Study on geometric properties of nanoparticles and their relation with biomolecular activities, especially protein is quite a new field to explore. This work was carried out towards this direction where images of gold nanoparticles obtained from transmission electron microscopy were processed to extract their size and area profile at different experimental conditions including and excluding a p...

In geometric constraint solving, constructing circles with indeterminate radius is an important sub problem. Such constructions are both sequential, meaning that we seek a circle tangent to three known geometric entities, as well as simultaneous, when several sets of entities, among them variable-radius circles, must be determined together. In Part I of our investigation, we considered sequenti...

Volume visualization is a common, very well-established visualization technique for volumetric data sets. Numerous advancements have been proposed and sophisticated improvements have been implemented to produce elaborated renderings that are capable of enhancing details within the volume. However, volume visualization alone is often not sufficient for the application domain. Often times, resear...

Skinning of an ordered set of discrete circles is discussed in this paper. By skinning we mean the geometric construction of two G1 continuous curves touching each of the circles at a point, separately. After precisely defining the admissible configuration of initial circles and the desired geometric properties of the skin, we construct the future touching points and tangents of the skin by app...

We present a new system for computing design rationales of geometric features on mechanical devices. Our system interprets dynamic simulations of mechanical devices and automatically generates an English text document for the purposes of the geometric features on the device. To identify the purpose of a particular feature, we simulate the behavior of the device with and without the feature pres...

In this research, we study a method to produce families of origami tessellations from given polyhedral surfaces. The resulting tessellated surfaces generalize the patterns proposed by Ron Resch and allow the construction of an origami tessellation that approximates a given surface. We will achieve these patterns by first constructing an initial configuration of the tessellated surfaces by separ...

We present the nrst practlcal, implemented configuration space computation algorithm for a curved planar object translating and rotating amidst stationary obstacles, The bodies are rigid, compact, regular, and bounded by a finite number of rational parametrlc curve segments. The algorithm represents the three-dimensional configuration space as two-dimensional slices in which the moving object h...

This paper presents a geometric framework for analysis of dynamics of flapping wing micro aerial vehicles (FWMAV) which achieve locomotion in the special Euclidean group SE(3) using internal shape changes. We review the special structure of the configuration manifold of such systems. This work addresses to extend the work in geometric locomotion to the aerial locomotion problem. Furthermore, th...

In geometric constraint solving, constructing circles with indeterminate radius is an important sub problem. Such constructions are both sequential, meaning that we seek a circle tangent to three known geometric entities, as well as simultaneous, when several sets of entities, among them variable-radius circles, must be determined together. In Part I of our investigation, we considered sequenti...

Optimal control problems for underactuated mechanical systems can be seen as a higher-order variational problem subject to higher-order constraints (that is, when the Lagrangian function and the constraints depend on higher-order derivatives such as the acceleration, jerk or jounces). In this paper we discuss the variational formalism for the class of underactuated mechanical control systems wh...