B-Splines have been popular for several purposes. In this work, B-Splines are used for modeling noisy multivariate data. A new algorithm is proposed to approximate image data with B-Spline surfaces, where image data is assumed to be corrupted by Gaussian noise mixed with outliers. The resulting surface gives a restored continuous representation of discrete data while preserving edges. A gradien...

The calculation of moments area is one the most fundamental aspects engineering mechanics for calculating properties beams or determination invariants in different kind geometries. While a variety shapes, such as circles, rectangles, ellipses, their combinations, can be described symbolically, symbolic expressions are missing freeform cross-sections. In particular, periodic B-spline cross-secti...

Pen-input is not a new means for CAD designers, in particular, in the concept design phase. Meanwhile, B-Splines are well known curve and surface design tool in 3D shape modeling in the final modeling stages in which neat curves and surfaces should be produced. In this paper, an intuitive B-Spline design method that can be used for the CAD systems both in conceptual modeling phase and in later ...

The space of $C^1$ cubic Clough-Tocher splines is a classical finite element approximation over triangulations for solving partial differential equations. However, such there no B-spline basis available, which preferred choice in computer aided geometric design and isogeometric analysis. A locally supported that forms convex partition unity. In this paper, we explore several alternative spline ...

This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method can be extended to functional differential and integro-differential equations. For showing efficiency of the method we give some numerical examples.

This paper describes the problem of shape preserving approximation for data with speci ed tolerances Using the tool of generalized B splines GB splines for short simple one and three point algorithms of shape preserving local approximation with automatic choice of the tension parameters are de veloped In the two dimensional case tensor products of one dimensional splines are employed The result...

Recently, we have introduced spaces of splines deened on triangulations lying on the sphere or on sphere-like surfaces. These spaces arose out of a new kind of Bernstein-B ezier theory on such surfaces. The purpose of this paper is to contribute to the development of a constructive theory for such spline spaces analogous to the well-known theory of polynomial splines on planar triangula-tions. ...

A series expansion with remainder for functions in a Sobolev space is derived in terms of the classical Bernoulli polynomials, the B-spline scale-space and the continuous wavelet transforms with the derivatives of the standardized B-splines as mother wavelets. In the limit as their orders tend to infinity, the B-splines and their derivatives converge to the Gaussian function and its derivatives...

This paper presents a B-spline based path planning approach for agricultural guidance applications which is able to handle successively generated trajectories. Additionally, the lateral controller which was used to calculate the steering angle is described and the method by which the required parameters were determined is introduced. We explain stepwise how the output of a perception system is ...

Recently, novel application areas in digital geometry processing, such as simulation, dynamics, and medical surgery simulations, have necessitated the representation of not only the surface data but also the interior volume data of a given 3D object. In this paper, we present an efficient framework for the shape approximations of spherical solid objects based on trivariate B-splines. To do this...