In recent years, high-altitude aerostats have been increasingly developed in the direction of multi-functionality and large size. Due to size high flexibility, new challenges for appeared configuration test deformation analysis. The methods analysis airship researched discussed. A tested method configuration, named internal scanning, is established quickly obtain spatial information all surface...

T-splines have recently been introduced to represent objects of arbitrary shapes using a smaller number control points than the conventional non-uniform rational B-splines (NURBS) or B-spline representatizons in computer-aided design, computer graphics and reverse engineering. They are flexible representing complex surface economic terms parameters as they enable local refinement. This property...

Given A spline curves and A patch surfaces that are implicitly de ned on triangles and tetrahedra we determine their NURBS representations We provide a trimmed NURBS form for A spline curves and a parametric tensor product NURBS form for A patch surfaces We concentrate on cubic A patches providing a C continuous surface that interpolates a given triangulation together with surface normals at th...

A-splines are implicit real algebraic curves in Bernstein-B ezier (BB) form that are smooth. We use these in an algorithm for active contouring of images. One advantage of A-splines is that any change to the controlling weights only a ects the curve locally, which results in fast convergence. Our active A-splines are also level sets of a time-dependent function with the added exibility of a dyn...

The interpolation of a sequence of points is an important task in Engineering. In this work, three different interpolation methods are studied and expanded. The first method is the conventional interpolation Spline. The second method is a subdivision based geometric algorithm. The third method interpolates a given set of points with additional point normal constraints. The last two methods were...

We propose a flexible and efficient wavelet construction for non-uniform B-spline curves and surfaces. The method allows to remove knots in arbitrary order minimizing the displacement of control points when a knot is re-inserted. Geometric detail subtracted from a shape by knot removal is represented by an associated wavelet coefficient replacing one of the control points at a coarser level of ...

We consider a problem of designing optimal smoothing spline curves using normalized uniform B-splines as basis functions. Assuming that the data for smoothing is obtained by sampling some curve with noises, an expression for optimal curves is derived when the number of data becomes infinity. It is then shown that, under certain condition, optimal smoothing splines converge to this curve as the ...

The recurrence algorithm is given for the calculation of NUAH B-splines in the space Sn+1 = span{sinh t, cosh t, t , · · · , t, t, 1} (n ≥ 3). The case of NUAH B-spline bases of low order with multiple knot sequences is studied. The limiting cases of UAH Bsplines are recovered when shape parameters α′s → 0and + ∞. Then the corresponding NUAH B-spline curve is defined and its main properties suc...

This article presents uniform B-spline interpolation, completely contained on the graphics processing unit (GPU). This implies that the CPU does not need to compute any lookup tables or B-spline basis functions. The cubic interpolation can be decomposed into several linear interpolations [Sigg and Hadwiger 05], which are hard-wired on the GPU and therefore very fast. Here it is demonstrated tha...

Isogeometric analysis (IGA) consists of using computer-aided design (CAD) models defining the geometry of the computational domain using both B-splines and nonuniform rational B-splines (NURBS) to represent the unknowns that are the solution of a partial differential equation using a finite element principle. In this paper, we review the main ideas of IGA and apply it to a reduced magnetohydrod...