Shape Modification of Parametric Curves

A technique of shape modification and deformation for parametric curvesthrough cosine extension function (CEF) is presented. First, a special extension function isdefined, based on which a shape operator matrix is constructed. Then combining such matrix with thecenter of extension and principal directions, two kinds of deformation matrices are defined.Finally, curve deformation is achieved through multiplying its position vector in a local coordinatesystem by deformation matrix or adding the multiplication of a vector field and quasi-deformationmatrix to its position vector in the original coordinate system. Since CEF contains several variableparameters, each of which generates a different effect of shape modification such as controllingthe degree of continuity of the modified part of curve with the unchanged part, ideal deformationeffects can be got fairly and easily. Examples of theoretical analysis show that the method ispotentially useful for geometric modeling, computer graphics and so on.

Shape modification of Bézier curves by constrained optimization

The Bézier curve is one of the most commonly used parametric curves in CAGD and Computer Graphics and has many good properties for shape design. Developing more convenient techniques for designing and modifying Bézier curve is an im- portant problem, and is also an important research issue in CAD/CAM and NC technology fields. This work investigates the optimal shape modification of Bézier curves by geometric constraints. This paper presents a new method by constrained optimi- zation based on changing the control points of the curves. By this method, the authors modify control points of the original Bézier curves to satisfy the given constraints and modify the shape of the curves optimally. Practical examples are also given.

Flap side-edge noise mechanism and shape modification noise reduction design

Flap side-edge noise is a significant noise source for airplane at takeoff and landing stages. The generation mechanism of flap side-edge noise is analyzed by numerical simulation on unsteady flow field using Very Large Eddy Simulation （VLES）. Two kinds of flap side-edge shape modifications are proposed, and their frequency spectrum and directivity of far-field noise are compared with the baseline configuration using permeable integral surface Ffowcs Williams and Hawkings （FW-H） acoustic analogy method to investigate their effects on noise reduction. Via the numerical simulation of flow field and acoustic field, it proves that the flap side-edge noise is broadband noise in nature. The different shapes of flap side-edge change the pattern of flow field, vortex structures and the development of vortex, thus having influences on noise source distributions and characteristics of far-field noise. The result shows that at the given 5° angle of attack, the proposed flap side-edge shape modifications can reduce the overall sound pressure level （OASPL） by 1 to 2 dB without decreasing the lift and drag aerodynamic performances.

Paths of algebraic hyperbolic curves

Cubic algebraic hyperbolic （AH） Bezier curves and AH spline curves are defined with a positive parameter a in the space spanned by {1, t, sinht, cosht}. Modifying the value of a yields a family ofAH Bezier or spline curves with the family parameter α. For a fixed point on the original curve, it will move on a defined curve called ＂path of AH curve＂ （AH Bezier and AH spline curves） when a changes. We describe the geometric effects of the paths and give a method to specify a curve passing through a given point.

An optimization method for rational Bézier curve design

Adjusting weights as a shape control tool in rational B6zier curve design is not easy because the weights have a global in- fluence. The curve could not approximate control polygon satisfactorily by an interactive manner. In order to produce a curve close enough to control polygon at every control vertex, an optimization model is established to minimize the distance between rational B6zier curve and its control points. This optimization problem is converted to a quadratic programming problem by separating and recombining the objective function. The new combined multi-objective optimization problem is reasonable and easy to solve. With an optimal parameter, the computing process is discussed. Comparative examples show that the designed curve is closer to control polygon and preserves the shape of the control polygon well.

Tailoring particle shape for enhancing the homogeneity of powder mixtures:Experimental study and DEM modelling

The effect of particle shape modification on the segregation reduction of enzyme granules in laundry detergent powder mixtures was investigated,both experimentally and computationally using Deseret Element Method(DEM).The shape of modified enzyme particles was in such a way that the large and dense enzyme particles were layered by other fine particles in the detergent powder,by means of a process known in the literature as“seeded granulation”.It is found that the homogeneity of modified enzyme particles could be improved significantly comparing to the original spherical enzyme particles in powder mixtures.Overall,the results of this research demonstrated that the segregation-induced properties of the dense/spherical enzyme particles could be lowered by altering their shape,which could enable the enzyme particles to behave almost similar to other ingredients during the pile formation process.

Removing local irregularities of triangular meshes with highlight line models

The highlight line model is a powerful tool in assessing the quality of a surface. It increases the flexibility of an interactive design environment. In this paper, a method to generate a highlight line model on an arbitrary triangular mesh is presented. Based on the highlight line model, a technique to remove local shape irregularities of a triangular mesh is then presented. The shape modification is done by solving a minimization problem and performing an iterative procedure. The new technique improves not only the shape quality of the mesh surface, but also the shape of the highlight line model. It provides an intuitive and yet suitable method for locally optimizing the shape of a triangular mesh.

The in vitro and in vivo toxicity of gold nanoparticles

Gold nanoparticles,owing to their unique physicochemical and optical properties,well-established synthetic methods and easy modifications,have been widely used in biomedical science.Therefore,for their safe and efficient applications,much attention has been given to the toxicological evaluations of gold nanoparticles in biological systems.A large number of studies focusing on this problem have been carried out during the past years.However,the researches on gold nanoparticles toxicity still remain fragmentary and even contradictory with each other.This may be caused by the variety in experimental conditions.In this review,we aim to provide a better understanding about the in vitro and in vivo toxicity of gold nanoparticles by reviewing and describing the up to date literatures related to this problem and we mainly focused on these properties such as the particle size and shape,the surface charge and modification.Besides,we also summarized the adverse effect of gold nanoparticles on immune systems and analyzed the origin of the toxicity.