is shown that a BCC-sampled B-spline kernel is not invertible, therefore the interpolation constraint cannot...

in this paper, a new numerical method for solving fractional optimal control problems (focps) is presented. the fractional derivative in the dynamic system is described in the caputo sense. the method is based upon biorthogonal cubic hermite spline multiwavelets approxima-tions. the properties of biorthogonal multiwavelets are first given. the operational matrix of fractional riemann-lioville i...

This paper explores the intrinsic link between natural cubic splines and subdivision. Natural cubic splines are deened via the varia-tional problem of minimizing a simple approximation of bending energy. A subdivision scheme is derived which converges to the minimizer of this particular variational problem. x1. Introduction Geometric design is the study of the representation of shapes with math...

We present a general framework for a higher-order spline level-set (HLS) method and apply this to bio-molecule surfaces construction. Starting from a first order energy functional, we obtain a general level set formulation of geometric partial differential equation, and provide an efficient approach to solve this partial differential equation using a C(2) spline basis. We also present a fast cu...

The (cubic) smoothing spline, of Schoenberg [S64] and Reinsch [R67], [R71], has become the most commonly used spline, particularly after the introduction of generalized cross validation by Craven and Wahba [CW79] for an automatic choice of the smoothing parameter. It is the purpose of this note to derive the computational details, in terms of B-splines, for the construction of the weighted smoo...

Most shapes are simply too complicated to define using a single Bézier curve. A spline curve is a sequence of curve segments that are connected together to form a single continuous curve. For example, a piecewise collection of Bézier curves, connected end to end, can be called a spline curve. Overhauser curves are another example of splines. The word “spline” can also be used as a verb, as in “...

New algorithms for the classical problem of fairing cubic spline curves and bicubic spline surfaces are presented. To fair a cubic spline curve or a bicubic spline surface with abnormal portions, the algorithms (automatically or interactively) identify thèbad' data points and replace them with new points produced by minimizing the strain energy of the new curve or surface. The proposed algorith...