In this work, we study a data visualization problem which is classified in the field of shape-preserving interpolation. When   function  is known to be bounded, then it is  natural to expect its interpolant to adhere boundedness. Two spline-based techniques are proposed to handle this kind of problem. The proposed methods   use quadratic SPLINES as basis and involve solving a linear programming or a mixed integer linear  programming problem which gives $C^1$ interpolants. An energy minimization technique is employed to gain the optimal smooth solution. The reliability  and  applicability of  the proposed techniques  have been illustrated through examples.

Introduction In industrial designing and manufacturing, it is often required to generate a smooth function approximating a given set of data which preserves certain shape properties of the data such as positivity, monotonicity, or convexity, that is, a smooth shape preserving approximation. ...

In this paper, an algorithm for fast defect detection in cloths based on fast B-spline transform is proposed. The algorithm can be applied to analyzing images at any integer scale for defect information. It can also be extended to a parallel algorithm that decomposes images at all desired scales simultaneously. A threshold parameter δth is used to adjust the defect detection reliability. A desired compromise between fault recognition and continuity of edge pixels can be reached by adjusting the value of δth properly.

In the previous research, shape of concrete arch dams were modeled using quadratic and cubic polynomials along dams height, but in these formulations some details such as joints location, variable thickness starting points, abutments excavation, intersections of horizontal arches with sound rock and etc. were ignored because of the lack of parameters for dam geometry modeling. In the case of existence of inflection points in canyon shape, equations are inaccurate; consequently modeling the whole shape for more details is not possible. In this paper a new formulation using Hermite Spline equations for defining the geometry of double curvature concrete arch dams with parabola horizontal arch has been presented. In this model the geometry of the arch dam is created using 37 design parameters or as design variables in optimization process for future developments. In geometry modeling the details such as site topography triangulation, crown cantilever shape, horizontal arches, intersection of horizontal arches with sound rock, constant and variable thickness zones formulation has been developed carefully. One of the advantages of this new formulation is creating smooth and flexible shapes in comparison with Bofang’s cubic polynomials method. For three dimensional finite element analyses, three dominant loading cases have been considered. In order to considering the real construction conditions, Multi-stage grouting for dead load has been intended. For stress analysis in dynamic case the response spectrum method is used. For this purpose, a package has been developed. In order to design professional software, the object- oriented capabilities of FORTRAN90, such as: Module, Inheritance, Type, Dynamic arrays and etc. have been applied frequently. This software has automatic mesh generation for any canyon shape. In addition, this software package provides some useful information for geometry, finite element model and information for future optimization process. The developed software has been applied successfully for Shahid Rajaee arch dam.