By a d-dimensional B-spline object (denoted as ), we mean a B-spline curve (d = 1), a B-spline surface (d = 2) or a B-spline volume (d = 3). By regularization of a B-spline object we mean the process of relocating the control points of such that they approximate an isometric map of its definition domain in certain directions and is shape preserving. In this paper we develop an efficient regul...

This paper studies the merits of using knot interval notation for B-spline curves, and presents formulae in terms of knot intervals for common B-spline operations such as knot insertion, differentiation, and degree elevation. Using knot interval notation, the paper introduces MD-splines, which are B-spline-like curves that are comprised of polynomial segments of various degrees (MD stands for “...

A personal account of the author's encounters with multivariate splines during their early history. 1 Tensor product spline interpolation My first contact with multivariate splines occurred in August 1960. In my first year at the Harvard Graduate School, working as an RA for Garrett Birkhoff, I had not done too well but, nevertheless, had gotten married and so needed a better income than the RA...

the hermit crab fauna of the larak island was investigated, which revealed seven species representing five genera and two families. the family diogenidae represents six species namely areopaguristes perspicax (nobili, 1906), clibanarius signatus heller, 1861, dardanus lagopodes (forskål, 1775), d. tinctor (forskål, 1775), d. avarus heller, 1865, d. tirmiziae siddiqui & mclaughlin, 2003, while t...

Asymptote is widely used in astronomy, mechanics, architecture and relevant subjects. In this paper, by analyzing the Frenet frame and the Darboux frame of a curve on the surface, the necessary and sufficient conditions for a quadrilateral boundary being asymptotic of a surface are derived. This quadrilateral is called asymptotic quadrilateral. Given corner data including positions, tangents an...

Gastropods are known for the presence of calcareous shells, even after their death. The diversity this resource can be reflected in local living gastropods. These shells used by hermit crabs as protection and against desiccation. Coastal lagoons biodiversity hotspots site recruitment continent-sea connectivity, is sometimes altered connectivity events with adjacent areas. Therefore, we sought t...

The paper introduces a new method for flexible spline fitting for copula density estimation. Spline coefficients are penalized to achieve a smooth fit. To weaken the curse of dimensionality, instead of a full tensor spline basis, a reduced tensor product based on sparse grids Zenger (1991) is used. To achieve uniform margins of the copula density, linear constraints are placed on the spline coe...

In this paper we study the sensitivity of a spline function, represented in terms of Bsplines, to perturbations of the knots. We do this by bounding the difference between a primary spline, and a secondary spline with the same B-spline coefficients, but different knots. We give a number of bounds for this difference, both local bounds and global bounds in general L-spaces. All the bounds are ba...

C-B spline can not represent semi-circle and semi-elliptical arcs precisely. This paper will discuss the nature of C-B spline’s and C-Bézier curve’s endpoints. Then, on the basis of the analysis of their characteristics and by means of adding control points to make C-B spline dominate the first and last vertices of the polygon and get tangency with the first and end sides. Thus it has given out...