Shape‐Up: Shaping Discrete Geometry with Projections

We introduce a unified optimization framework for geometry processing based on shape constraints. These constraints preserve or prescribe the shape of subsets of the points of a geometric data set, such as polygons, one‐ring cells, volume elements, or feature curves. Our method is based on two key concepts: a shape proximity function and shape projection operators. The proximity function encodes the distance of a desired least‐squares fitted elementary target shape to the corresponding vertices of the 3D model. Projection operators are employed to minimize the proximity function by relocating vertices in a minimal way to match the imposed shape constraints. We demonstrate that this approach leads to a simple, robust, and efficient algorithm that allows implementing a variety of geometry processing applications, simply by combining suitable projection operators. We show examples for computing planar and circular meshes, shape space exploration, mesh quality improvement, shape‐preserving deformation, and conformal parametrization. Our optimization framework provides a systematic way of building new solvers for geometry processing and produces similar or better results than state‐of‐the‐art methods.     

Transfer Considerations in Standby Generator Application

The overall reliability and performance of a standby generator system is related to the design of the switching circuits and their components. Ease of exercising the equipment without the system experiencing an extended interruption of power, cogeneration of power with the utility in the event of a brownout, and freedom of problems caused by reenergization of motors which are still generating a residual voltage can be achieved by providing the necessary switching and protective relay circuits. These circuits can be designed with manual or automatic synchronizing equipment built into packaged units or with individual switching devices having protective relay functions as required by the owner and the utility.     

Mechanical behavior at nanoscale of chitosan‐coated PE surface

Chitosan coating of polyethylene (PE) was proposed as a new procedure to improve its biocompatibility and surface properties. The functionalization of the PE film surface by covalent bonding of chitosan coating and its effect on the surface mechanical properties, as surface elasticity, stiffness, and adhesion (that are important in different biological processes) were investigated by nano‐indentation, scratch, and atomic force microscopy. It has been established that chitosan grafting onto corona functionalized PE surface using various coupling agents significantly improves the surface hardness and elastic modulus although they decrease in depth of the layer. Compared to the neat PE substrate, the chitosan coated samples show significant improved friction properties and tear resistance. The surface roughness features correlate with the micro‐mechanical parameters. Therefore, the covalent immobilization of the chitosan onto PE leads to a stable coating with better mechanical performance being recommended as a promising material for medical applications and food packaging. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42344.