In this paper, we propose basic and improved algorithms based on polynomial B-spline form for constrained global optimization of multivariate functions. The proposed are a branch-and-bound framework. algorithm introduce several new ingredients, such as box consistency hull to prune the search regions make more efficient. performance is tested compared set test problems. results tests show super...

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The Body Centered Cubic (BCe) and Face Centered Cubic (FCC) lattices along with a set of box splines for sampling and reconstruction of trivariate functions are proposed. The BCC lattice is demonstrated to be the optimal choice of a pattern for generic sampling purposes. While the FCC lattice is the second best choice for this purpose, both FCC and BCC lattices significantly outperform the accu...

In this paper we calculate the Ehrhart’s polynomial associated with a 2-dimensional regular polytope (i.e. equilateral triangles) in Z. The polynomial takes a relatively simple form in terms of the coordinates of the vertices of the triangle. We give some equivalent formula in terms of a parametrization of these objects which allows one to construct equilateral triangles with given properties. ...

We propose a novel approach for the approximate parameterization of an implicitly defined curve in the plane by polynomial parametric spline curves. The method generates the parameterization of the curve (which may consist of several open and closed branches) without using any a priori information about its topology. If needed the topology of the approximate parameterization can be certified ag...

This paper presents a new segmentation algorithm by tting active contour models (or snakes) to objects using adaptive splines. The adaptive spline model describes the contour of an object by a set of piecewisely interpolating C 2 polynomial spline patches which are locally controlled. Thus the resulting description of the object contour is continuous and smooth. Polynomial splines provide a fas...

In this paper, we study polynomial spline collocation methods applied to a particular class of integral-algebraic equations of Volterra type. We analyse mixed systems of second and first kind integral equations. Global convergence and local superconvergence results are established.

A general theory of quasi-interpolants based on trigonometric splines is developed which is analogous to the polynomial spline case. The aim is to construct quasi-interpolants which are local, easy to compute, and which apply to a wide class of functions. As examples, we give a detailed treatment including error bounds for two classes which are especially useful in practice.